Current Opinion in Colloid & Interface Science 18 (2013) 311–323

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Current Opinion in Colloid & Interface Science

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Microrheology and particle tracking in food gels and emulsions

Thomas Moschakis ⁎Department of Food Science and Technology, School of Agriculture, Aristotle University of Thessaloniki, GR-541 24, Thessaloniki, Greece

⁎ Corresponding author. Tel./fax: +30 2310 991680.E-mail address: tmoschak@agro.auth.gr.

1359-0294/$ – see front matter © 2013 Elsevier Ltd. Allhttp://dx.doi.org/10.1016/j.cocis.2013.04.011

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 February 2013Received in revised form 23 April 2013Accepted 23 April 2013Available online 3 May 2013

Keywords:Particle tracking microrheologyVideo microscopyViscoelasticityHeterogeneityEmulsionsGelation

Particle tracking microrheology, an emerging experimental technique, which utilizes the Brownian motion ofembeddedparticles to probe local dynamics of softmaterials, is presented. Particle trackingmicrorheology is a pow-erful technique that enables themeasurement of viscoelastic responses in small sample volumes,which are inacces-sible to macrorheology and to spatially map structural heterogeneities at a microlevel. Therefore, particle trackingmicrorheology has considerable potential in food emulsions and gels, since these systems are commonly inhomo-geneous. Recent advances and achievements are discussed, including the basic principles, operating regimes andlimitations of the technique. The application of the technique in the field of food gels and emulsions to study theevolving dynamics of inhomogeneous at microscale length systems and during sol–gel transition is highlighted.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Food gels and emulsions are typically complex heterogeneousmulticomponent and multiphase systems consisting of dispersed parti-cles and macromolecules in various stages of organization [1]. The un-derstanding of such complex structures and dynamics with multiplecharacteristic length and timescales is of major importance for food sci-entists. Therefore, new experimental techniques are required to capturesufficient detail of the intrinsic complexity of the food systems over avery large range of length and timescales, in order to elucidate the under-lying mechanisms that affect the interactions of the food componentsand thus their physical properties. In acidifiedmilk gels, for instance, dif-ferent theoretical approaches (adhesive sphere models, percolation andfractal models) have been proposed to characterize the gelation process,but none of them is capable of explaining in an explicitmanner thekinet-ics of network formation and growth [2,3].

The great majority of foods are emulsions such as milk and sauces(typical low-volume fraction emulsions) and butter-margarine (high-volume fraction). Moreover, foods can be found as soft solids in highlyviscoelastic states such as yoghurt and cheese. Food emulsions andgels exhibit a great diversity of rheological characteristics, rangingfrom low-viscosity Newtonian liquids (e.g., milk), to viscoelastic mate-rials, exhibiting both a viscous and an elastic response (e.g., salad dress-ings, cream), and plastic materials (e.g., butter, margarine) [4]. Thisdiversity is the outcome of the organization and rearrangements of

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the food components–mainly proteins, polysaccharides and lipids–duringfood processing and upon storage.

Lately, the microstructure and local dynamics of food systems haveattracted considerable attention and attempts have beenmade to relatethe microstructure of food systems to their macroscopic properties andstability. Various methods, such as rheometry, ultrasound measure-ments and more recently microrheology have been used to investigatethe dynamics of food systems. Moreover, the microstructure of foodsystems has been studied with techniques such as light microscopy,confocalmicroscopy and electronmicroscopy. Despite substantial prog-ress, a clear correlation between particle forces/interactions, micro-structure and bulk mechanical properties has not been established.

Macroscopic (bulk) rheology, which studies the deformation ofmaterials in the presence of a stress at a particular time, has provento be an important and useful tool to study the mechanical propertiesof food colloids with major practical significance. However, bulk rhe-ological measurements describe the overall mechanical response of amaterial on a macroscopic scale. Therefore, they do not provide anyinformation on local variations in the microstructure and their contri-bution into the overall mechanical response of a material.

In order to understand the origins of the overall response, it istherefore necessary to probe rheology over shorter length scales. Inrecent years significant progress has been made in the developmentof techniques to study and characterize the structure and dynamicsof complex fluids at themicroscopic level. These dynamic experimentaltechniques are known as “microrheology”. Microrheology is an emerg-ing technique, which has the potential to overcome some limitations ofbulk rheology. It is used to probe spatial mechanical properties on thescale of microns in a non-invasive way by using tracer particles embed-ded in complex fluids [5–7•]. The movement of particles, which is

312 T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

related to the resulting deformation, is recorded by using modern highresolution microscopy and their motion is analyzed quantitatively interms of the local viscoelastic properties of the surrounding medium.The tracer particle displacements are sensitive to local viscous and elas-tic forces aswell as to chemical and steric interactions between the par-ticles and the network [7•]. Particles can be either embedded or they canbe part of the actual system [8,9]. By analyzing the motion of the parti-cles following the fundamental work of Mason and Weitz [10••], it ispossible to obtain quantitative information about the rheological prop-erties of complex fluids such as emulsions and gels. These measure-ments can reveal important mechanistic insights into the evolvingdynamics at shorter length scales. Moreover, it has been reported thatthe microrheological data can be in excellent agreement with mechan-ical macrorheological measurements [11••–14•].

This article presents the emerging area of multiple-particle trackingmicrorheology focused on the trends, potential and pitfalls of the tech-nique for the potential application to food gels and emulsions. Themainadvantage of this method is that the diffusivemotions of many particlescan be recorded simultaneously,while retaining the information of eachof the individual particle trajectories [15–18]. Therefore, measurementson ensembles of particles can be employed to provide statistical accura-cy, while spatial heterogeneities can also be revealed [18,19••]. At thebeginning, a brief overview of the two different microrheological ap-proaches (active and passive) is given, which are distinguished by thedriving force upon the tracer particles. Afterwards, the strengths andlimitations of themethod are discussed, followedby data analysis, oper-ating regime and resolution of particle tracking microrheology. Finally,the potential of the technique in the field of food gels and emulsionsto study the evolving dynamics of inhomogeneous microscale lengthsystems and during sol–gel transitions is highlighted.

2. Microrheology techniques

Microrheology techniques are usually classified into two maincategories: active techniques that require particle manipulation byexternal forces and passive techniques that are based on thermalfluctuations of the embedded particles [5–7•,20•,21••]. Passive tech-niques are typically more useful for measuring low viscosity samples,whereas active techniques can extend themeasurable range to samplescontaining significant amounts of elasticity [6].

2.1. Active methods

The idea of manipulating microscopic probe particles to measuremechanical properties was first introduced in the 1920s when mag-netic particles were embedded to study qualitatively the mechanicalproperties of gelatin gels and cellular cytoplasm [22,23]. Since then,the technique has been improved by fabricating high-precisionmagneticparticles without shape irregularities for quantitative microrheologicalcharacterization [24].Magnetic tweezers combine the use of strong mag-nets to manipulate magnetic probe particles with video microscopy torecord the motion of particles upon application of external controllabledriving forces. There is no significant heat generation in the sampleexamined and there is a uniform generated force across the magneticparticles in the related areawhere the probes aremoving [21••]. An alter-native active technique uses optical tweezers to manipulate small dielec-tric particles. A highly focused laser beamgenerates a local trapping forcefor the particle and the motion of particle is simultaneously imaged. Bymoving the beam and observing the particle's response, the local rheo-logical properties of themedium can be determined [20•,21••]. This tech-nique uses single particles and can also probe inhomogeneous materialsover higher frequencies (~10 kHz) and much smaller particle displace-ments [25,26]. Nonetheless, the applied forces are typically limited tothe pN range, local heating of the sample can occur, and damage ofphoto sensitive biological materials can take place [5,21••,27]. A recentlydeveloped active method is atomic force microscopy (AFM). The

technique is mainly used to image the structure of surfaces, in somecases with atomic resolution [28] and simultaneously to study interac-tional forces at molecular level [28,29] and local viscoelasticity [30,31].The sample is scanned with a pointed tip, mounted on a cantileverspring, and a topographic image of the surface structure is generated[32,33]. The small tip is deflected when placed in contact with a surfaceand the motion of the tip is measured by the deflection of a laser. Thus,the local viscoelasticity of soft samples such as gels and cells can bemea-sured [30,31,34]. Because large forces can be applied, AFM is also capableof studying stiff materials with elastic moduli of order 1 GPa [5].

2.2. Passive techniques

In this type of microrheology the intrinsic Brownian motion of theembedded particles is used to measure the mechanical properties ofmaterials. The only driving force to probe the rheological propertiesis the thermal energy of the particles, determined by kBT. Unlike ac-tive microrheology methods, no external force is required. Becausethe thermal driving force is small, materials must be relatively “soft”(e.g., polymer solutions) in order for the embedded particles to gen-erate detectable motion [5–7•,20•,21••]. However, the small drivingforce implies that the sample deformation is limited and thus onlythe linear viscoelastic response of the medium is probed.

The most common passive experimental techniques that mea-sure rheological properties on the microscale level are single-particlelaser tracking microrheology, ensemble averaged light-scattering, andmultiple-particle tracking microscopy [5,21••,27]. In single-particle lasertracking microrheology a laser light targets exactly one particle, which isobserved through a microscope over time. This technique is similar tooptical tweezers, except for the fact that the laser power and therebythe applied forces are minimal. The deflection of the laser beam by themoving probe particle is detected; the trajectory of the particle is trackedand correlated to the viscoelastic response of the examined material[21••]. This technique has sub-nanometer spatial resolution and canmeasure the displacement of the particle at much shorter time scales(frequencies up to 100 kHz) [5,21••]. However, the statistics are verylow, since a single particle is tracked. Moreover, the freely movingparticle can diffuse out of the laser beam relatively fast, depending onthe viscoelasticity of the material, and thus the lower frequencystatistics are quite poor. On the contrary, light scattering techniques canonly be applied to homogeneous samples and average a large ensembleof particles. Therefore, these techniques have better statistical accuracy.The most common experiments involve two different methods:dynamic light scattering (DLS) and diffusing wave spectroscopy.In dynamic light scattering the motions of ensemble particles aredetermined by analyzing the temporal change of the scattered light.As the particles diffuse and rearrange in the sample, the intensity oflight reaching the detector fluctuates with time [7•,21••]. The intensityfluctuations of scattered light over time reveal the dynamics of themedium [7•,21••,27]. DLS is usually applied to dilute and transparentmedium of colloidal particles to avoid multiple scattering. On theother hand, this limitation is exploited by diffusing wave spectroscopy(DWS), which is applicable to opaque and highly scattering systems,e.g., emulsions, colloidal suspensions, and gels. DWS has been demon-strated to be a powerful tool for studying highly scattering colloidal sys-tems [35,36]. Similarly, the sample is illuminated with a coherent laserbeam and the outgoing light is scattered from the large amount of em-bedded particles many times (several thousands) before exiting thesample [20•,21••]. DWS can performmeasurements at spatial resolutionclose to sub-nanometer level while the temporal resolution frequenciesare as high as 1 MHz; i.e., at ranges inaccessible to conventional bulkrheology. The intensity correlation function can be directly transformedinto a time-dependent mean-squared displacement (MSD) with the ad-vantage of better averaging and statistical accuracy. Moreover, DWS hasthe ability to study the dynamics and kinetics of aggregating systemswithout the need for extensive numerical analysis. However, this

313T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

method requires relatively large sample sizes and the inherent ensembleaveraging eliminates the spatial information, and thus this method can-not be used in multiphase media [5,7•,21••,27,37].

Multiple-particle tracking microrheology (also known as video particletracking microrheology or simply particle tracking microrheology) isprobably the simplest andmost powerful passive method. Particle track-ing microrheology has grown rapidly, due to its low cost, experimentalsimplicity and the free availability of particle tracking software [38••]. Inthis method, a large ensemble of embedded particles is imaged simulta-neously using eitherfluorescence or brightfieldmicroscopy and themea-surements are conducted at a constant temperature. Fluorescent tracerparticles offer the ability to observe nano-sized particles aswell as the op-portunity to study heterogeneous sampleswith different dyed tracer par-ticles [13••]. In a typical experiment, a time series of microscope images isobtained and converted to digital format [39•] and subsequently, the localviscoelastic properties of a material can be measured (see Section 4). Inthis technique, spatial resolution can be achievedwith sub-pixel accuracy[40••] while temporal resolution can be easily achieved up to 60 Hz.

3. Advantages and disadvantages of multiple-particle trackingmicrorheology over current methods

The most important advantages and strengths of passive particletracking microrheology are summarized as follows: i) it is a low bud-get technique as it mainly requires a microscope, a camera, and a fastcomputer; ii) only small sample volumes (fewmicroliters) are required,i.e., it can beused for expensive and scarcematerials and in systems thatare inherently small like biological cells, although there is a difficulty touniformly disperse the tracer particles especially in extremely smallvolumes of viscous samples; iii) the driving force is exceptionallysmall, and thus there is no sample deformation, i.e., only trivial distur-bance and perturbation of the medium take places and therefore thekinetics as well as themicrostructural changes or ordering can bemon-itored (e.g., gelation). Moreover, all the measurements are always tak-ing place in the linear regime; iv) data from a large ensemble can becaptured simultaneously, which improves the overall statistics of therheological results, while keeping the individual tracer trajectories;v) with appropriate analysis it gives the opportunity to extract use-ful information on the local viscoelastic properties of the mediumon the micron scale. This gives the opportunity to map structuralheterogeneity at a micro-level (see Section 7.2); vi) it has a high sen-sitivity with a sub-pixel accuracy of ≤20 nm spatial resolution [40••]and can measure viscoelastic responses at relatively low values incomparison to bulk rheology [18,41•]; and vii) multiple-particle trackingmicrorheology requires relatively short times of data collection, typicallyless than 1 min tomeasure directly both the viscosity and viscoelasticity.

The limitations of passive microrheology are: i) the driving force isfixed and limited to kBT and therefore only “soft” materials with rela-tively low viscoelastic moduli (typically less than 10 Pa) can be ex-amined; ii) all the measurements are taking place always in thelinear regime. Thus, non-linear responses cannot be studied with pas-sive microrheology; iii) particle tracking microrheology is typicallysuited for relatively transparent materials while many food systemsare quite opaque; and iv) possible effects of depletion zones can affectthe particle motion. Generally, the probe particles should not modifythe structure of the material. That is, the probe particles should notinteract with or locally modify the material structure and with eachother to form aggregates (see Section 4).

4. Data analysis to extract the viscoelastic properties in particletracking microrheology

In passive microrheology, there is no external driving force appliedto the tracer microspheres and the local particle motion is driven solelyby Brownian forces generated by the thermal energy kBT. Brownianmotion is a random physical process (stochastic), where the particles

receive a random displacement by collision with other molecules, as-suming no external force. Therefore, we are interested in averages.

Typically, images are captured below the level of the coverslip,>10 μm, to minimize hydrodynamic interactions with the coverslip.The position of each tracer particle is identified by finding thebrightness-weighted centroid position in order to achieve sub-pixel ac-curacy [39•,40••]. The tracer microspheres appear consistently bright,even when they move in the z-direction, allowing a more precise andlonger determination of the centroid location. Particles slightly out offocus appear smaller than they really are, but this is not of great impor-tance, because only the displacements of their centroids are actuallymonitored. Movies of the movements of the diffusing embedded parti-cles usually in the x–y plane are analyzed using procedures such asthose developed by Crocker and Grier [40••]. By using confocal micros-copy particle tracking can be also performed in 3D [42,43]. In confocalmicroscopy, the most significant limitation of the imaging depth isestablished by the opacity of the sample [44,45]. Tracking particles in3D is a difficult task since both the buoyancy and the refractive indexof the particles should be closelymatchedwith the sample (dispersant).In addition, the temporal resolution (scanning speed) of confocal mi-croscopy is limited; i.e., typical speeds for a 512 × 512 pixel imagecan be as fast as ~20 Hz, or even faster for confocal microscopes thatemploy Nipkow discs at the expense of sharpness [44]. In addition, con-focal microscopy provides the ability to focus on local regions withinsamples, making the local mapping of the rheological properties ofhighly heterogeneous samples possible [13••].

Tracking macro-routines are used to correct imperfections inthe images, to form particle trajectories, and finally to extract themicrorheological data [38••]. In particular, noise is strongly suppressedby convoluting the images with a Gaussian mask and concomitantlysharpening the image. The position of each microsphere is identifiedby finding the brightness-averaged centroid position [40••]. Modernmi-croscopes have a relatively high signal-to-noise ratio, which lowers theminimum detectable displacement. After removing the spurious fea-tures (noise, artefacts, clipped particles at the edge of the field of viewetc.), identification of the particles is conducted automatically and thepositions of the particles found in each frame are linked to generate tra-jectories. Therefore, it is also important to ensure that the inter-particlespacing is longer than the distance that the particles move betweensuccessive frames in order to identify the individual particles and suc-cessfully link their positions to generate individual trajectories. Anybackgrounddrift due to large-scaleflowormicroscope stagemovementshould be eliminated before [38]. When there is a steady drift or flow inthe system (e.g., due to convection or fast sedimentation), the plot ofmean-squared displacement (MSD) versus lag time τ has positive cur-vature. If a motion is added to the thermally driven particles, the MSDis given by [46]

MSD ¼ 4Dτþ Vτð Þ2 ð1Þ

where V is the imposed velocity due to the overall movement of thesample. Even if the drift is only slow, the contribution from the quadrat-ic term (Vτ)2 becomes predominant at long timescales. Systematic driftcan be found by examining the average values of dx and dy for all thevisible particles from successive frames [21••,38••].

The trajectories of the embedded particles due to solely Brownianmo-tion are then used to compute the ensemble-averagedmean-squared dis-placement ⟨Δr2(τ)⟩. The time-averaged mean-squared displacement inthe image plane is defined by

Δr2 τð ÞD E

¼ x t þ τð Þ–x tð Þ½ �2 þ y t þ τð Þ–y tð Þ½ �2D E

ð2Þ

where x and y are the time-dependent coordinates of the centroids of themicrospheres, τ is the lag time or time interval between successiveframes, and the angular brackets ⟨..⟩ indicate an average over all initialtimes and over several particle trajectories in the field of view. Many

Log(τ)

Log

A

Elastic medium slope ~ 0

slope ~ 1

slope > 1

B

C

D

Fig. 1. Typical mean-squared displacement curves of embedded microspheres as afunction of lag time τ in three different media: (A) superdiffusion motion, m > 1;(B) Newtonian medium, m = 1, (C) viscoelastic medium 0 b m b 1, and (D) elasticmedium m = 0.

314 T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

researchers prefer to calculate the one-dimensional mean squared dis-placement in the x direction (⟨Δx2(τ)⟩), because in isotropic systemsoptical microscopy has higher spatial resolution in x than in the z direc-tion and also in charge-couple devices (CCD cameras) the resolutionperpendicular to the interlacing (y direction) is usually lower at the ex-pense of temporal benefits. If the material in the proximity of the tracerprobes is isotropic, i.e., thematerial has the samemechanical propertiesin all directions [47,48], the measured one dimensional MSD (⟨Δx2(τ)⟩and ⟨Δy2(τ)⟩) should be equal: ⟨Δx2(τ)⟩ = ⟨Δy2(τ)⟩ = 2 Dτ. There-fore, by measuring and comparing the one dimensional MSDs the an-isotropy of materials can be revealed [8].

In order to understand the theoretical basis of passivemicrorheology,it is convenient to consider two extreme cases: a purely viscous Newto-nian liquid, and an ideal elastic medium [49].

4.1. Viscous medium

When tracer particles are dispersed in a Newtonian fluid of shearviscosity η, the particles should undergo simple Brownian movement[21••] with a diffusion coefficient (D), given by the Stokes–Einstein re-lation,

D ¼ kBT=6πηa ð3Þ

where a is the particle radius, kΒ is the Boltzmann's constant, and T is theabsolute temperature. For purely diffusive motion, the d-dimensionalMSD is given by

Δr2 τð ÞD E

¼ 2dDτ ¼ 2d kBT=6πηað Þτ ð4Þ

from which the fluid viscosity η, can be calculated:

η ¼ 2dkBT6πα

τΔr2 τð Þ� � : ð5Þ

If the medium is viscous then τ/⟨Δr2(τ)⟩ should be constant [50],independent of τ; i.e., the MSD increases linearly with the lag time(see Fig. 1) with the more viscous materials exhibiting a slower rateof growth.

4.2. Elastic medium

When the particle is embedded in an ideal elastic medium withstorage modulus G′, there will be a maximum displacement. In thiscase the MSD is constant and independent of the timescale and there-by the frequency, ω [20•,51]:

Δr2 τð ÞD E

¼ dkBT=3πaG′: ð6Þ

The viscous modulus is G′′ = 0, and the G′ can be calculated fromthe above equation considering that the ⟨Δr2(τ)⟩ is larger than thedetection limit (the smallest detectable MSD) of the experimentalset-up (see Section 6).

In practice, most food emulsions and gels are viscoelastic with afrequency dependent response that has both viscous and elasticcomponents and therefore their behavior falls between the two ex-treme cases. In viscoelastic materials G′ = d kBT/3πa⟨Δr2⟩p where⟨Δr2⟩p is the plateau value occurring when the thermal energy kBTof the tracer particle equals the elastic energy associated with the de-formed network. The MSD data obtained from the multiple-particletracking can be converted to elastic and viscousmoduli [10••]. The gener-alized Stokes–Einstein relation (GSER) for materials with viscoelasticproperties, which was firstly introduced by Mason and co-workers

[10••] and later placed on firmer theoretical foundations [52••] ispresented in the form:

Δr̃2 sð ÞD E

¼ dkT=3πasG̃ sð Þ ð7Þ

where Δr̃2 sð ÞD E

is the Laplace transform of the tracer particle mean-squared displacement (MSD), s is the Laplace frequency, and G̃ sð Þ isthe Laplace representation of the complex modulus, which encom-passes both storage (G′) and loss (G″) moduli. The MSD data obtainedfrom particle tracking can be converted accordingly to elastic and vis-cous moduli from the log slope of the MSD [12••] and subsequently im-proved [53••,54] with a changing slope to include cases where themean-squared displacement is sharply curved to diminish significanttruncation errors (especially at frequency extremes) onmoduli estima-tion. The modified algebraic form of the GSER is

G′ ωð Þ ¼ G ωð Þ 11þ β0 ωð Þ

� �cos

πα0 ωð Þ2

−β0 ωð Þα0 ωð Þ π2−1

� �� ð8Þ

G″ ωð Þ ¼ G ωð Þ 11þ β0 ωð Þ

� �sin

πα0 ωð Þ2

−β0 ωð Þ 1−α0 ωð Þ � π2−1

� �� ð9Þ

G ωð Þ ¼ kBTπα Δr2 1=ωð Þ� �

Γ 1þα ωð Þð Þ 1þ β ωð Þ=2½ � ð10Þ

whereω = 1/τ,α(ω) and β(ω) are the first and second order logarith-mic time derivatives of theMSD data, α′(ω) and β′(ω) denote the localfirst and second order logarithmic derivatives of G(ω), respectively,while Γ is the gamma function.

Another useful viscoelastic parameter, the creep compliance, J(t),which is the time-dependent strain following an applied low stress,can also be directly calculated from the MSD and the GSER is expressedin the time domain as [50]:

J tð Þ ¼ Δr2 τð ÞD E

3πa=dkBT: ð11Þ

The creep compliance can also be directly converted to frequency-dependent elastic and viscous moduli without the need for Laplace/inverse-Laplace transformations of the experimental data [55•,56•]. Inthis straightforward method, the fitting and smoothing proceduresthat disguise experimental noise are eliminated.

315T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

When theMSD for a viscoelastic material is plotted as a function oftime on a double logarithmic plot (see Fig. 1), it is given by

Δr2 τð ÞD Eeτm ð12Þ

where the slopem is equal tom = d log⟨Δr2 (τ)⟩/d log τ. In viscoelas-tic materials, the slopem is falling between the viscous limit (m = 1)and the elastic limit (m = 0). A value of m b 1 indicates that the mo-tion is sub-diffusive, or hindered, whereas a slope of m ~ 1 indicatesthat the motion can be regarded as entirely diffusive. Superdiffusionis revealed by m > 1, which indicates that the probes are subjectedto active (ballistic) motion (e.g., external applied forces, flow). In vis-coelastic materials, 0 b m b 1, at very short lag times, the embeddedparticles exhibit Newtonian response and the MSD rises diffusively.However, at intermediate lag times the MSD reaches a plateau indi-cating that the particles are becoming constrained and the elasticityprevails. The lower the plateau, the stronger the elasticity. At evenlonger lag times, the particles may in some cases escape (diffuseout) from the confined space (cage) as the network relaxes the stressand the MSD grows linearly with time reflecting a diffusive behavior[43,57,58]. The viscosity estimated at long displacements can be relat-ed to the macroscopic (bulk) viscosity. In most cases the particletracking microrheology is able to detect the plateau and the relaxa-tion process (green part of curve C), since very short lag times are in-accessible (a very fast camera is required) with this technique. Awider frequency range is typically observed with DWS where suchhigh frequency ranges can be achieved [12••,59]. Fig. 1 shows sche-matically the possible mean-squared displacement curves of a parti-cle embedded in various media.

A new advanced technique, namely two-particle (or point)microrheology, has recently been developed [11••,52••] to measurebulk rheological properties in heterogeneous samples. Two-particlemicrorheology requires more data to obtain sufficient statistics thanparticle trackingmicrorheology. In two-particle microrheology, the dis-placement of a particle is correlated with the displacement of anotherparticle separated at a distance. Materials are inhomogeneous on thelength scale of a single tracer, but homogeneous on the length scale ofseveral particles [11••]. The correlated motion of pairs of particles is onlength scales only greater than the inter-particle separation distance,and thus the two-particle microrheology is insensitive to the local het-erogeneities and the results are independent of the tracer particles(shape, size).

4.3. Comparison between bulk rheology and particle tracking

The Stokes–Einstein relation as well as the GSER are certainly validfor a simple Newtonian fluid as well as for a homogeneous, isotropicstable or quasi-steady materials. However, they may not be applicablefor a heterogeneous system, where the size of the probe microspheresis comparable to or smaller than the characteristic structural length(see Section 7.2) [14•,18,60•]. There are many examples in the litera-ture that demonstrate the excellent agreement between bulk rheo-logical measurements and particle tracking microrheology when thecharacteristic structural length of the homogeneous materials is shortcompared to the size of the probe particles and there are no unfavorableinteractions between thematerial and the tracer particles. The latter cancause underestimation of the viscoelastic properties if depletion zonesare formed around the particles increasing their mobility [61,62]. Innon-homogeneous materials, two-particle tracking can be used toprobe bulk viscoelastic responses [11••], otherwise discrepancies be-tweenmicroscopic andmacroscopic measurements are undoubtedlyobserved due to the fact that many regions of different local struc-tures and viscoelasticities simultaneously exist.

5. Tracer particles: effects of different microsphere surfacechemistries and particle sizes

Multiple-particle tracking microrheology is based on the intrinsicBrownian motion of the embedded tracer particles to measure themechanical response of the materials. The tracer particles are added ata relatively low concentration (~0.2 vol.%) to minimize the distortionor perturbation of the existing or developing microstructure of the ma-terial. The number of simultaneously tracked microspheres in a typicalexperiment should be in the range of 60–100 per field of view inorder to increase the recorded displacements and thus the statisticsbut avoid having significant particle–particle interactions and perturba-tion of the microstructure.

The choice of appropriate tracer particles is of great importance inthis technique. This implies that careful selection of the probe parti-cles should be made prior to the experiments and according to thematerial properties that need to be investigated. In particular, the sur-face chemistry and the size of the particles should be selected careful-ly to minimize the interference of the particles with the componentsof the sample [52••].

The tracer particle size in relation to the characteristic structuralsize of the medium is very crucial to probe the viscoelastic propertiesat the desired length scale. That is, the particle's size should be suffi-ciently larger than all the structural length scales of the material inorder to probe a valid macroscopic response. Otherwise, when theparticle size is smaller than the characteristic structural length, theparticles experience the mechanical properties of the continuousphase and/or the local microheterogeneities [14•,18,49,63]. In theparticular case where the particle size is comparable to the charac-teristic structural length of the medium, anomalous sub-diffusion(cage-hopping) behavior may be observed due to the fact that someparticles “jump” between “cages” [60•]. For samples with unknowncharacteristic lengths, preliminary experiments are recommended tobe carried out with different sizes of trace particles. The different setsof size-normalized mobility data should be directly compared(usually the quantity, particle size × ⟨Δr2(τ)⟩ [13••,64], is calculated toinvestigate the effect of probe particle sizes on the same system).Similar trends imply that the different particles probe the samemechanical properties at the length scales of their diameter.

In viscoelastic materials having a network formation with a char-acteristic porosity, the MSD observed plateau (see Fig. 1) measuresthe average pore size of the network when the particle size is smallerthan the characteristic structural length. In heterogeneous samples,the pore size (p) can be measured from the MSD's plateau (⟨Δx2⟩p)and is equal to [19••]

p ¼ aþ Δx2D E

p

� 1=2ð13Þ

where a is the probe's radius. On the other hand, the MSD plateau is ameasure of sample elasticity when the tracers are very large com-pared to the average pore size [19••,48].

Moreover, it is well known that the nature of the interactions be-tween the probe and the investigated material plays an importantrole in interpreting the extracted microrheological data, since these in-teractions affect themovement of the particles [14•,41•,64,65]. Therefore,the particle's surface chemistry (coating) should be carefully consideredin the interpretation of the results. Non-specific binding is a commonlyencountered problem when working with embedded particles. In sys-tems containing proteins, interactions between the probes and the pro-teins occur quite often [37,41•]. The tracer surface can be tuned toallow specific and controllable binding. Tracer particles with differentsurface chemistries are commercially available or can be prepared inthe laboratories with certain coupling (adhering) protocols that can beutilized for different applications. Usually, carboxylate-modified (hydro-philic and anionic), sulfate and aldehyde-sulfate (relatively hydrophobic

316 T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

and anionic), amine-modified (hydrophilic and cationic), biotin, avidin,and streptavidin are used to tune the interactions between the micro-spheres and the structural entities. Moreover, polyethylene glycol, pro-teins (e.g., bovine serum albumin, caseins), and non-ionic surfactants(e.g., Tween 20) are common blocking agents, which are often used tominimize non-specific interactions between the tracer particles and themolecules in the sample.

Adsorption of the particle onto the structuring (material) ele-ments of the sample can modify the structure of the material aroundthe particle leading to unusual hydrodynamic interactions [19••]. Inthis case the particle diffusion is affected and therefore the resultsare questionable. In some cases, it is difficult to distinguish whetherparticles actually adsorb strongly onto the sample's structural entitiesor whether they become tightly trapped within very small poreswithin a formed network. Particles with different surface chemistriesare commonly used to clarify the nature of interactions by direct com-parison of the resulting MSDs. Another way to resolve this problem isto examine under a microscope whether the different particles formaggregates at relatively low concentrations of the structuring material.If the particles do not aggregate even at very lowbiopolymer concentra-tions due to bridging, no significant interactions between the particlesand the material are expected [41•]. In that case, a good agreement be-tweenparticle tracking and bulk rheologicalmeasurements is anticipat-ed in systems homogeneous on the particle size length scale.

In some studies, particle trackingmeasurements havebeenperformedwith particles that have a surface chemistry deliberately designed to ad-sorb to the network-formingmaterial in order to avoid the formation ofa depleted layer or the confinement of the probes in small cavities,which results in a better correlation between themicrorheologicalmea-surements and the bulk rheology results [41•,63,66,67]. In a study withF-actin, the important role of particle surface chemistry has been dem-onstrated [63]. Particles that bound to actin filaments probed the me-chanical properties of the network more accurately, while particlesthat prevented binding penetrated the actin network and thus were in-effective to measure bulk rheological properties.

6. Spatial and temporal resolution of particle trackingmicrorheology

The main concept in particle tracking microrheology is to observeand record the thermal response (probe force) of small particles of aknown size. Usually, in a typical experiment, several thousands tomillions of particle positions for each sample are recorded (thousandsof particle trajectories) to obtain statistically meaningful results. Thatis, more than 1000 independent particle displacements are requiredfor each lag time τ that is measured to increase the statistical accuracy[21••,46]. The longer the trajectory and the higher the recorded fre-quency, the more displacements can be recorded. In general, the sta-tistical accuracy decreases with lag time due to the reduction in thenumber of events corresponding to each point since fewer particlesremain in focus and within the field of view at long times. This ismore pronounced for systems with low viscosity.

Additionally, it is required that the recorded successive particlepositions are captured with sufficient spatial and temporal resolution[46,68••]. One of the main advantages of particle tracking microrheologyis that sub-micron resolution can be achieved (~10 nm for a typical ex-periment with a 100× objective and a 100 nm/pixel) [40••]. The diffrac-tion resolution, δ, of an opticalmicroscope is given by δ = 0.61 × λ / NAwhere λ is the wavelength of light and NA is the numerical aperture ofthe microscope's objective. For an advanced microscope the resolutionis in the range of a few hundred nanometers [44]. Sub-pixel resolutionis possible due to advances in image processing to extract the tracerparticle's coordinates. Moreover, fast recording systems should be usedto encompass most of the successive position history of rapid movingparticles to extend the frequency range. That is, the recorded positionsof a tracer particle at a certain time interval do not include information

about the different successive positions that this tracer particle mayhave occupied at the time interval.

In a typical experiment of particle tracking microrheology two dif-ferent types of errors occur: the “static error” and the “dynamic error”[68••]. The “static error” arises from the spatial resolution of the instru-ment in locating the centroid of the tracer particles, while the “dynamicerror” originates from the finite frame acquisition time (also called theexposure or shutter time) due to particle motion when the camera'sshutter is open [69].

The spatial resolution is limited by both the intrinsic thermal fluc-tuations of the tracer particles and the instrumental (microscope andcamera) ability to determine the particle position. The static error isassociated with locating the exact center of the tracer particles andit is dependent on the signal-to-noise ratio, the actual size of eachpixel, and on the image processing algorithms [40••,68••]. The dynamicerror, which is related to exposure time, depends on the particle dy-namics and can be reduced by increasing the shutter speed [69]. The ex-posure time of a single image should be adjusted to values where thetracer particles do not exhibit a significant motion during the genera-tion of each image. Otherwise, if the exposure time is too long, the cap-tured image of the particle will not be spherical. The dynamic error isrelated to the ratio of the lag time, τ, and the exposure time, σ, and ithas been reported [68••,69] that for relatively soft materials the ratioshould be τ/σ ≫ 1 to diminish the dynamic error; i.e., the dynamicerror increases with decreasing the ratio τ/σ. However, at high shutterspeeds the signal-to-noise ratio can be reduced thus increasing the stat-ic error. In case of low viscosity fluids an exposure time of 1000 μs is suf-ficient enough in a typical experiment.

In practice, the inherent tracking system error of an experimentalset-up can be determined by tracking identical probe tracers in a solidsample e.g., by performing particle tracking experiments and measur-ing the MSD with time (observed scatter in particle position) on fixed(e.g., glued) tracer particles on a microscope slide or an image ofmicro-dots. The estimated detection limit of the experimental setupis usually underestimated [70] due to the enhanced signal-to-noiseratio of a tracer particle fixed to a substrate, as it has less interferencewith the material's microstructure.

In a particle tracking experiment, the measured MSD correspondsto the real MSD taking into account the effects of the dynamic andstatic errors. In the case of a one-dimensional MSD in a Newtonianfluid for τ ≥ σ, the MSD takes the form [68••],

Δx2 τð ÞD E

¼ 2D τ−σ=3ð Þ þ 2ε2 ð14Þ

where ε is the spatial resolution and 2ε2 is the static error contribution,while the dynamic contribution is −2Dσ/3. In general, the error of thesystem becomes larger at short lag times and for samples with high vis-cosity (Fig. 2). As can be seen fromFig. 2, if the errors of an experimentalset-up are not properly accounted for, they can lead to misinterpreta-tions of the extracted microrheological data. In a Newtonian medium,when the static error is quite large, a curvature in mean squared dis-placement can be observed especially at short lag times (MSD artificial-ly large), resulting in a non-real sub-diffusive behavior. The parameter2ε2/2D [70] determines the discrepancy: the larger the parameter(smaller D, higher viscosity), themore sub-diffusive themotionwill ap-pear and at wider range of recorded lag times (Fig. 2). At longer timesthe contribution of static error is diminished, since the displacementsare much larger than the noise. On the contrary, when the dynamicerror is large, then the magnitude of the measured MSD is artificiallysmall than the magnitude of the true MSD, resulting in an apparentsub-diffusive behavior at short lag times (Fig. 2).

The limited particle driving forces available from Brownian motionindicate that the technique of passive microrheology is inapplicable tosystems of very high viscosity, since the tracer microsphere must moveover a distance significantly greater than the detection resolution.

317T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

Assuming that the dynamic error is diminished (τ/σ ≫ 1), the upperviscosity limit accessible by passive microrheology is restricted by thespatial resolution i.e., the tracer particles should diffuse more than thespatial resolution. The maximum capable measurement of viscositywith video particle tracking microrheology is given by [20•]

ηmax ¼ 2kBT τ=3πaε2 ð15Þ

and the maximummodulus is

Gmax ¼ 2kBT=3πaε2: ð16Þ

If we consider microspheres of diameter 0.2 μm (approximately theoptical microscopy resolution limit) and with an estimated sub-pixelresolution of ε ~ 10 nm, we can calculate the low shear rate viscosityof ηmax ~ 8.7 Pa s and 87 Pa s at 25 °C for a lag time of τ = 0.1 s and1 s respectively and a corresponding maximum storage modulus of87 Pa. However, themaximum lag time for which theMSD can bemea-sured depends on the acquisition time and the material viscosity. Lon-ger lag times acquire longer acquisition times. The minimum lag time(and lag time interval) for which the MSD can be measured dependson the frame acquisition rate, (τmin = 1/fps, fps: frame per second) ofthe detector. Nowadays, the progressing developments on digital cam-eras and video recording technology offer superb temporal resolution(acquisition rate of the images) in the range of 103–105 Hz combinedwith smaller pixel size (more pixels for the same field of view area)

Fig. 2. Effect of errors on the MSD of Newtonian fluids at 20 °C: (a) calculated MSD of0.5 μm diameter particles in water (0.001 Pa s) and (b) calculated MSD of 0.5 μm par-ticles in a Newtonian fluid (0.1 Pa s). The black line represents the “real (true)” datawithout considering any experimental error, while the colored lines represent themeasured MSD taking into consideration the contribution of the system's errors: inthe red line (sub-diffusive behavior at short lag timesm b 1) the static error dominateswhile for the blue line (super-diffusive behavior at short lag timesm > 1) the dynamicerror prevails. The static error contribution was set to 2 × 10−4 μm2 (ε = 10 nm) forthe dotted blue line and 2 × 10−2 μm2 (ε = 100 nm) for the solid blue line. The staticerrors had a considerable influence on the MSD at short lag times in the fairly viscoussample. For the dynamic error an exposure time σ = 100 ms was considered.

andwith the possibility to record the images directly on a fast computerin real time. However, substantial care should be taken to use lag timesbeyond the influence of the dynamic and static errors (see Fig. 2).

In addition, materials with high viscosity result in long trajectoriesand thereby in long lag times (~10–20 s), while for materials withlow viscosity the extracted longest lag time is considerably sorter(~1–2 s). This occurs because when a sample has very low viscosity,the tracer particles are expected to exhibit quite large displacementsat a certain lag time, whichmeans that the particles will not remain inthe field of view for long. These particles cannot be tracked for a longtime since they enter the recording focal plane many times and eachtime that they reappear in the field of view a new trajectory isassigned to the sameparticles. In samples of high viscosity if the observ-er waits long enough, sufficient diffusion will occur to permit adequatemeasurement, making it possible to distinguish theMSD from the errordetection limits. However, many food systems are aging with time andtherefore in the acquisition time no considerable changes in particlemobility should be taking place. Furthermore, in samples with high vis-cosity and thus shorter Brownian displacements the errors of the mea-surement play an important role and thus only log lag times should beconsidered (see Fig. 2).

Moreover, by using fluorescencemicroscopy, smaller size fluorescentparticle tracers can be tracked assuming the number of particles is suffi-ciently low, so that particles do not overlap and are adequately separat-ed. The emerging technology of quantum dots (inorganic nanocrystals,~1–6 nm,with unique optical properties) with the advances in video re-cording technology can reduce the detection limit and the dynamicrange of the method further and is expected to resolve displacementsthat are orders of magnitude smaller.

7. Applications to food gels and emulsions

Microrheology has recently gained popularity mainly for the com-plementary information that it can provide and for its potential tomeasure mechanical responses in small sample volumes inaccessibleto bulk rheology. Microrheology combines knowledge and techniquesfrom many scientific disciplines including chemistry, physics, statistics,microscopy, and image processing and analysis. The microrheology ap-proach has been widely employed by biologists–for example the groupof Wirtz and others that have employed particle tracking to study livingcell mechanics [50,71–74]–as well as material scientists to probe dynam-ics andmicrorheology innon-uniformsystems [5,6,46,75].Microrheologyhas been also used to study gels frombiomaterials; the group of Furst andothers have employedmicrorheology to examine the viscoelastic proper-ties of gels [66,76–88]. More information about the use of microrheologyon hydrogels can be found in a recent review article [86]. However,its application within the food sector has apparently not been fullyexploited [49]. Table 1 provides a list of various food-related systemswhere particle tracking microrheology has been applied. Moreover,other microrheological techniques such as laser trap microrheometry[89], DWS [59,90,91] and AFM [34] have been used to characterizefood-related systems. The food systems studied were predominantlytransparent and relatively soft, since opacity and magnitude of visco-elasticity restricts the method's applications.

Recently, particle tracking microrheology has been utilized to studythe motion of particles with different surface chemistries through thegastrointestinal mucus [100•–102] and a strong dependence of particlemobility on surface charge was observed. The addition of bile salts andparticle surface chemistry modification (carboxylate- and sulfate mod-ified particles) resulted in an increase in negative charge and therebythe diffusion of the particles increased remarkably [100•,101]. In con-trast, the surface charge of gram negative bacteria (Escherichia coli)was not altered significantly in the presence of bile salts, their mobilitywas not affected and thus the bacteria could not penetrate the mucuslayer [101]. These results show that the electrostatic repulsion preventsparticle interaction and adhesion on the mucus matrix and hence

318 T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

facilitates the particle's transport across the small intestine mucosalbarrier. In addition, a significant degree of particle heterogeneity wasobserved indicating that the native mucus contains a distribution ofpore sizes [100•].

Particle tracking can also be applied at liquid interfaces to providea different perspective on surface microrheology due to the superiorsensitivity and dynamic range [17•,93,103]. The diffusion of tracerparticles can be successfully monitored at an interface. Two-particlemicrorheology can provide very accurate measurements of themacroscopic interfacial rheology [103,104] even for samples thathave microheterogeneities while particle tracking microrheologycan probe spatial inhomogeneities at an interface. For instance,the mechanical properties and local microheterogeneities of an interfa-cial protein layer (β-lactoglobulin) at different pH values were investi-gated by using active and passive particle tracking microrheology at anair–water and an oil–water interface [17•,93]. Different behaviors of theparticle mobility were observed between air–water and oil–water in-terface, with the oil–water interface having a more rapid layer forma-tion with larger viscoelasticity. In addition, the heterogeneity of thewater–air surface was higher than the more spatially homogeneousoil–water interface [17•,93].

7.1. Sol–gel transitions

A particularly interesting phenomenon is the liquid-like (sol) togel-like (gel) transition, which is frequently encountered in food sys-tems (e.g., in yoghurt or during cheese manufacture). The transitionsare caused primarily by a change in environmental conditions, suchas pH, temperature and presence of divalent ions, as well as enzymat-ic actions. For example, gels can be created from casein either by en-zymatic action followed by precipitation with Ca2+ (e.g., in mostcheeses) or by acid coagulation (e.g., yoghurt).

Particle tracking microrheology observes the Brownian motion oftracer particles within a system and therefore it is expected that duringthe sol–gel transition themotion of the embedded tracer particlewill benegatively affected (decelerated). On this ground, the sol–gel transitioncan be successfully investigated with particle tracking microrheology.However, in order to relate the thermal fluctuations of the tracer parti-cles directly to the frequency-dependentmobility, it is assumed that thechanges in microstructure are slow compared to the sampling time;i.e., the system is in a quasi-steady state.

Particle tracking microrheology is usually employed to study thegelation of soft materials or the initial stages of stiff materials comple-mentary with other techniques e.g., bulk rheology or DWS [18,37,94].In general, particle tracking microrheology has high sensitivity andcan detect subtle changes in a developing network structure, beforesuch events are registered by other techniques e.g., convential bulkrheological measurements [18,41•]. That is, the bulk rheological mea-surements exhibit a lot of noise when there is no significant bulk vis-coelasticity, thus making it difficult to study the early (commencing)stages of gelation.

Table 1Microrheological studies in food-related systems.

Investigatedsystem

Application

Acid milk gel Gelation and probing microheterogeneities [37,41•]β-Lactoglobulin Gelation [77,92] and interfacial microrheology [17•,93]Gellan gum Gelation and probing microheterogeneities [61]Pectin Gelation and comparison with DWS [94]Wheat gliadin Mapping microheterogeneities [95]β-Glucans Gelation [18] and probing microheterogeneities [18,96]Honey Measuring viscosity and comparison with bulk rheology [97]Emulsions Measuring viscosity-comparison with bulk rheology and probing

microheterogeneities [13••,49]Liposomes Probing microheterogeneities and aggregation [9,98,99]Intestinal mucus Barrier properties [100•,101]

Recently, the sol–gel transition upon slow acidification of a modeldairy protein systemwas investigated via multiple-particle tracking uti-lizing confocalmicroscopy [37,41•]. Confocalmicroscopy provides sharp-er images than conventional light microscopy and can non-invasivelyprobe opaque samples at different depths [44,45,105,106]. Fig. 3ashows a typical time evolution of theMSD of probe particles during gela-tion (slow acidification of sodium caseinate) [41•]. At the beginning, thelog–log plot had a slope of m ~ 1 (⟨Δr2(τ)⟩ ~ τ), indicating a purely vis-cous response of the surrounding medium (Fig. 3a). As the proteinsstart aggregating, the slope m (m = d log⟨Δx2(τ)⟩/d log τ), of the log–log plot of MSD continuously decreases as the particles become progres-sively more constrained and trapped by the casein network and themo-tion of the particles becomes sub-diffusive. At long times, the MSDbecomes independent of the lag time, and eventually m approacheszero resembling the behavior of a purely elastic material.

Multiple-particle trackingmicrorheology has been also used to studythe sol–gel transition of aqueous barley β-glucan solutionswhich under-go gelation upon aging [18]. As gelation proceeds, themagnitude and theform of the MSD curve alter significantly (Fig. 3b). At the beginning,when no gel network has been formed, the movement of the particlesis purely diffusive and the log–log plot has a slopem ~ 1, over the entirelag time range, implying a purely viscous response of the surroundingmedium. As time progresses, there is a continuous decrease in the mag-nitude of the mean-squared displacement and a curve dependence onlag time. That is, over some time (t ≥ 100 min), the particles showdiffu-sive behavior at short lag times; however, at the longest lag times theMSD appears to attain a plateau, indicating that the particles are becom-ing constrained. At longer aging times (t > 150 min), the MSD becomesindependent of the lag time, resembling the behavior of a purely elasticmaterial.

The discrepancy between Fig. 3a and b about the formation of pla-teau at long lag times is that in protein solutions (Fig. 3a) the particlesadsorb strongly onto the sample's structural entities, while in thebarley β-glucan solutions (Fig. 3b) the particles were not adhered tothe polysaccharide network. As a consequence, although both sys-tems are heterogeneous at probe scale, only in the latter case dothe particles experience different microenvironments due to localmicroheterogeneities and therefore the ensemble mean-squared dis-placement was affected by the different local microenvironments.That is, the particles embedded in polysaccharide gels are confined incages and therefore their motion is constrained at long lag times. More-over, the particles embedded in the high viscosity microenvironmentsexhibited much smaller displacements and they remained in focus inthe field of view longer than the particles placed in network pores. Asa result, the slow particles make a higher contribution to thedisplacement's distribution, especially at long lag times while the parti-cles located in the pores have an influence mainly at short lag times.

Particle tracking microrheology can measure the viscoelastic prop-erties (G′, G″, J) and it can also detect the gel point with a minimal dis-turbance of the incipient gel structure. It is well known that the precisedefinition of the gel state is somewhat subjective. The criterion dependson changes in the arbitrarily chosenmechanical or structural propertiesmeasured and on the technique used tomake themeasurement [41•]. Agel may be defined as a material having a loss modulus G″ considerablysmaller than theG′ for several decades of frequency [107] or less restric-tively when G′ is greater than G″ (phase angle less than 45°) at somefixed frequency (say 1 Hz).

At the gel point, the viscoelastic moduli and tanδ should ex-hibit frequency-independent behavior (G′(ω) ~ G″(ω) ~ ωn) and⟨Δr2(τ)⟩ ~ τn where n is the critical relaxation exponent [107].When the logarithmic slopem of theMSD is lower than the critical relax-ation exponent value (m b n), the viscous behavior prevails, while whenit is higher (m > n) the elastic character dominates. The value of the crit-ical relaxation exponent n at the gel point depends on the gelling mate-rial [80••,107–109] and it takes values in the range 0.1 b n b 0.9. A highvalue of the critical relaxation exponent indicates a weak, not rigid

319T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

cross-linked gel while, a low value implies a densely cross-linked gel[107–109]. Many studies assume for simplicity n = 0.5, correspondingto tanδ = 1 (tanδ = tan(n π/2)). The critical relaxation exponent maybe identified by measuring the local slope m of the MSD as in Fig. 3a.The gel point is defined at the inflection point, where the curvaturechanges on either side [41•] and thus the critical relaxation exponentcan be extracted. At times before the gel point, stress can relax quickly.As more and more clusters are formed, the longest relaxation time in-creases and becomes measurable (i.e., becomes greater than the mea-sured frequency) and the motion of tracer particles becomes sub-diffusive (m b 1) asmore time is required for theMSD scaling to recoverthe diffusive behavior. Beyond the gel point, the longest relaxation timestarts to decay again, since relaxable components gradually integrateinto the network [107] and theMSD curves downwards as an elastic net-work has been formed [41•].

To characterize further the gel properties, master curves can alsobe constructed (known as time-cure superposition), firstly applied byLarsen and Furst [80••]. In short, theMSD curves are superposed bymul-tiplying the ordinate and abscissa with the appropriate shift factors aand b, respectively. In this way, the range of lag time (frequency) cov-ered becomes effectivelywider. From this analysis usefulmaterial prop-erties can be estimated, such as the critical extent of reaction, bondprobability, and the critical relaxation exponent [77,79,80••,86].

Moreover, it is possible to quantify the microstructural length scale(cage effect), by examining temporal correlations between successivedisplacements [41•,57,58,88,110•,111]. Typically, the average subsequentdisplacement ⟨x12⟩ is plotted as a function of r01 (Fig. 4), where x12 is thecomponent of vector r12 parallel to vector r01 [57,58]. If the tracer parti-cles execute a random walk (e.g., Newtonian fluid) the successive dis-placement vectors (r01 and r12) will be uncorrelated at a certain (fixed)lag time. When the particles are confined in a cage, the successive dis-placements will be correlated during sequential time intervals. That is,

Fig. 3. (a) Ensemble-averaged mean-squared displacements (MSDs) versus lag time(τ) of carboxylate-modified microspheres (0.5 μm) in 5% w/w sodium caseinate at dif-ferent times of acidification. The dotted line indicates the limiting value of slope = 1(pure diffusive response) while the solid line indicates a slope = 0 (pure elastic re-sponse). (b) Ensemble-averaged mean-squared displacements (MSDs) versus lagtime (τ) of carboxylate-modified fluorescent microspheres (0.75 μm) in 2% w/wβ-glucan aqueous solution during aging; the solid line indicates the limiting value ofslope = 1, while the dotted line indicates a slope = 0.(A) Data taken from [41•]. (B) Data taken from [18].

if a particle moves in one direction, the existence of a “cage”will inhibitfurther motion in that direction and the particle will move back(rebound) to the inside of the cage. In that case, the successivedisplacement vector, r12, will move in the opposite direction andtherefore it will be negatively correlated to r01. The negative correlationbetween successive displacements is the signature of the cage effect andindicates that the particle's motion is confined by the microstructure.The value of r01 at the endof the linear correlation (regime) is ameasureof the cage size (Fig. 4). The slope of the linear regime is ameasure of thestrength of the cage effect [58] and is directly related to the apparentelasticity [111].

7.2. Probing heterogeneity

Many colloidal food systems (physically and enzymatically cross-linked gels and micro phase separated emulsions) are heterogeneousat the microlevel. In order to understand the origins of the overallviscoelastic response of such inhomogeneous materials, it is neces-sary to probe mechanical properties over shorter length scales. Ashas been already mentioned, bulk rheological measurements andother microrheological techniques such as DWS describe the overall(average) mechanical response of a material whereas multiple-particletracking microrheology has the ability to obtain the ensemble averagemean-squared displacement, while retaining information for each ofthe individual particle trajectories. The motion of individual particlescan reveal new insights into the length scale dependent dynamics ofthe evolving microstructure. Each individual MSD represents the in-dividual dynamic of the tracer particles at various locations andhence can successfully map the spatial local microenvironments onthe microscale.

In homogeneous materials, all the particles should experience thesame dynamics while in heterogeneous materials the tracer particlesexplore different microenvironments. Statistical techniques havebeen developed to study the heterogeneity and map spatial and tem-poral variation in mechanical properties [112–114]. In addition, thetrajectories of particles that are embedded in different microenviron-ments can be grouped together and statistical meaningful viscoelasticproperties of local variations can be obtained [17•–19••].

Fig. 5 shows representative trajectories of particles and the indi-vidual mean squared displacements of probe particles embedded in2% w/w β-glucan aqueous solution upon aging [18]. At early stages,uniform trajectories are observed from freely diffusing particles andthe entire particles exhibit MSDs that increase almost linearly withlag time, indicating unconstrained motion of the particles. Upon aging,themotion of the particles is restricted and the trajectories are less spa-tially extended and the particles experience different microenviron-ments, while broader MSDs are found due to the developed structuralmicroheterogeneities (Fig. 5b). That is, some trajectories are spatially

Fig. 4. Correlation between successive probe particle displacements at different agingtimes embedded in 1% laponite. The dashed lines show the linear fit of ⟨x12⟩ with r01.The value of r01 at which correlations deviate from linearity can be taken as the micro-structural length scale of the system.Reproduced with permission from [111].

320 T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

extended and some others are dynamically arrested in the evolving bio-polymer network structure. Moreover, it is also observed that a smallnumber of tracer particles appear to move between the confined struc-tures (arrows in Fig. 5b). Such behavior is observedwhen the pores andthe particles are of similar size [60•]. Twodistinct groups of displacementscan be registered close to gel point of the system (Fig. 5b): some particlesmaintain pure diffusive motion (viscosities in the range of pure water~1 mPa s), while others are displaying almost time-independent MSD(viscosities up to 465.8 mPa s) [18]. This can be attributed to substantialspatial microheterogeneities present in the sample as a result of differentlocal viscoelasticities and microstructures. This reveals that some of thepores are being depleted or contain a few β-glucanmolecules at this par-ticular time of the experiment. As the intermolecular network formationfurther advances (Fig. 5c), all the large clusters aggregate togetherdiminishing the available aqueous space and themotionof all the embed-ded particles in the β-glucan network is constrained. In addition, none ofthe particles has extended trajectories and the individual MSDs becomeindependent of the lag time, resembling the behavior of a purely elasticmaterial.

It is noteworthy to mention that a few trajectories of particles atdifferent microenvironments cannot provide statistically accurate re-sults (see Section 6). As diffusion is a stochastic process, variances inthe displacements are expected even for homogeneous materials e.g.,glycerol solutions. The variancewill decrease as the number of recordeddisplacements increases; i.e., by increasing the experimental capturingtime, or the number of the embedded particles and/or the recorded fre-quency (the length of particle trajectories). Therefore, the informationextracted from individual trajectories is limited in statistics.

The structural heterogeneity is typically demonstrated by the distri-bution of displacements (P(Δx, τ)), known as the van Hove correlationfunction [18,19••,112,114]. In a randomwalk, the distribution of displace-ments for a purely diffusive medium is expected to be Gaussian withP(Δx, τ) = (4πDτ)−1/2 exp (−⟨Δx2(τ)⟩/4Dτ). Instead, a non-Gaussiandistribution signifies that some of the probe particles experience differ-ent microenvironments. Fig. 6a shows a typical example that shows

Fig. 5. Trajectories and data sets of individual mean-squared displacements of probe particdifferent times after sample preparation: (a) before gelation, (b) close to gelation point, anData taken from [18].

the distribution of particle displacementsΔx at a lag time of τ = 1 s dur-ing gelation of 2% w/w of barley β-glucan [18]. The solid lines are theGaussianfits of theΔxdistributionwith a zeromean. Thewidth of the dis-tribution is related to the mobility of the particles. At the early stages ofgelation the displacement's distribution at lag time τ = 1 s is Gaussian,indicating that all the particles diffuse isotropically and experience thesame microenvironment; i.e., the sample is homogeneous. As the timeadvances, the distribution of Δx largely deviates from Gaussian withbroad tails (see inset in Fig. 6a), implying that the particles are not inequivalent microenvironments and the system is heterogeneous on thescale probed by the tracer particles.

The deviations from Gaussian behavior can be quantified using anon-Gaussian parameter NG, which compares the fourth moment of thedistribution to the second moment and is defined as [18,19••,112,114]

NG ¼ Δr4 τð ÞD E

=3 Δr2 τð ÞD E2

� –1 ð17Þ

which is zero for a Gaussian distribution (homogeneous system) andgreater than zero when the distribution is broader and deviates fromGaussian (heterogeneous system). The non-Gaussian parameter is usual-ly calculated over all the lag times and/or duringmicrostructure evolutionto quantify and compare samples with different microheterogeneities.Fig. 6b shows the increase of NG of particles embedded in 2% w/wβ-glucan aqueous solution upon aging. As can be seen during aging theparticles become trapped inside pores of the aggregated β-glucan chainclusters that have different sizes and shapes. Upon gelation, relativelyhigh values of the NG parameter were calculated, implying that particlesexperience different microenvironments. After the gel point (~110 min),a decrease of NG at longer τ was observed, suggesting a more homoge-neous environment at larger spatial scale.

Another useful application of particle tracking microrheology is toprobe the dynamics and microrheology of emulsions that exhibitphase separation at a microscale level. The presence of a non-adsorbingbiopolymer in a stable emulsion leads to the formation of a transient

les (0.75 μm diameter, carboxylate-coated) embedded in 2% w/w β-glucan solution atd (c) at long time after the gel point.

Fig. 6. (a) van Hove correlation plots for microspheres moving in 2% w/w β-glucanaqueous solutions. The displacements over a lag time τ = 1 s are shown. The Gaussianfits are shown as solid lines. The inset shows the same data as at 111 min but atnarrower x-axis, for clarity. (b) The non-Gaussian parameter NG in 2% w/w β-glucanaqueous solution upon aging calculated from displacements over all lag times.(A) Data taken from [18]. (B) Data taken from [18].

• of special interest.•• of outstanding interest.

321T. Moschakis / Current Opinion in Colloid & Interface Science 18 (2013) 311–323

(but potentially long-lasting) network from droplets that have becomeflocculated under the influence of attractive depletion interactions in-duced by the presence of a very small concentration of non-adsorbingbiopolymer [115]. As a result, a microphase separated system is generat-ed consisting of two distinctive regions: the oil-droplet-rich region andthe non-adsorbing biopolymer-rich region. On the macroscopicscale, this type of emulsion can exhibit substantial serum separa-tion and strongly shear-thinning rheological behavior. Increasingthe non-adsorbing biopolymer concentration causes immobilization ofthe microstructure due to an increase in the local viscoelasticity and aweak gel-like network is generated. It has been mentioned in the liter-ature that the addition of non-adsorbing thickening agents modifiesthe rheological behavior of the aqueous continuous phase, thereby sta-bilizing the emulsions. In order to elucidate the underlyingmechanismofstabilization in such systems, the contribution of each microphase intothe overall mechanical properties should be estimated. Particle trackingmicrorheology can be used to study the dynamics of the two phase-separated regions utilizing the ability of confocal microscopy to focuson different regions [13••]. Therefore, the number of the recorded dis-placements for both regions can be quite high (several thousands) andhence the results will be extracted with high statistical accuracy. Itwas observed [13••] that the motion of particles located in the oil-richregions wasmore constrained in comparisonwith the particles embed-ded in the polysaccharide-rich regions; i.e., the viscosity in the oil-droplet-rich regions was considerably greater than in the non-adsorbingbiopolymer-rich phase. These results illustrate the dominant role of theinterconnected depletion-flocculated network of close-packed oil drop-lets to control the creaming instability. In this type of emulsion, the kinet-ics of phase separation system is predominantly determined by therheological behavior of the interconnected oil droplet regions [13••].

8. Conclusions

The potential of passive particle tracking microrheology to studythe local dynamics of food emulsions and gels has been demonstrated.The method utilizes the forces generated by Brownian motion andtherefore the system is distorted with the minimal strain possible,allowing the monitoring of the viscoelastic properties at microscalelengths. Particle tracking microrheology probes the linear viscoelastici-ty and can provide accurate measurements of the local and bulk me-chanical properties of complex fluids. It is an emerging techniquemainly due to its high sensitivity and because it can provide comple-mentary information to other techniques and also owing to its potentialto measuremechanical responses in small sample volumes inaccessibleto macrorheological techniques. Gelation can be efficiently studiedand the accurate estimation of the gel point and other useful param-eters such as the pore size of the gel can be extracted. Moreover, themicroheterogeneity of certain food systems can be successfully in-vestigated, revealing the local structural contributions to the overallmechanical response and materials behavior, an attribute that mac-roscopic mechanical measurements cannot provide.

Particle tracking microrheology has not yet been widely used tostudy the mechanical properties of food systems, possibly due to thefact that it requires knowledge from different scientific disciplines andit needs extensive numerical analysis. Taking into account that mostfood gels and emulsions are quite complex systems, particle trackingmicrorheology could help to elucidate the mechanisms responsible forstability and structure–function relationships. The commercial produc-tion of an automated particle trackingmicrorheology instrument, as hasbeen recently introduced for diffusivewave spectroscopy, might lead toa more extended use of particle tracking microrheology and might at-tract considerable attention from food scientists.

Acknowledgments

Special gratitude is given to the editor Prof. E. Dickinson for hisvaluable and useful corrections.

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