Experimental and Numerical Studies on fluid flow in evaporating droplets

Mohd Aslam

Department of Chemical EngineeringIndian Institute of Technology

Guwahati2015

By

144107016

IntroductionApplicationLiterature reviewObjectiveMechanismMathematical modelReferences

Outline

Introduction In physics, a "coffee ring" is a

pattern left by a puddle of particle-laden liquid after it evaporates. The phenomenon is named for the characteristic ring-like deposit along the perimeter of a spill of coffee.

When a coffee droplet is spilled on a solid surface, it leave a dense ring-like stain along the perimeter as shown in Fig 2. This is called coffee ring effect.

Fig.2:coffee ring effect

Fig.1:droplets evaporation

Type of evaporation mode

Pinned-contact line evaporation

Depinned-contact line evaporation

Fig.3:pinned contact line Fig.4:depinned-contace line Fig.5:Both contact angle

and contact area decrease

Both contact angle and contact area decrease

Introduction

1-Pinned-contact line evaporatoin

Fig.4: Ring-like deposition

Fig.3: Constant contact area mode evaporation

unchanged contact area between liquid and solid surface. The contact angle decreases while the contact radius remains the same.

Edges the rate of evaporation is much higher than the Centre. Consequently, a flow is generated toward the edges.

The roughness of the surface favors the pinning phenomena .

If solute particles are present, then after evaporation we get ring-like deposition

Introduction

Fig.1: Small contact angle

Fig2: at different Time like t1,t2,and t3

(a) Small receding angle prevents depinning at the ring

show that a smaller wetting angle (φ’rec) for the pure liquid air-particles substrate leads to a situation. where the ring forms without depinning.

Introduction

Fig.1:Constant contact angle mode evaporation

Fig.6: Centre spot deposition

2. Depinned-contact line evaporation The contact angle remains unaltered during

evaporation while the contact radius decreases.

Rate of evaporation of solvent at the edges is more than the rate of replacement. The resulting Marangoni flow carry particle from the edge towards the apex .

It is generally seen if the surface on which droplet placed is smooth.

If solute particles are present, then after evaporation we get centre-spot deposition.

Introduction

Fig.1:Large contact angle

(b)Large receding angle induces depinning at the ring

(b) show that depinning at point (I)occurs during drying of the colloidal drop on a smooth solid substrate when φrec is reached atpoint (I).

Fig2: at different Time like t1,t2,and t3

Introduction

Time

Evap

orati

on p

aram

eter Wetted radius(r)

Wetting angle(Φ)Volume of drop

=Φ>Φ𝑟𝑒𝑐=

Receding at Wetting line start to recedeSubstrate pinned wetting line

Fig.1: Depinning mechanism for the evaporation of a pure liquid drop. Recedingstarts when the wetting angle reaches a given receding value φrec and then proceeds at constant wetting angle.

Introduction

ApplicationApplications:-

Disease diagnosis: Sompol et al.(2011) found that the dried drop blood of persons suffering from a anemia disease show similar kind of deposition profile.

Drops of blood from individuals (a) in good health, (b) with anemia, (c) in good health, and (d) with hyperlipidemia

• a polymer solution is fed to an inkjet head and small sized droplets are ejected onto a substrate.• flat shape is required for

electrical devices such as picture element of display .

Ink-jet printing

J. Biomed. Opt. 18(12), 127003 (Dec 16, 2013)

Zhang et al. have utilized coffee-ring drying pattern to pre-concentrate the protein solutions prior to Raman analysis in so called Drop Coating Deposition Raman (DCDR) technique.

DCDR used in biomedical.

ApplicationDCDR Technique

DNA micro arrays• Use in Gene analysis.

• Li et al. (2001) found that stretching behavior is strongly affected by evaporation rate.

• At a low evaporation rates folded or coiled DNA molecules are found such as Fig.1.

• At high evaporation rate, the shape become dumbell like Fig.2

Application

Fig.1: folded or coiled DNA

Y Wang et al. Nature 491, 51-55 (2012) doi:10.1038/nature11564

Fig.2:dumbbell shape DNA

Literature review Larson et al.(2014) Transport and Deposition Patterns in Drying Sessile Droplets . In this theory he explained that common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking-and-slipping contact lines, and Marangoni effects Hua et al.(2005) Analysis of the effect of Marangoni Stresses on the Micro flow in an

Evaporating Sessile Droplet. find that surfactant contamination, at a surface concentration as small as 300 molecules/ím2, can almost entirely suppress the Marangoni flow in the evaporating droplet.

Bhardwaj et al.(2010) Pattern formation during the evaporation of a colloidal nanoliter droplets . Measured evaporation times, deposit Shape and sizes, and flow fields are in very good agreement with the numerical results.

Ristenpart et al.(2007) Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops. demonstrated experimentally that thermal Marangoni flow in evaporating droplets depends sensitively on the ratio of thermal conductivities of the liquid and substrate,

Zhang et al.(2013) Temperature distribution along the surface of evaporating droplets. analyses indicate that a non monotonic spatial distribution of the surface temperature should occur

Mechanism

Larson et al.(2006) suggests the evaporation induces a Marangoni flow inside a drople.

Marangoni Stress

Fig.1:Marangoni stress

The marangoni effect is the mass transfer along an interface between two fluids due to surface tension gradient.

Mechanism

Deegan et al.(1997) pattern is due to capillary flow induced by the differential evaporation rates across the drop: liquid evaporating from the edge is replenished by liquid from the interior

In the case of temperature dependence, this phenomenon may be called thermo-capillary convection.Fig.1

Fig.1 Thermo capillary convection

Objective To study of Experimental and Numerical fluid flow

inside evaporating droplets at study state heating of substrate.

Mathematical modelThe system is an axis-

symmetric sessile droplet of incompressible fluid (water) of constant viscosity and having the shape of a spherical cap resting on a flat surface.

AssumptionFig. 9: Sessile drop resting on a flat surface

Ashish et al . Analysis of fluid flow and particle transport in evaporating droplets exposed to infrared heating

I. At steady state, the solution will remain constant with time.

II. No evaporation is taking place.III. The droplet is pinned to the substrate i.e. the contact

radius and contact angle do not change with time. R and Ѳ are constant

1. Continuity equation :

)1(0)()(

y

v

x

u

)2()()(

2

2

2

2

y

u

x

u

x

P

y

uv

x

uu

)3()()()(

02

2

2

2

ygTTy

v

x

v

y

P

y

vv

x

vu

In the y-momentum equation, the buoyancy force term due to temperature is considered by Boussinesq approximation.

Buoyancy force term

)4()()(

2

2

2

2

y

T

x

Tk

y

Tv

x

TuC p

2. Momentum equations :

3. Energy equation:

Mathematical modelFollowing are the governing equations considered for steady state

Mathematical model Boundary condition:The boundary conditions considered in the

are given belowI. The temperature of the solid as well as free surface of the droplet are

specified in the form of linear profile obtained from the experimental values of temperatures at the apex as well as left and right edge.

II. The no –slip boundary condition is applied on the bottom solid surface. III At the liquid–gas interface, a tangential Marangoni stress due to surface temperature variation is considered as follows:

=

A constant value of temperature coefficient of surface tension = 0.0001657 N m1 C1

(as reported by Hu and Larson )

Mathematical modelDiscretizetion of the equations of continuity,

momentum and energy and solve by ANSYS Fluent software

Kai Zhang et.al ;Temperature distribution along the surface of evaporating droplets .phys.rev.2014

Larson et .al ;Transport and Deposition in drying droplets sessile droplets.fluid.Mech.2014

Singh A et al; Thokchom.A.K et.al Fluid Flow and Particle Dynamics Inside an Evaporating Droplet Containing Live Bacteria Displaying Chemotaxis.Langmuir .2014

Bhardwaj et.al;Pattern formation during the evaporation of colloid nanoliter drop. New Journal of Physics

Savva et.al; Asymptotic analysis of evaporating droplets. phys.fluids 2014

References