Bistability in a simple fluid network due to viscosity contrast
Brian Storey, John Geddes, David GardnerFranklin W. Olin College of Engineering
Russell CarrUniversity of New Hampshire
Problem and model
Fluids in inlet 1 and 2 have different viscosities, but are otherwise simple Newtonian fluids.
node aat 0
loop a around 0
flow)(laminar 128
4
i
i
Q
P
D
LR
QRP
One non-linearity – Arrhenius Law
Set flow Q1 and Q2– 2 statesQ1
Q2
Qc
Q1
Q2
Qc
Viscosity ratio = 1Q1
Q2
Qc
Q1
Q2
Qc
Viscosity ratio = 2Q1
Q2
Qc
Q1
Q2
Qc
Viscosity ratio = 10Q1
Q2
Qc
Q1
Q2
Qc
Viscosity ratio = 1,3,5,10,20,200
Pressure driven- 4 statesP1
P2
Qc
P1
P2
Qc
P1
P2
Qc
P1
P2
Qc
Viscosity ratio =1
Q2=0
QC=0
Q1=0
Viscosity ratio=10
Q2=0
QC=0
Q1=0
Viscosity ratio=200
Experimental setup
P1
P2
Qc
Water
Water+Sugar
P=0
Experimental procedure
Experimental data
of sugar in inlet 2 (μ2)
Criterion for existence of bistability
Arrhenius viscosity law
General viscosity law
Conclusions
• This work could have been done ~100 years ago.• We predict and observe bistability in a simple network with
laminar flow of Newtonian fluids. Flow direction depends on history.
• Perhaps the simplest example of bistability in (micro)fluidics?Quake
Prakash and GershenfeldGroisman et al
Stratified flow – effective viscosity
Immiscible
Fully mixed
Miscible, diffuse
Stratified flow experiment
Viscosity ratio = 5Q1
Q2
Qc
Q1
Q2
Qc
Viscosity ratio=5
Q2=0
QC=0
Q1=0
Q1
Q2
Qc
Q1
Q2
Qc
Q1
Q2
Qc
Q1
Q2
Qc
