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Bistability in a simple fluid network due to viscosity contrast. Brian Storey, John Geddes, David Gardner Franklin W. Olin College of Engineering Russell Carr University of New Hampshire. Problem and model. Fluids in inlet 1 and 2 have different viscosities, - PowerPoint PPT Presentation
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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