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, but are otherwise simple Newtonian fluids.

One non-linearity – Arrhenius Law

Set flow Q1 and Q2– 2 states Q1 Q2 Qc Q1 Q2 Qc

Viscosity ratio = 1 Q1 Q2 Qc Q1 Q2 Qc

Viscosity ratio = 2 Q1 Q2 Qc Q1 Q2 Qc

Viscosity ratio = 10 Q1 Q2 Qc Q1 Q2 Qc

Viscosity ratio = 1,3,5,10,20,200

Pressure driven- 4 states P1 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 + Sugar P=0

Experimental procedure

Experimental data of sugar in inlet 2 (μ 2 )

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 Gershenfeld Groisman et al

Stratified flow – effective viscosity Immiscible Fully mixed Miscible, diffuse

Stratified flow experiment

Viscosity ratio = 5 Q1 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