Viscosity-dependent steady state position of droplets in Poiseuille flow
Shih-Hao Wang1*, Yeng-Long Chen1,2,3
1Institute of physics, Academia Sinica, Taipei, Taiwan
2Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan
3Department of Physics, National Taiwan University, Taipei, Taiwan
* presenting author:Shih-Hao Wang, email:chaosgeometry@gmail.com
Hydrodynamic-induced migration in microfluidic flow can be applied to separate cells and particles with different properties. For hard sphere, inertial-driven migration leads to particle migrate away from a wall. For a soft deformable particle, particle migration is due to deformation-induced hydrodynamic forces near a wall. The inertial-driven and the deformation-induced forces can be quantified by the particle Reynolds number Re, which characterizes the competition between inertia and viscosity dissipation, and the capillary number Ca, which characterizes the competition between flow shear and particle surface tension/elasticity. For many cells, capsules, and droplets with inner fluid, the lift forces further depend on the internal-to-external fluid viscosity ratio λ. Prior first order analyses predicted that the lateral steady state particle positions migrate more towards the walls for 1 < λ < 10 and more towards the center for lower and higher λ[1]. Recently, experiments with oil-in-water droplets found that the lateral steady state particle positions have different dependences on the viscosity ratio[2].
In this study, we used a lattice Boltzmann-immersed boundary method to investigate the dependence of particle migration on Re, Ca, and λ. We found that the steady state position d* is determined by competition between the inertial-driven and deformation-induced forces. We also observed whether a droplet migrates towards the wall or to the center at steady state depends strongly on λ. In the deformation-dominated regime, droplets migrate to the channel center as λ is small enough. In the inertial-dominated regime, droplets migrate towards the wall as λ increase. In the intermediate regime, we observed non-monotonic dependence of d* on λ at λ = 0.05 to 0.5. This trend qualitatively agrees with the experimental results[2]. Our results suggest this non-monotonic trend is due to the comparable contributions due to inertial- and deformation- driven migration.

References

[1] P. Chan and L. G. Leal, J. Fluid Mech. 92, 131 (1979).
[2] S. C. Hur, N. K. Henderson-MacLennan, E. R. B. McCabe, and D. Di Carlo, Lab Chip 11, 912 (2011).


Keywords: Droplet migration