Dynamics of drops in branched tubes

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Abstract
The flow of two-dimensional deformable drops through branching (bifurcating) tubes is studied numerically using a boundary integral formulation. The undeformed drop diameter is assumed to be less than the tube diameter. Capillary numbers between 10−2 and 1 are considered. Flow in the branching tube is characterized by the fraction of fluid which enters each of the two downstream branches. The likelihood of drops entering the high-flow-rate branch increases as (i) the viscosity ratio between the drops and suspending fluid decreases, (ii) the capillary number increases, and (iii) the drop size increases. Hydrodynamic interactions between the suspended drops increase the number of drops which enter the low-flow-rate branch. The implications of these results for dispersion processes and local transport are explored. The disturbance flow created by drops passing over ‘dead-end’ pores or cavities results in fluid transfer between the pore and the free stream; suspensions may then be effective in improving the ‘cleaning’ of porous materials.

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