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Shape stability of deflated vesicles in general linear flows
Phys. Rev. Fluids 4, 123606 – Published 26 December, 2019
DOI: https://doi.org/10.1103/PhysRevFluids.4.123606
Abstract
The dynamics of vesicles in simple shear or extensional flows has been extensively studied, but the conditions where vesicles experience more complex flow types, such as those seen in microfluidic devices or industrial processing conditions, warrant greater investigation. In this study, we use the boundary element method to investigate the shape stability of deflated vesicles in a general linear flow, i.e., linear combinations of extensional and rotational flows. We model the vesicles as a droplet with an incompressible interface with a bending resistance. We simulate a range of flow types from purely shear to extensional at viscosity ratios ranging from 0.01 to 5.0 and reduced volumes from 0.60 to 0.70. The vesicle's viscosity ratio appears to play a minimal role in describing its shape and stability for many mixed flows, even in cases when significant flows are present in the vesicle interior. We find in these cases that the critical capillary number for shape instabilities collapses onto similar values if the capillary number is scaled by an effective extensional rate. These results contrast with droplet studies where both viscosity ratio and flow type have significant effects on breakup. Our simulations suggest that if the flow type is not close to pure shear flow, one can accurately quantify the shape and stability of vesicles using the results from an equiviscous vesicle in pure extension. When the flow type is nearly shear flow, we start to see deviations in the observations discussed above. In this situation, the vesicle's stationary shape develops asymmetric cusps, which introduces a stabilizing effect and makes the critical capillary number depend on the viscosity ratio.
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