# Hydrodynamics and rheology of a vesicle doublet suspension

## TL;DR

This study numerically investigates the hydrodynamics and rheology of vesicle doublets under various flow conditions, revealing how adhesion influences their formation, dynamics, and suspension viscosity.

## Contribution

It introduces a high-order boundary integral method to analyze vesicle doublet behavior and identifies flow conditions affecting their stability and rheological properties.

## Key findings

- Vesicle doublets form at equilibrium under quiescent flow due to adhesion.
- A critical extensional flow rate can measure vesicle adhesion strength.
- Vesicle doublet suspension viscosity depends on vesicle reduced area.

## Abstract

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.