  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.
