The motion of a closely fitting vesicle in a tube

Abstract eng:
The motion of a lipid bilayer vesicle through a narrow, cylindrical tube is modeled theoretically. The vesicle is treated as a sac of fluid enclosed by a thin, elastic sheet that admits resistance to bending deformation. The governing equations of viscous flow are simplified in the “quasi-parallel approximation” and solved numerically. The pressure drop across the vesicle is found to increase when the reduced volume is decreased or confinement is increased. The “critical tube radius,” below which the vesicle cannot pass through the tube without rupturing, is determined as a function of reduced volume. Under high confinement, bending resistance can be neglected and an asymptotic solution is developed, in the spirit of F. P. Bretherton’s original work on bubble transport [1], using singular perturbation methods. In this limit, vesicles of all reduced volume approach a spherocylindrical shape and the pressure drop scales inversely with gap thickness.

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