  Lipid bilayer membranes have a native (albeit small) permeability for water
molecules. Under an external load, provided that the bilayer structure stays
intact and does not suffer from poration or rupture, a lipid membrane deforms
and its water influx/efflux is often assumed negligible in the absence of
osmolarity. In this work we use boundary integral simulations to investigate
the effects of water permeability on the vesicle hydrodynamics due to a
mechanical load, such as the viscous stress from an external flow deforming a
vesicle membrane in free space or pushing it through a confinement.
Incorporating the membrane permeability into the framework of Helfrich free
energy for an inextensible, elastic membrane as a model for a semipermeable
vesicle, we illustrate that, in the absence of an osmotic stress gradient, the
semipermeable vesicle is affected by water influx/efflux over a sufficiently
long time or under a strong confinement. Our simulations quantify the
conditions for water permeation to be negligible in terms of the time scales,
flow strength, and confinement. These results shed light on how microfluidic
confinement can be utilized to estimate membrane permeability.
