Hydrodynamics of a semipermeable inextensible membrane under flow and confinement

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 hydrodynamics of an inextensible membrane under a mechanical load, such as the viscous stress from an external flow deforming an inextensible 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 (a 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 timescales, flow strength, and confinement. These results shed light on how microfluidic confinement can be utilized to estimate membrane permeability.