Instability of a biomimetic membrane in a DC electric field*

The linear instability of a zero-thickness lipid membrane, separating electrolytes with different conductivities, subjected to a uniform electric field, is investigated within the electrokinetic framework. The Poisson-Nernst-Planck equations are solved and the flow driven by the charge in the Debye layers formed near the membrane are studied. 

 

An undulation of the membrane compresses and expands the charges on the two opposing interfaces. Our calculation of the electric fields and the space charge shows that the force on the membrane due to the Maxwell stress is destabilizing, while the force due to the bulk charge is stabilizing. The instability is suppressed as the conductivity of the electrolytes becomes more asymmetric, due to a decreased intensity of the base state electric field near the membrane. This result contrasts with the enhanced destabilization predicted  by the leaky dielectric model in cases of asymmetric conductivity [1]. The effect of an ion current though the membrane is also discussed.

 

[1]J.  Seiwert, M. J. Miksis, and P. M. Vlahovska (2012) “Stability of biomimetic membranes in DC electric fields”, J. Fluid Mechanics, 706:58-70