The electrokinetic sonic amplitude effect in filtration membranes: Part II – Theory

In this paper we set out the mathematical problem for calculating the sound waves generated by a MHz voltage – the ESA effect – for a saturated filtration membrane. Three asymptotic solutions are derived, to help build up an understanding of the physical processes involved, and these solutions are then compared with numerical solutions to the full problem. We illustrate the effect of various parameters on the ESA spectra and discuss the problem of extracting membrane properties from ESA measurements.

► We present the theory for the membrane ESA measured in paper 1.
► We set out the equations and boundary conditions to be solved.
► We present approximate solutions under various asymptotic limits.
► We compare the approximate solutions with full numerical solutions.
► We discuss the problem of determining membrane properties from ESA measurements.