Time evolution of near membrane layers

TL;DR

This paper investigates the time-dependent growth of the near membrane layer in substance transport, demonstrating experimentally and theoretically that its thickness increases proportionally to the square root of time, independent of initial conditions.

Contribution

It provides experimental validation for a theoretical model describing the square root time growth of near membrane layers in transport processes.

Findings

Layer thickness grows as a√t over time.

Experimental results agree with theoretical predictions.

Growth coefficient is independent of initial concentration and permeability.

Abstract

The near membrane layer is defined as a region where the concentration of the substance transported across the membrane drops $k$ times. The time evolution of such a layer is studied experimentally by means of the laser interferometric method. It is shown that within the experimental errors the thickness of the near membrane layer grows in time as $a \sqrt t$ with the coefficient $a$ being independent of the initial concentration and the membrane permeability. Time evolution of the near membrane layers is also analyzed within the theoretical approach earlier developed by one of us. The regularities found experimentally fully agree with the theoretical expectations.