The near membrane layer is a region where the concentration of the substanc
e transported across the membrane is significantly decreased. Its thickness
is defined as a length over which the concentration drops k times with k b
eing an arbitrary large number. The time evolution of such a layer is studi
ed experimentally by means of the laser interferometric method. It is shown
that within the experimental errors the thickness of the near membrane lay
er grows in time for any k as a roott with the coefficient a being independ
ent of the initial concentration and the membrane permeability. Time evolut
ion of the near membrane layers is also analyzed theoretically. The regular
ities found experimentally are naturally described within the model which h
as been earlier developed by one of us. In particular, a scales as erfc(-1)
(1/k).