  In the present paper a simple dynamical model for computing the osmotically
driven fluid flow in a variety of complex, non equilibrium situations is
derived from first principles. Using the Oberbeck-Boussinesq approximation, the
basic equations describing the process of forward osmosis have been obtained.
It has been shown that these equations are very similar to the ones used to
model the free Rayleigh-Benard convection. The difference is that while in the
case of thermal convection the volume expansion is driven by the coefficient of
thermal expansion, the key role for the osmotic instability is played by the
coefficient of isothermal compressibility. In addition, it has been shown that
the osmotic process represents a propagation of standing waves with
time-dependent amplitudes and phase velocity, which equals the current velocity
of the solvent passing through the semi-permeable membrane. The evolution of
the amplitudes of the osmotic waves is exactly following the dynamics of a
strange attractor of Lorenz type with corresponding control parameters.
