Osmotic volume changes studied with stop-flow technique

In analysis of osmotic flow and net solute movement, the two basic equations 

Again the same convention as described earlier is used, and flow into the cell is considered to be in the positive direction. The osmotic pressure due to the permeant solute is denoted by which is defined as = RT(Cf - Att has units of dyne/cm. In these equations we speak of differences in concentrations in bulk phases since the partition coefficient which relates the concentration in the membrane phase to that of the bulk phase is incorporated in the permeability coefficients. The subscripts i and s refer to impermeant and permeant solute respectively. Lpj is the cross-coefficient for the volume flow arising from differences in the osmotic pressure of the permeant solute, Aw, when there is no difference of either hydrostatic or osmotic pressure produced by impermeant solutes ( Attj = 0). L p is the relative diffusional solute mobility per unit hydrostatic (or impermeant solute) pressure difference when Asr = 0. Although is always positive, and L p are both negative and have the same units as L. If the Onsager reciprocal relation holds, then is the diffusional flow and is a measure of the relative 

When the membrane is completely impermeable to the solute (case a), Eqn. 14 reduces to zero. In Eqn. 13, s will be equal to 0 and a = since by definition 

When the membrane is permeable to the solute under study, the reflection coefficient a can be calculated by the zero time method developed by Goldstein and Solomon [18]. In this method, use is made of volume change at t = 0, when 1.0 and j - 0 so that 

Solving for s from Eqn. 13, differentiating with respect to t to obtain dj/dr and then equating dj/dr with Eqn. 14, one obtains the following differential equation 

---