Volume Flow in Response to a Difference in Pressure

Volume flow (Jv) across a membrane in response to a difference in hydrostatic pressure, AP, is given by the linear relation:

where Kf is a proportionality constant referred to as the hydraulic conductivity of the membrane (or, the filtration coefficient); Eq. 22 is analogous to Fick's law of diffusion (Eq. 2) inasmuch as it describes a linear relation between a flow and its driving force, which in the case of volume flow is the pressure difference across the barrier. Now, AP can be the difference in hydrostatic pressure, the difference in osmotic pressure, or a combination of both. For example, referring to Fig. 13, if the concentration in compartment o is equal to that in compartment i so that An = 0, application of pressure to the piston will bring about the flow of volume from i to o given by Eq. 21. Alternatively, if Co < Ci and no pressure is applied to the piston, there will be a flow of volume from o to i given by:

An important empirical observation made many years ago is the equivalence of osmotic and hydrostatic pressure as the driving forces for volume flow. That is, Jv across a given membrane will be the same when it is driven by a hydrostatic pressure difference as when driven by the equivalent osmotic pressure difference. In other words, for a given membrane, the same value of Kf applies to both forces. Thus, we can combine Eqs. 22 and 23 and derive a general equation that describes the situation when there are both osmotic and hydrostatic pressure differences across the membrane:

Thus, when AP = Aneff, Jv = 0; this is the definition of osmotic pressure. When AP = Aneff, there will be a flow from one compartment to the other, driven by the difference.

Equation 24 provides a general description of the effects of hydrostatic and osmotic forces on volume flow across all membranes. In the physiologic sciences, it is often referred to as the Starling equation, after the great British physiologist Ernest Starling, who applied it to the study of fluid movements across the walls of capillaries.

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