Streaming Potentials: Their Genesis and Role in Biology

STREAMING POTENTIALS: THEIR GENESIS AND ROLE IN BIOLOGY R. I. DUNCAN* Introduction Whenever two substances, or two different phases of the same substance , are connected together electrically, there arises an electrical potential between them. This potential is known technically as the ? potential . It arises thermodynamically from the differences in the electrochemical potentials of the substances and physically from the differences in energy of the Fermi Levels [1, esp. pp. 4, 534]. If one of these substances is an ionizable solid and the other, an ionizing liquid, there is, in addition to the ? potential, another electrical potential, due to the loss (or gain) of charges by the solid, due to ionization , and a concomitant gain (or loss) of charges by the liquid. (Whatever charged atoms are lost by the solid are of course dissolved by the liquid). In addition to the ? potential and this ionization potential, there are the Donnan potential, the Gouy potential, the surface potential, the contact potential and the inner and outer distribution potentials [1,2, pp. 56—77]. Most of these are ofreal interest only to the physical chemist. Problems arise when an attempt is made to separate one of these potentials from the rest, as each is, to some degree, dependent on the others. In a physicochemical experiment where purity, cleanliness, and well-defined substances can be used and interchanged at will, these problems are not insurmountable; but in biology the most heuristic approach is to lump all of these potentials (including the ? potential) together and call this algebraic sum the ? potential. This has been the procedure in the past (in biology), and, although it would have been better ifa term other than ? had been chosen to avoid confusion, this same terminology will be adhered to in the following development. The important liquid/solid system in biology is blood and the artery wall. Because of the tubular structure of the artery and the flowing ?Department of Biophysics, Health Sciences Centre, University of Western Ontario, London 72, Canada. Publication ofthis paper was aided by a grant from the Ontario Heart Foundation. 392 J R. I. Duncan · Streaming Potentials blood, this system very conveniently gives rise to what is known as a streaming potential (which is reasonably easy to measure). Theory Whenever there is a potential difference between a liquid and a solid (blood/artery wall), the ions in the liquid of opposite sign to the sign of the solid are attracted to the solid, and those of like sign are repelled by the solid. As these two classes of ions are in a liquid, they are free to move; therefore they distribute themselves into a diffuse double (or multiple) layer as in figure 1 [2, pp. 56-77]. If the fluid now moves in a direction parallel to the wall, and if the potential of the wall is assumed to be negative relative to the fluid, the less restrained negative charges are more likely to move with the fluid, LIQUID - 4 + 4 +¦ (a) LIQUID -3-4 X- -I-® F L 0 W V + ? (b) Fig. 1.—Diffuse ionic layers, a, No fluid flow, b, Fluid flow with streaming potential generated. Perspectives in Biology and Medicine · Spring 1974 | 393 and the more constrained positive ions will stay behind. Thus the direction toward which the fluid is moving becomes negative and that from which the fluid is moving becomes positive. This potential is the streaming potential and is usually measured in volts cm -1 in the direction of the motion of the fluid. It is obvious that the size of the streaming potential will be, in some way, proportional to the size of the ? potential and also proportional to the rapidity with which the fluid is moving. It is not so obvious that it is also proportional to the dielectric constant and inversely proportional to the specific conductivity of the fluid (these latter points are explained below). Because the most convenient parameters to measure are the volume flow rate and the driving pressure, and not the arterial diameter, the following derivation incorporates the radius into the volume flow rate and thus introduces the pressure and viscosity into the formula: 47TT7KE ? DP ' where ? = viscosity (3 x 10-2 poise in...