Kinematic Stabilization of Continuous-flow Electrophoresis against Thermal Convection.

The Problem of Thermal Convection.-Electrophoresis presupposes the m ain tenance of an electric field in a conductive fluid (usually a buffer solution). The electric field dV/dx cannot be maintained without a concomitant current density J2 = u(dV/dx). In an electrophoretic column of uniform cross section, the heat generated in a unit volume per unit time will thus be: dQ/dt = Jxlla = (dV/dx)2a. In the absence of turbulence, this heat would escape by heat conduction through the walls of the electrophoretic channel at a rate determined by the temperature gradients in the fluid and in the walls confining it. Actually, however, the transfer of heat from the fluid to its surroundings is greatly accelerated by the phenomenon of thermal convection which is normally engendered in the presence of a temperature gradient transverse to the walls. There are two special cases in which thermal convection is avoided: (1) when the density of the fluid is independent of its temperature (this condition is approached in the vicinity of 40C near the density maximum of water and is utilized for stabilization in the Tiselius electrophoresis apparatus); (2) when the direction of a temperature gradient which is parallel to the gravitational field is such that the fluid density increases in the gravitational field direction. (Lord Rayleigh' showed that under certain special conditions a horizontal fluid sheath may remain undisturbed by thermal convection even if the temperature gradient is inverted.) The steady-state convection pattern depends on the direction of the temperature gradient relative to the gravitational field axis and on the geometry as well as orientation of the fluid container relative to the field of gravity. The mathematical treatment of thermal convection is extremely difficult and has been successful only in a few special cases under simplifying conditions.'-3 Generation of Thermal Convection in Configurations of Practical Interest.-Several configurations, which are relevant to the present considerations, will be discussed qualitatively with the aid of photographs and schematic diagrams based on observations. Figures 1-3 illustrate convection patterns which will be considered below in connection with methods of inhibition of thermal convection. (a) Convection between two vertical walls: In Figure la, the fluid of initial temperature To is introduced into a vertical container whose opposite walls Wa and Wb are maintained at the constant temperatures Ta > To and Tb = To. g represents the direction of the gravitational field. Under usual circumstances when the density of the fluid decreases-with temperature, the buoyant force upon a heated fluid element adjacent to wall Wa will exceed its weight, and a circulation of the pattern indicated in the figure will result, as can be easily ascertained by observing streak patterns of injected dye. In Figure lb, the temperature of the fluid introduced between the walls Wa Wb exceeds the temperature of both walls'-(Ta < To > Tb; Ta = Tb). The liquid in the central plane rises for the reasons given in the previous case, while the denser