Non-newtonian carriers in a batch electrophoretic cell with joule heating: hydrodynamic considerations and mathematical aspects

Abstract

The Joule heating effects on hydrodynamics are examined for the case of a non-Newtonian fluid flowing in a batch electrophoretic cell. The potential benefits of using non-Newtonian fluids in electrophoretic separations could lead, for example, to an increase in the efficiency of separations and to a better scale-up of the operation for the processing of large quantities on a pilot or even an industrial scale. The analysis conducted in this research is based on the formulation of simplified mathematical models that can capture the most relevant aspects of the physics of the free convection that takes place in a batch electrophoretic cell. The first aspect is associated with the carrier fluid when no solute sample (of particles or macromolecules) is added to the device. This is, indeed, a carrier fluid completely free of solute problem. This aspect of the research is referred to as the carrier fluid problem. The second aspect involved in the investigation is the analysis of the mass transport (i.e., convective-diffusive) process associated with the motion of a solute sample added to the carrier fluid. This particular aspect of the research is referred to as the solute problem of the free-convection electrophoretic cell. The two problems are sequentially coupled and the solution of the carrier fluid problem must be performed first in order to have the velocity profile to study the solute problem. Details about hydrodynamic considerations and the solution approach are discussed in this contribution

Batch electrophoretic cells with Eyring fluids: Analysis of the hydrodynamics

“…It is observed that the effect of the Joule heating promotes the increase of the velocity in both directions; this effect is smaller when the Joule heating number decreases. This behavior is in agreement with that shown by fluids that obey the power-law and CEF model in the region near the high-temperature wall [9,10].…”

“…The velocity profile computed in this investigation is useful in making comparisons among the carrier fluids with different rheologies [1,2,9,10] value of the Joule heating number is high enough to produce a temperature value at the center of the cell which is higher than the temperature values at the walls. Figure 5 shows the remarkably different behavior that non-Newtonian carrier fluids may demonstrate under the influence of the Joule heating effect, compared to the behavior of Newtonian carriers.…”

“…Modification of the carrier-fluid rheology to decrease free convection currents has also been suggested [1,9]. More recently, this aspect has been studied systematically by Bosse et al [9,10] for the case of the power-law model. With the same objective, fluids that follow the Eyring model have been used in the present investigation to study the potential effect of such a rheology on decreasing the impact of the Joule heat generation on free convection currents.…”

Dispersive mixing in a batch electrophoretic cell with Eyring fluids

“…The denomination of "effective coefficient" is used here to indicate the fact that this coefficient comes as a result of and averaging process conducted on the "microscopic" differential equation for the solute transport, i.e., the species continuity equation. The procedure was applied first to Newtonian carriers [12,13] and has been extended to power-law model carriers as well [16,23,24]. Experimental evidence of the effect of material rheology on the motion of solutes under an applied field has been reported earlier in the literature [14,15] but no systematic analysis from first principles has been offered.…”

“…This justifies the need for further study of new strategies for the abatement and control of the Joule heating effect, especially from a fundamental point of view. Since the power-law model yielded promising results [23,24], rheology analysis in this contribution is centered on fluids that follow the Eyring model.…”