Batch electrophoretic cells with Eyring fluids: Analysis of the hydrodynamics

Abstract

Mixing and dispersion phenomena caused by the carrier fluid in an electrophoretic cell is the main subject of this study. In particular, the effects of Joule heating on temperature and velocity profiles for Eyring-model fluids (EMF) are studied. The heat transfer is sequentially coupled with momentum transfer to derive an analytical expression for both the temperature and the velocity profiles. These results are then used to show the hydrodynamic behavior of the fluid in a batch electrophoretic cell. Furthermore, the results obtained are useful to compare with the fluid behavior of other carriers of different rheology, such as Newtonian fluids, power-law fluids, and viscoelastic fluids that obey the CEF model. The results show that EMF are potentially good carriers for relatively high Joule heat generation and therefore good candidates to control mixing inside the electrophoretic cell.

Dispersive mixing in a batch electrophoretic cell with Eyring fluids

“…(25) is simply the conservation of total mass in the separation chamber as described by Bosse et al [1]. The result of Eq.…”

“…Bosse and Arce [1] suggest that, after having computed the temperature and velocity profile for the case of an Eyring fluid [1,17], the analysis of the solute problem is the next logical step to follow. Accordingly, in this section, the procedure that yields the effective dispersion coefficient valid for the flow inside the electrophoretic device is fully introduced.…”

“…* Since the velocity profile is known [1], the value of the deviation velocity ṽ z (y) is also a known quantity. This is not the case for the concentration field.…”

“…For this purpose, the velocity profile for an Eyring fluid obtained by Bosse et al [1,17] is considered. Its equation, in terms of nondimensional variables, is given simply by:…”

“…Specifically, this study will focus on (i) the influence of Joule heating on the hydrodynamic velocity profiles for non-Newtonian carriers; and (ii) analysis of the sensitivity shown by the carrier-fluid rheology in promoting free convection currents within the cell [12,13]; this second important aspect will be studied by using the Eyring model. The analysis performed in this contribution will use the areaaveraging approach to derive effective dispersion coefficients as a function of Joule heat generation from the species continuity equation of the solute molecule; it also needs the results of a companion contribution published in this issue [1] when the veocity and temperature profiles are studied.…”