Joule heating induced stream broadening in free‐flow zone electrophoresis

Abstract

The use of an electric field in free-flow zone electrophoresis (FFZE) automatically leads to Joule heating yielding a higher temperature at the center of the separation chamber relative to that around the channel walls. For small amounts of heat generated, this thermal effect introduces a variation in the equilibrium position of the analyte molecules due to the dependence of liquid viscosity and analyte diffusivity on temperature leading to a modification in the position of the analyte stream as well as the zone width. In this article, an analytic theory is presented to quantitate such effects of Joule heating on FFZE assays in the limit of small temperature differentials across the channel gap yielding a closed form expression for the stream position and zone variance under equilibrium conditions. A method-of-moments approach is employed to develop this analytic theory, which is further validated with numerical solutions of the governing equations. Interestingly, the noted analyses predict that Joule heating can drift the location of the analyte stream either way of its equilibrium position realized in the absence of any temperature rise in the system, and also tends to reduce zone dispersion. The extent of these modifications, however, is governed by the electric field induced temperature rise and three Péclet numbers evaluated based on the axial pressure-driven flow, transverse electroosmotic and electrophoretic solute velocities in the separation chamber. Monte Carlo simulations of the FFZE system further establish a time and a length scale over which the results from the analytic theory are valid.

Structure and effective charge characterization of proteins by a mobility capillary electrophoresis based method

“…With the introduction of a separation voltage into the MCE system, the effects of thermal heating68,69 need to be considered and corrected for before we can accurately calculate the ion hydrodynamic radius. Although most commercial CE instruments have temperature control, the heat generated inside the capillary may not be conducted instantaneously, and a higher temperature may be present inside the capillary 70. In turn, temperature also affects the viscosity of the solvent, which is another important parameter when calculating the ion hydrodynamic radius.…”

Estimating Stream Broadening in Free-Flow Electrophoretic Systems Based on the Method-of-Moments Formulation

“…The use of an electric field in free-flow zone electrophoresis (FFZE) automatically leads to Joule heating yielding a higher temperature at the center of the separation chamber relative to that around the channel walls. For small amounts of heat generated, this thermal effect introduces a variation in the equilibrium position of the analyte molecules due to the dependence of liquid viscosity and analyte diffusivity on temperature leading to a modification in the position of the analyte stream as well as the zone width [11]. The Joule heating of the background electrolyte under these conditions leads to a fully developed temperature ( T ) profile across the channel gap determined by the following expression based on Fourier’s law ddy(kdTdy)=−λE2 boundary conditions: T=T0 at y=±d2 where T 0 refers to the absolute temperature at the parallel plates and the quantities k and λ denote the ionic and thermal conductivities of the background electrolyte, respectively.…”

“…For example, while the thermal conductivity of water is known to increase by less than 1% for small variations in T (< 10°C) around room temperature (25°C), the corresponding change in λ can be as large as 25%. In this situation, the leading order effect of Joule heating may be captured by assuming k to be spatially constant (0.6 W/m/K for water at T 0 = 25°C) [11] and the ionic conductivity to vary as λ = λ 0 I 0 [1 + α ( T − T 0 )] where λ 0 = 0.14 m 2 S/mol (for aqueous KCl solutions), α = 0.025 /K (for water) and I 0 equals the ion concentration in the background electrolyte in mol/m 3 [12].…”

Purification of low‐abundance lysozyme in egg white via free‐flow electrophoresis with gel‐filtration chromatography

“…FFZE was conducted in accordance with the manual provided by the manufacturer. In order to ensure the separation efficiency of FFE, a high applied voltage of 350 V with maximum current of 80 mA was used, resulting in certain Joule heating [51][52][53]. Thus, the limit temperature was set at 14°C thanks to requirement of smooth flow in FFE chamber and maintain of lysozyme activity in accordance with the previous works [31,50].…”