Joule heating induced interfacial instabilities in free-surface electro-osmotic flows

Application of an external electrostatic field across a conducting electrolyte results in the development of a thermal gradient within the fluid domain as a consequence of the heat generated due to Joule heating. The generalized Gouy-Chapman theory for symmetric electrolytes is used to explain the explicit dependence of the electrical potential and velocity distribution on this differential temperature distribution within the fluid. Subsequently the highly coupled system of Orr-Sommerfeld equations is solved using a Chebyshev collocation algorithm to perform a linear stability analysis of the free-surface electro-osmotic flow system of a conducting electrolyte. An extensive parametric study, consisted with the electrokinetic and thermal properties of the electrolyte as well as the applied field strength characteristics, is performed. In particular, the role of the two important dimensionless parameters representing the applied field strength and the electrical conductivity of the fluid in regulating the length and time scales of instability occurring at the free liquid-air interface is summarized in this study, as well as their combined influence on the inception and growth of the interfacial mode of instability.