Proceedings of IMECE2003 2003 ASME International Mechanical Engineering Congress and RD&D Expo November 15-21, 2003, Washington, D.C. USA IMECE2003-43272 ELECTROTHERMAL LIQUID MOTION IN MICROSYSTEMS SUBJECTED TO ALTERNATING AND ROTATING ELECTRIC FIELDS Antonio Gonz ´ alez Dpto. F´ ısica Aplicada III Universidad de Sevilla 41092 Sevilla (SPAIN) Email: gonfer@esi.us.es Antonio Ramos ∗ Dpto. E. y Electromagnetismo Universidad de Sevilla 41012 Sevilla, (SPAIN) Email: ramos@us.es Antonio Castellanos Dpto. E. y Electromagnetismo Universidad de Sevilla 41012 Sevilla, (SPAIN) Email: castella@us.es Hywel Morgan Dpt. Electronics and Electrical Engineering, Univ. of Glasgow, Glasgow GL12 8LT, UK. Email: hywel@elec.gla.ac.uk Nicolas G. Green Dpt. Electronics and Electrical Engineering, Univ. of Glasgow, Glasgow GL12 8LT, UK. Email: n.green@elec.gla.ac.uk ABSTRACT Electrothermal motion in an aqueous solution appears when an electric field is coupled with thermally-induced gradients of conductivity and permittivity in the fluid. The temperature field can be produced by external sources, such as strong illumina- tion, or caused by the applied electric field through Joule heat- ing. Electrothermal flow in microsystems is usually important at frequencies around 1 MHz and voltages around 10 V. In this work, we consider first the two-dimensional problem of an aque- ous solution placed on top of two co-planar electrodes that are subjected to an ac potential difference when there is either a ver- tical or horizontal temperature gradient. Secondly, we study the three-dimensional problem of an aqueous solution lying on four co-planar electrodes which produce a rotating field. This electric field when combined with a vertical temperature gradient rotates the liquid. The resulting electric field and liquid motion in these problems are characterised using self-similar solutions. Finally, these analytical solutions are compared with numerical and ex- perimental results. ∗ Address all correspondence to this author. INTRODUCTION Flows of electrothermal origin often appear in the manip- ulation of colloidal particles by means of ac electric fields in microsystems [1–4]. Electrothermal fluid flow is due to the cou- pling of an electric field with thermally-induced gradients of con- ductivity and permittivity in the fluid. The temperature field can be produced by external sources, such as strong illumination [3], or caused by the applied electric field through Joule heating. Ob- servations show that the electrothermal effect is important in mi- crosystems for frequencies of the order of 1 MHz and voltages of the order of 10 V. In this work, we present some analytical solutions for the fluid flow induced by electric fields coupled with externally im- posed gradients of temperature in microelectrode structures. We consider first the two-dimensional problem of an aqueous solu- tion placed on top of two co-planar electrodes with parallel edges that are subjected to an ac potential difference when there is ei- ther a vertical or a horizontal gradient of temperature. The re- sulting electric field and liquid motion are characterised using self-similar solutions. These solutions are relevant to some fluid flows observed under strong illumination [4]. Secondly, we study the three-dimensional problem of an aqueous solution lying on 1 Copyright c  2003 by ASME