Under the influence of an ac electric field, electrolytes on planar microelectrodes exhibit fluid flow. The nonuniform electric field generated by the electrodes interacts with the suspending fluid through a number of mechanisms, giving rise to body forces and fluid flow. This paper presents the detailed experimental measurements of the velocity of fluid flow on microelectrodes at frequencies below the charge relaxation frequency of the electrolyte. The velocity of latex tracer particles was measured as a function of applied signal frequency and potential, electrolyte conductivity, and position on the electrode surface. The data are discussed in terms of a linear model of ac electroosmosis: the interaction of the nonuniform ac field and the induced electrical double layer.

Frequency-dependent fluid flow in electrolytes on microelectrodes subjected to ac voltages has recently been reported. The fluid flow is predominant at frequencies of the order of the relaxation frequency of the electrodeelectrolyte system. The mechanism responsible for this motion has been termed ac electro-osmosis: a continuous flow driven by the interaction of the oscillating electric field and the charge at the diffuse double layer on the electrodes. This paper develops the basis of a theoretical approach to this problem using a linear double layer analysis. The theoretical results are compared with the experiments, and a good correlation is found.

Planar microelectrodes, used for the electrokinetic manipulation of particles, generate high strength AC electric fields, resulting not only in forces on the particles but also on the suspending fluid. Observations of electrolytes on microelectrode structures at applied signal frequencies of the order of 1 MHz have shown the importance of the illumination in generating fluid flow. In this paper, these experiments are analysed in terms of the theory of electrothermally induced fluid flow. Numerical calculations are made of the electric field, temperature field and fluid flow, arising both from Joule heating and from light heating. The results verify that Joule heating is not important under the experimental conditions. The temperature gradient generated by the light that is required in order to match the experimental fluid velocities is determined. #

Net flow of electrolyte induced by a traveling-wave electric potential applied to an array of microelectrodes is reported. Two fluid flow regimes have been observed: at small-voltage amplitudes the fluid flow follows the direction of the traveling wave, and at higher-voltage amplitudes the fluid flow is reversed. In both cases, the flow seems to be driven at the level of the electrodes. The experiments have been analyzed with a linear electroosmotic model based upon the Debye-Huckel theory of the double layer. The electrical problem for the experimental interdigitated electrode array is solved numerically using a truncated Fourier series. The observations at low voltages are in qualitative accordance with the electroosmotic model.

Electrothermal motion in an aqueous solution arises from the action of an electric field on inhomogeneities in the liquid induced by temperature gradients. The temperature field can be produced by the applied electric field through Joule heating, or caused by external sources, such as strong illumination. Electrothermal flows in microsystems are usually observed at applied signal frequencies around 1 MHz and voltages around 10 V. In this work, we present self-similar solutions for the motion of an aqueous solution in a constant temperature gradient placed on top of: (a) two coplanar electrodes subjected to an a.c. potential difference, and (b) four coplanar electrodes subjected to a four-phase a.c. signal, generating a rotating field. The first case produces two-dimensional rolls whereas the second case produces a liquid whirl. Finally, we present experimental results of electrothermal liquid flows generated by alternating and rotating electric fields under strong illumination, and these experiments are compared to the analytical solutions. The induced rotating flow could be used in the mixing of analytes and of liquids in microsystems.

Abstract. The electrokinetic manipulation of particles suspended in a fluid medium is accomplished using microelectrodes that generate non-uniform fields of significant strength from low applied potentials. The high strength fields produce not only forces on the particles but also on the fluid medium used for suspension. This paper presents qualitative and semi-quantitative observations of the movement of the fluid at applied field frequencies of the order of 1MHz and higher. The importance of the illumination in generating the fluid flow is described, the flow depending on both the intensity of illumination and the applied electric field. The theory of electrothermally induced fluid flow is briefly described and compared with the experimental observations. Reasonable agreement is found between the experiments and the theory, with the light generating temperature gradients, and therefore gradients in fluid permittivity and conductivity, and the electric field responsible for the motive force.(Some figures in this article appear in colour in the electronic version; see www.iop.org)Microelectrode structures, such as those used for dielectrophoresis (DEP) [1], generate high strength, non-uniform ac electric fields. Microelectrodes have been used for the dielectrophoretic manipulation of particles in solution over a range of sizes, from cells (∼10 µm diameter) down to viruses (∼100 nm diameter) [2][3][4][5]. However, the strong electric fields can also interact with the suspending fluid medium, to produce forces on the fluid and hence flow. The study of this interaction is referred to as electrohydrodynamics (EHD) [6][7][8].There are a number of mechanisms through which an electric field can interact with a fluid to produce a force. Recently, we reported a new type of fluid flow occurring in microelectrodes at frequencies below 100 kHz [9][10][11] arising from the interaction of the non-uniform field and the induced charges in the electrical double layer at the electrode-solution interface. This flow, referred to as ac electro-osmosis, is not fully understood and has been characterized and discussed in other publications [9][10][11].This communication is concerned with fluid flow patterns observed in microelectrodes at frequencies around 1 MHz and above [5], where electrode polarization and ac electro-osmosis are negligible. The mechanism has been § Corresponding author. postulated to be electrothermal [7], where the electric field acts on gradients in permittivity and conductivity produced by non-uniform heating of the fluid [6]. For small changes in temperature, where the relative increments in permittivity ε/ε and conductivity σ/σ are much smaller than 1, the force on the fluid per unit volume is [7]:(1) where E is the applied electric field and i = √ −1. The first term on the right-hand side represents the Coulomb force and the second the dielectric force. The gradients of the permittivity and conductivity are related to the temperature gradient by the expressions, ∇ε = (∂ε/∂T )∇T and ∇σ = (∂σ/∂T )∇T . The volum...

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a b s t r a c tWe study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to obtain lower and upper bounds on that maximum, and exact computations when restricting to some specific families of graphs. Our approach requires very diverse tools and connections with well-known objects in graph theory; among them: a classical result in graph domination by Ore, a Ramsey-type result by Erd} os and Szekeres, a polynomial time algorithm to compute distinguishing sets and determining sets of twin-free graphs, k-dominating sets, and matchings.