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The dynamic effect of an electric field on dielectric liquids is called liquid dielec-trophoresis. It is widely used in several industrial and scientific applications, includ-ing inkjet printing, micro-fabrication and optical devices. Numerical simulations ofliquid-dielectrophoresis are necessary to understand the fundamental physics of thephenomenon, but also to explore situations that might be difficult or expensive to im-plement experimentally. However, such modelling is challenging, as one needs to solvethe electrostatic and fluid dynamics equations simultaneously. Here, we formulate anew lattice-Boltzmann method capable of modelling the dynamics of immiscible dielec-tric fluids coupled with electric fields within a single framework, thus eliminating theneed of using separate algorithms to solve the electrostatic and fluid dynamics equa-tions. We validate the numerical method by comparing it with analytical solutions andpreviously reported experimental results. Beyond the benchmarking of the method, we study the spreading of a droplet using a dielectrowetting setup and quantify the mecha-nism driving the variation of the apparent contact angle of the droplet with the appliedvoltage. Our method provides a useful tool to study liquid-dielectrophoresis and can beused to model dielectric fluids in general, such as liquid-liquid and liquid-gas systems.
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