Interdisciplinary Applied Mathematics

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18.3 Compact Model for Electrowetting

In Chapter 8, we discussed electrowetting and the associated physical phenomena. Here we revisit electrowetting and discuss a compact model. Figure 18.26(a) shows the equivalent circuit diagram for the liquid-drop-dielectric solid system. Here ф is the electrical potential inside the drop, and pi and ps are the resistivities of the liquid and solid, respectively. The total impedence for the circuit diagram shown in Figure 18.26 is (Shapiro et al., 2003a)



where s is the Laplace variable. For a sinusoidal signal V(t) = V cos(wt) of frequency u>, s    is    taken as s =    iu>.    The voltage    drop    across    the    solid    Vioi(s)

is given by

In the steady state (i.e., s = ш ^ 0), the voltage and energy stored in the dielectric are

where V is the applied DC voltage. The dependence shown in equation (18.17) is similar to the energy in the perfectly insulating solid; Ede(R, 9) =

^    7ГR2 sin29, except for the new Riq/Rao term. Hence, the resistance

of the liquid drop Riq is shape-dependent. This dependence of resistance on the droplet shape gives rise to contact angle saturation in this model, see (Shapiro et al.,    2003a;    Shapiro    et    al.,    2003b),    for    more    details.    The corre

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