Electrohydrostatics of capillary switches

Abstract

A capillary switch is a system of two liquid drops, one sessile and the other pendant, obtained by overfilling a hole of radius R in a plate. When surface tension dominates gravity, the equilibrium shapes of the drops are spherical sections of equal radii. If the combined volume of the top V T and bottom V B drops exceeds 4pR 3 =3, the system has three equilibrium states of which two are stable. This bistability is exploited in applications by toggling the system between its two stable states. Here, we examine the effectiveness of using an electric field for toggling. Bifurcation diagrams are obtained that depict how the system's response varies with applied field strength E, and show loss of stability at turning points and the possibility of hysteresis. A phase diagram in E2ðV T 1V B Þ space is presented to readily infer when an electric field is an effective means for toggling.

Oscillations of a ring-constrained charged drop

“…These extensions are all based on exploiting the equilibria and stability of DDSs in the absence (Hirsa et al. 2005) and presence of electric fields (Sambath & Basaran 2014). The equilibrium shape of a DDS consists of two identical subhemispherical drops when the combined volume of the two drops is smaller than that of a sphere of the same radius as the hole in the associated solid substrate (figure 1).…”

“…Many applications of DDSs are based on toggling the system between the state where the top drop is large and the bottom drop is small and that where the top drop is small and the bottom drop is large. Sambath & Basaran (2014) have theoretically analysed the equilibrium states and stability of electrified DDSs and how electric fields can be used to toggle the system between its equilibrium states. The latter work can be extended by coupling net charge on the drops with an applied electric field for improved control.…”

Electrohydrodynamics of lenticular drops and equatorial streaming

“…The steady-state version of the algorithm reduces to that used by Wagoner et al (2020). Further details on the algorithm can be found in publications where similar versions and/or certain portions of the algorithm employed here are described and which have been used for solving equilibrium (Basaran & Scriven 1990;Sambath & Basaran 2014), steady state (Basaran & Scriven 1988;Wagoner et al 2020) and transient (Collins et al 2008(Collins et al , 2013 problems in EHD. In all simulations, Pe = 10 3 (Collins et al 2008(Collins et al , 2013.…”

Electric-field-induced transitions from spherical to discocyte and lens-shaped drops

“…Far from the drop's centre-of-mass, the electric potential is set to asymptotically approach that of a uniform field and the flow field is taken to be stress-free. Similar versions of the algorithm employed here have been used for solving equilibrium (Basaran & Scriven 1990;Sambath & Basaran 2014), steady-state (Basaran & Scriven 1988) and transient (Collins et al 2013) problems in EHD. The algorithm relies on elliptic mesh generation (Christodoulou & Scriven 1992) and continuation with adaptive parameterization (Abbott 1978) to determine steady-state solution families (Feng & Basaran 1994), and automatically detects points where changes of stability occur (Brown & Scriven 1980;Ungar & Brown 1982;Yamaguchi, Chang & Brown 1984).…”

“…Far from the drop's centre-of-mass, the electric potential is set to asymptotically approach that of a uniform field and the flow field is taken to be stress-free. Similar versions of the algorithm employed here have been used for solving equilibrium (Basaran & Scriven 1990; Sambath & Basaran 2014), steady-state (Basaran & Scriven 1988) and transient (Collins et al. 2013) problems in EHD.…”