A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops

Abstract

We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate interacting 3D drops (no axisymmetric simplification) in close proximity, can consider different viscosities, is adaptive in time and able to handle substantial drop deformation. For each drop global representations of the variables based on spherical harmonics expansions are used and the spectral accuracy is achieved by designing specific numerical tools: a specialized quadrature method for the singular and nearly singular integrals that appear in the formulation, a general preconditioner for the implicit treatment of the surfactant diffusion and a reparametrization procedure able to ensure a high-quality representation of the drops also under deformation. Our numerical method is validated against theoretical, numerical and experimental results available in the literature, as well as a new second-order theory developed for a surfactant-laden drop placed in a quadrupole electric field.

An accurate integral equation method for Stokes flow with piecewise smooth boundaries

“…Future work could include extending this model to three dimensions. A boundary integral method for three-dimensional drops in free space has been developed [37,38]. In three dimensions Lipschitz domains admit both corners and edges, so the RCIP algorithm described in Sect.…”

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

“…The high voltage is supplied across the electrodes and dynamics are captured by using cameras. In these studies, some authors have also introduced surfactants at the liquid-liquid interface [ 27 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 ]. A summary of the most prominent works related to droplet EHD are summarized in Table 1 .…”

“…The influence of interfacial properties on the droplet deformation and breakup under an electric field has also been a topic of profound interest for decades [ 27 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 ]. The surface-active molecules prompt to change in the interracial and rheological properties, leading to interfacial perturbations and breakups [ 23 , 71 , 136 , 137 , 138 ].…”

Numerical-asymptotic models for the manipulation of viscous films via dielectrophoresis

“…Related work on the simulation of electrified fluid droplets and liquid bridges has been carried out using a range of techniques including asymptotic approaches (Yeo & Chang 2006), level set methods (Walker & Shapiro 2006), finite element approaches for coupled fluid flow and dynamic interface models (Falk & Walker 2013) and boundary integral methods for coupled potential and dynamic interface problems (Volkov, Papageorgiou & Petropoulos 2005; Sorgentone, Tornberg & Vlahovska 2019). A number of researchers have proposed nonlinear long-wave asymptotic theories for two-fluid systems, where one fluid region is assumed to be slender and the other region has an electric field applied; see, for example Papageorgiou, Maldarelli & Rumschitzki (1990) and Kalogirou et al.…”