Accurate low-order modeling of electrified falling films at moderate Reynolds number

On the effect of electrostatic surface forces on dielectric falling films

“…The good agreement is achieved due to SMICFoam (Rohlfs et al 2017), which uses a limiter of artificial interface compression. The model of reduced dimensionality is closely related to WIBL models developed by Wray et al (2017) with the first-order formulations of the electrostatic forces and zero surface charges. Contrary to the leaky dielectric case studied by Wray et al (2017), the surface forces acting on a perfectly dielectric liquid are always of destabilizing character.…”

“…Note, it is shown later in comparison to full numerical simulations that the first-order approximation is well suited to describing the effect of the electric field. For higher-order approximations of the electric field, also taking into account tangential stresses and surface charges, the reader is referred to the work of Wray et al (2017). Figure 1 illustrates the one-dimensional case where a liquid column with heighth is located between two capacitor plates of distanceH c .…”

“…A recent review on the different model approaches is provided by Papageorgiou (2019). For leaky dielectric films exposed to an electric field normal to the substrate, a two-and three-dimensional weighted residuals integral boundary-layer (WIBL) model was developed by Wray, Matar & Papageorgiou (2017). The model developed and applied in the present study is closely related to the models of Wray et al utilizing first-order electrostatic effects only and omitting the free charges at the interface which are not present in a perfectly dielectric liquid.…”

Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

“…The regularising effect of dispersion for the non-electrified gKS equation was analysed in detailed by Chang et al (1995) and . Recently Wray et al (2017) have derived a fully nonlinear model for an electrified falling film which is valid at finite Reynolds number using a weighted residuals approach. We note that most previous studies have focused on acute inclination angles.…”

Reduced-order modelling of thick inertial flows around rotating cylinders

“…Explicit computation of the a n (and their corresponding basis functions) A. W. Wray and R. Cimpeanu can be avoided by a suitable choice of weighting function w. This weight is the solution of the adjoint of the leading-order problem, and hence depends on the problem being solved, including its geometry (Ruyer-Quil et al 2008). For viscous flow on a rotating disk, this weight is (Wray et al 2017b)…”