On the effect of electrostatic surface forces on dielectric falling films

Abstract

Abstract

Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

“…Therefore, the increase in values of the electric field increases the amplitude of the interfacial waves, and this amplitude is directly proportional to the thickness of liquid film. This results in an agreement with the study of Di Marco & Grassi [33] and Rohlfs et al [31] for a flat horizontal gas-liquid interfaces subjected to gravity and electric fields. Using the continuity equation ( 12) together with the no-slip boundary condition on w, one can replace w everywhere by w − h 0 ∂ x udz and the streamwise velocity component u which, according to the concept of the WIBL method, is replaced by separation of variables as an expansion taken in the form u j a j (x, t) f j (z/ h), (21) where the expansion coefficients a j (x, t) and test functions f j (z/ h) are assumed to be slowly varying functions of time t and the streamwise coordinate x.…”

“…In the absence of electrostatic force, the evolution equation ( 23) is reduced to the model of Samanta [29] but with Shkadov scales. Also, the model of Rohlfs et al [31] is obtained in the limit τ 0. The electrostatic force corresponding to a negative gravitational force at ζ −E and χ 0.…”

“…For the constant dielectric permittivity in each phase, the electric force will take values at the phase boundary only. It means that this force will be rewritten as a surface force (Zakaria & Sirwah [30] and Rohlfs et al [31]). The electric field Ēi ∇ ψi (i 1, 2) can be analytically determined based on the Laplace equation…”

“…Up to a first-order approximation for boundary conditions of the normal electric field, the solutions of the Laplace equations are(Rohlfs et al [31]):…”

Spanwise structuring and rivulet formation in suspended falling liquid films

“…In the special case of a film flow on the underside of a substrate (suspended film) with sufficient inclination from the vertical, dripping, i.e., fluid detachment from the substrate, might occur [9][10][11]. The fluid dynamical instability associated with dripping is the Rayleigh-Taylor (RT) instability [12][13][14], which arises if a denser fluid (film) is accelerated towards a less dense fluid (ambient gas), for example, through gravitational acceleration [15] or centrifugal acceleration [16] or even through electric forces [17]. Reinforcement or prevention of dripping is of significant importance in many engineering situations.…”