Dynamics of a liquid film on a porous layer under the action of electric force
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Dynamics of a liquid film on a porous layer under the action of electric force Kadry Zakaria1,a , Magdy A. Sirwah1,b , Ahmed Assaf2,c 1 Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt 2 Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt
Received: 16 December 2019 / Accepted: 27 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The motion of a Newtonian conducting liquid film is studied under the influence of a uniform voltage in a channel past a Darcy–Brinkman layer. The Benney equation of the considered system is derived under a weak inclination assumption. The stability criteria of the linearized system are investigated. Numerical solutions for the Benney equation are achieved with varying some physical properties. The results showed the rise of stability areas in the linearly unstable region and instability ones in the linearly unstable zone as well as and the dissimilarity between the effect of some parameters in certain situations from that expected by linear theory; namely the linear approach becomes no longer sufficient to accurately describe the nonlinear problem. The above results can be utilized by designing a device to control the system stability and obtain the optimum conditions.
1 Introduction Many of the surfaces on which a fluid flows in the food, chemical, energy, biochemical, environmental and pharmaceutical applications are permeable or rough. The fluid–porous interface exists in applications involves permeable or rough substrates [1] on which fluid drops or layers extend then it is imbibed. Sometimes we need the liquid-film motion to be unstable such as liquids cooling [2] while in other cases, the stability is required as in coating process where the flat interface is requested. Such reasons motivated the appearance of empirical, analytical and numerical investigations such as [3–8], respectively, which discussed the film dynamics over permeable mediums. The aim of such studies is to obtain a mechanism in order to adjust the onset of instability by means of a certain physical property. Tomlin et al. [8] concluded that hanging liquid films can be stabilized by a tangential electric field of sufficient strength while a normal field leads to the model instability. Anjalaiah et al [2] expected the existence of insoluble surfactants still has a stable effect on the film dynamics even if it moves on a porous surface. In the case of uniform heating [9,10] the effect of thermocapillary convection is unstable, while linearly variable heating plays a stable or unstable role depending on the value of the Prandtl number used in the model [11]. In fact, the continuity of tangential speed (no-slip) and normal one (no-penetration) restrictions are
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:699
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