The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer |
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| Institution: | 1. Department of Applied Sciences, University of the West of England, Bristol BS16 1QY, UK;2. School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK;1. División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, col. Vicentina, 09340 Mexico, Mexico;2. Instituto Mexicano del Petróleo, Eje Central Lázaro Cardenas no 152, Apartado Postal 14-805 07730 México, D.F., Mexico;3. Laboratoire EM2C, UPR-CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, Cedex, France;1. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, 721302, India;2. Indian Register of Shipping, Adi Shankaracharya Marg, Opp. Powai Lake, Powai, Mumbai, 400 072, India |
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| Abstract: | The effect of vertical vibration on the onset of Marangoni convection in a horizontal layer of a viscous incompressible uniform liquid with a free surface and a hard (solid) or soft (impermeable and stress-free) wall is investigated. In the case of harmonic vibration, a dispersion relation is constructed in explicit form using continued fractions. From this, equations are obtained for determining the critical values of the parameters for all three main types of loss of stability. Neutral curves of the monotonic and oscillatory instability are constructed, for fixed frequency and amplitude of the vibration, in the form of a graph of the Marangoni number against the wave number. The regions of parametric resonances, corresponding to synchronous and subharmonic modes are determined. The frequency values for which a high-frequency asymptotic form is reached are obtained. The long-wave Marangoni oscillatory instability is investigated, and it is shown that in this case the Marangoni numbers are negative and depend only on the Prandtl and Biot numbers. |
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