SONE PROBLEMS ON VISCOUS POTENTIAL FLOW ANALYSIS OF CAPILLARY INSTABILITY

Abstract

Viscous potential flow analysis is a new idea to deal with stability problems, as it includes viscous effects unlike the inviscid potential theory. Tangential stresses are not considered in viscous potential theory and viscosity enters through normal stress balance. The phenomenon of heat and mass transfer across the interface occurs in situations like film boiling of fluids. The externally imposed fields (electric or magnetic) are used as a controller of the system admitting heat and mass transfer. Viscous potential flow analysis of capillary instability problem with heat and mass transfer in the presence of external fields in the frame work of linear theory have not been considered in earlier studies. So it is important to study effect of heat and mass transfer in capillary instability through viscous potential theory. Hence "Viscous Potential Flow Analysis of Some Problems on Capillary Instability" admitting heat and mass transfer through the interface is studied in this thesis in general. The chapter wise summary of the thesis is as follows: Chapter 1 consists of introduction to the general stability theory, the capillary instability, viscous potential theory, some definitions and basic equations involved in the present work. A brief account of the related studies made by various authors in the field and a summary of the thesis are presented. In Chapter 2, viscous potential flow analysis of capillary instability with heat and mass transfer in the presence of an axial electric field has been made successfully. The effect of gravity and free surface charges at the interface is neglected. A dispersion relation is derived and stability is discussed theoretically and numerically. The effect of electric field and heat and mass transfer on growth rates is observed. Various neutral curves have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, on the stability of the system. A comparison has been made between the results of present study with the results obtained by Moatimid [122] for inviscid fluids. In Chapter 3, viscous potential flow analysis of capillary instability with heat and mass transfer in the presence of radial electric field has been carried out. Both the fluids are taken as conducting and viscous with different kinematic viscosities. A dispersion relation is derived for the case of radially imposed electric field and stability is discussed in terms of various parameters such as Ohnesorge number, heat transfer capillary number and etc. A comparison has been made between the results of present study with the results obtained in chapter 2 in the presence of an axial electric field. In Chapter 4, viscous potential theory is applied to the capillary instability problem of conducting viscous fluids with heat and mass transfer in the presence of an axial electric field. The effect of gravity is neglected but effect of free surface charges at the interface is taken into account. Both axisymmetric and asymmetric disturbances are considered and a dispersion relation which accounts for the growth of the disturbances is derived. Various stability diagrams have been drawn to show the effect of various physical parameters such as wave number, viscosity, electrical conductivities of fluids, heat and mass transfer coefficient, on the stability of the system. Finally a comparison has been made between the results of present study with the results obtained by El-Sayed et al. [57] for inviscid fluids. In ChapTi 5, viscous potential- theory is applied to investigate the eapillary instability of conducting viscous fluids with heat and mass transfer in the presence of radial electric field taking the effect of free surface charge at the interface into consideration. The stability of the system is insured when three conditions on electric field are satisfied. A detail analysis in terms of physical parameters such as viscosity, electrical conductivities of fluids, and heat and mass transfer coefficient has been made. Finally a comparison has been made between the results of present study with the results obtained in chapter 4 for viscous fluids in an axial electric field. In Chapter 6, viscous potential flow analysis of capillary instability with heat and mass transfer has been carried out in presence of an axial magnetic field in absence of gravity. A dispersion relation is derived and stability is discussed theoretically as well as numerically. Finally a comparison has been made between the results of present study with the results obtained by Elhefnawy and Radwan [45] for a system of inviscid fluids. In Chapter 7, an attempt has been made to apply VPF theory to capillary instability problem when the inner fluid is viscoelastic in the cylindrical annulus in the presence of an axial electric field. A dispersion relation is derived for axisymmetric disturbances. The stability conditions for the system are obtained by applying Routh Hurwitz criterion. Various stability diagrams have been drawn to depict the effect of various parameters on the stability of the system. Finally in Chapter 8, based on present study, conclusions are drawn and future research work in this direction is suggested. ii