General Theoretical Description of Dissipative Structures

Disruption of hydrodynamical stability may take place either as a result of local fluctuations in volume properties of a continuous medium (viscosity or density) or due to disturbances introduced into the boundary conditions. A general equation system for the differential balance of forces can be written as  

The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids Editor V. E. Kazarinov Springer-Verlag Berlin, Heidelberg 1987 

In these expressions n is the dynamic viscosity of a liquid, 6 is a dielectric permeability, E,- and are the electric field intensity components. These components in principle cannot be obtained from Eqs. (l)-(2) to determine them it is necessary to use the Maxwell equation  

For instability appearance analysis it is essential not only to develop the main equations of transfer but to formulate boundary conditions, because dissipative structures appear more frequently near phase boundaries and may be caused by fluctuations of boundary conditions. It is of great practical interest to investigate the role of capillary [5] and electrosurface [6] forces in inducing the instability of mobile phase boundaries. That is the reason for determining boundary conditions for the transfer equation system characterizing the interface of two mobile media (liquid-gas or liquid-liquid). Let be the radius-vector drawn from any fixed space point to another on the phase boundary and n a unit vector normal to the interface and directed towards the interior of phase 1 (the second phase would be written as phase 2). The tangential unit vector at the interfacial surface would be t. Then conjugation conditions for velocities, temperatures, concentrations and electric fields at the interface would be  

Equations (10) and (11) describe a continuous velocity field at the phase boundary Eqs. (12) and (13) formulate the normal and tangential force balance (where a is the surface tension, and R2 the principal surface curvature radii, the 

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