Coalescence of Drops with Fully Retarded Surfaces in a Turbulent Emulsion Flow

Coalescence of Drops with Fully Retarded Surfaces in a Turbulent Emulsion Flow 

Consider the coalescence of drops with fiilly retarded (delayed) surfaces (which means they behave as rigid particles) in a developed turbulent flow of a lowconcentrated emulsion. We make the assumption that the size of drops is much smaller than the inner scale of turbulence R Ao), and that drops are non-deformed, and thus incapable of breakage. Under these conditions, and taking into account the hydrodynamic interaction of drops, the factor of mutual diffusion of drops is given by the expression (11.70). To determine the collision frequency of drops with radii Ri and Ri (Ri Ri), it is necessary to solve the diffusion equation (11.36) with boundary conditions (11.39). Place the origin of a spherical system of coordinates (r, 0,0) into the center of the larger particle of radius i i. If interaction forces between drops are spherically symmetrical, Eq. (11.36) with boundary conditions (11.39) assumes the form 

The diffusion flux of drops 2 toward the given drop 1 is determined by the relation (11.40), which in spherically symmetrical case is written as 

Here t = (ve/so) is the characteristic time scale in a turbulent flow with specific energy dissipation so, W — AnfiRlrio/ i is the volume concentration of drops of type 2 in the flow, C is the parameter whose value depends on the chosen model of drop coagulation in a turbulent flow. 

All of the above-mentioned works offer simple models of particle interaction, neglecting the hydrodynamic forces of resistance, which arise when particles approach each other and become especially noticeable at small clearance between particles. Also neglected are the forces of molecular interaction responsible for the coupling of particles at the collision stage. This is why the discrepancy between theoretical and experimental results for hydrosols is much greater than for aerosols. 

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Coalescence of Drops with Fully Retarded Surfaces in a Turbulent Emulsion Flow 431 The final result is ... 

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