Hydrodynamic Boundary Layers at Solid Wall—A Tool for Separation of Fine Solids

A theoretical study is performed about the hydrodynamic interaction of fine species entrapped in the boundary layer (BL) at solid wall (plate). The key starting point is the analysis of the disturbance introduced by solid spheres in the background fluid flow. For a neutrally buoyant entity, the type of interaction is determined by the size of the spheres as compared to the thickness of the BL region. The result is granulometric separation of the solids inside the BL domain at the wall. The most important result in view of potential applications concerns the so-called small particles Rp < L/ReL5/4 (ReL is the Reynolds number of the background flow and Rp is the radius of the entrapped sphere). In the case of non-neutrally buoyant particles, gravity interferes with the separation effect. Important factor in this case is the relative density of the solid species as compared to this of the fluid. In view of further practical uses, particles within the range of Δρ/ρ < Fr2/ReL1/2 (Fr is Froude number and Δρ/ρ is the relative density of the entrapped solids) are systematically studied. The trajectories inside the BL region of the captured species are calculated. The obtained data show that there are preferred regions along the wall where the fine solids are detained. The results are important for the assessment of the general efficiency of entrapment and segregation of fine species in the vicinity of solid walls and have high potential for further design of industrial separation processes.

DRAG COEFFICIENT OF A SOLID SPHERE UNDER NON-ISOTHERMAL CONDITIONS

The results of an experimental study of gravitational settling of a cooled (T = 82 K, 250 K) and a heated (T = 373 K, 473 K, 573 K) steel ball in glycerin and polymethylsiloxane liquids (PDMS-10000, PDMS-30000) in the range of the Reynolds numbers Re = 10−3–1 are presented. It is shown that the stationary velocity of gravitational settling of a particle decreases with its cooling and, conversely, it increases with heating of the particle. A time dependence of the distance traveled by the particle is found to be linear for both heated, cooled, and etalon (T = Tl) solid spheres. The effect of the difference in the particle and carrier medium temperatures on the drag coefficient of the solid sphere is analyzed. For the considered Reynolds numbers, it is revealed that the drag coefficient of a single solid sphere is determined by CD = a /Re , where a is the empirical coefficient depending on the ratio of the particle and liquid temperatures T = T /Tl . Using the regression analysis method, the expression for a drag coefficient of a solid particle under non-isothermal conditions at T >> 1 is found to be similar to the Hadamard –Rybczynski expression CD = 16/Re, which is obtained for a spherical bubble (or a drop). The empirical dependences of the drag coefficient for a cooled and a heated solid sphere on the difference in the particle and liquid temperatures δТ = 1− T are obtained.

Viscosity coefficients in nonideal liquid mixture

To calculate various heat and mass transfer processes, reliable data on the molecular momentum transfer coefficient are required, which should fit seamlessly in to the General algorithm for modeling and calculating various mass transfer processes and devices in the chemical and petrochemical industries in the form of unified programs. This approach is proposed in the description of the momentum transfer mechanism, which is implemented by generalizing the kinetic equations of the model of solid spheres of a system of dense media with the help of methods of the thermodynamics of irreversible processes for associated Prigogine solution model. This allows a more accurate description of the momentum transfer in nonideal solutions. Within the framework of this model, the expression of the collision therm in kinetic equations is refined, which significantly expands the boundaries of the theory’s application. A method for calculation activity coefficient is developed based on experimental data in the liquid-vapor system and the Wilson the equation. This will allow us to improve quantitatively the description of the phenomena of momentum transfer. A comparision was made between the calculated and experimental viscosity coefficients for a highly nonideal aceton-water solution, in which the activity coefficient varies on both components from 1 to 5 units. The average discrepancy between the data at different concentrations is 30%. At the sesame, the discrepancy between the coefficients, calculated according to the theory of solid spheres and experimental data reaches up to 10 times. When specifying the values of the activity coefficients and the interaction parameter between molecules the proposed method will improve the result.