The paper deals with the derivation of governing propagation equations of nonlinear waves in thin liquid films applying to two basic cases, namely for the perfect fluid flow with a weak mass source at the bottom and for the thin film of viscid liquid flow with a mass source and surface activity at the free moving boundary. The second case is considered on the example of a condensate film flow under the low heat transfer intensity. The conditions under which the model equation has the left-hand side of a type of the Korteweg-deVries equation with slowly evolved parameters, and perturbed right-hand side have been established for the both cases. The conditions under which the solitary wave solutions are possible have been defined too.
Abstract. Until the present time, modeling of the pores form influence on the hydraulic resistance of membranes and their permeability has not been analyzed. The present study suggests the determination of the optimum form of pores and the thorough consideration of the issue on the productivity of polymer membranes with the profile pores.
The calculation of the characteristics of the selectivity in the membrane separation of mixtures, based on basic physicochemical characteristics of the solution, is a difficult task due to the large number of influencing factors. To solve this problem, for a theoretical evaluation of the selectivity of ultrafiltration membranes, modern distributed algorithms are used for a probabilistic approach, in which the mechanism of the separation process differs significantly from the separation mechanism in nanomembranes. As a result of the proposed models and modern distributed algorithms, estimates of the selectivity of nanofiltration membranes for individual ions were obtained. It was found that an important feature of mixing with the mixture flowing through the membrane is the dependence of the effective diffusion coefficient on time. Also, as a result of calculations by the proposed model, it was found that this feature is modeled by the coefficient of anomalous fractal diffusion in time, as well as by the displacement of the effective separation zone in the membrane.
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