Search Results (3)

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation. Full article

In recent years, the number of adverse and dangerous natural and anthropogenic phenomena has increased in coastal zones around the world. The development of mathematical modeling methods allows us to increase the accuracy of the study of hydrodynamic processes and the prediction of extreme events. This article discusses the application of the modified Upwind Leapfrog scheme to the numerical solution of hydrodynamics and convection–diffusion problems. To improve the accuracy of solving the tasks in the field of complex shapes, the method of filling cells is used. Numerical experiments have been carried out to simulate the flow of a viscous liquid and the transfer of substances using a linear combination of Upwind and Standard Leapfrog difference schemes. It is shown that the application of the methods proposed in the article allows us to reduce the approximation error in comparison with standard schemes in the case of large grid numbers of Péclet and to increase the smoothness of the solution accuracy at the boundary. The soil dumping and suspended matter propagation problems are solved using the developed schemes. Full article

Increased influence of abiotic and anthropogenic factors on the ecological state of coastal systems leads to uncontrollable changes in the overall ecosystem. This paper considers the crucial problem of studying the effect of an increase in the water’s salinity in the Azov Sea and the Taganrog Bay on hydrobiological processes. The main aim of the research is the diagnostic and predictive modeling of the geographic dynamics of the general phytoplankton populations. A mathematical model that describes the dynamics of three types of phytoplankton is proposed, considering the influence of salinity and nutrients on algae development. Discretization is carried out based on a linear combination of Upwind Leapfrog difference schemes and a central difference scheme, which makes it possible to increase the accuracy of solving the biological kinetics problem at large values of the grid Péclet number (Pe_h > 2). A software package has been developed that implements interrelated models of hydrodynamics and biogeochemical cycles. A modified alternating-triangular method was used to solve large-dimensional systems of linear algebraic equations (SLAE). Based on the scenario approach, several numerical experiments were carried out to simulate the dynamics of the main species of phytoplankton populations at different levels of water salinity in coastal systems. It is shown that with an increase in the salinity of waters, the habitats of phytoplankton populations shift, and marine species invasively replace freshwater species of algae. Full article