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We developed a novel treatment for the problem of the diffusive collision dynamics of colloidal nano- and macromolecular-particles on the surface boundaries of mesopores. A theoretical and numerical model was intensively developed to treat a number of basic ingredients in the simulation algorithms, i) the Brownian motion, ii) hydrodynamic flow, and iii) molecular dynamics for the restitution of the nano-particles due to their diffusive collisions at the surface boundaries, These, and other ingredients for the numerical codes, are designed to calculate the PDF distributions for the colloidal particles, under equilibrium dynamics.Furthermore, we also deal with the mechanisms leading to the adhesion of these particles under different and sometimes conflicting influences of non-equilibrium conditions in the hydrodynamic flow, due to the diffusive collisions of the particles and to the attraction that Hamaker forces exercise on these particles when they are in neighborhood of surface.