Segregation of penetrable soft spheres under gravity: Mean-field approach

We study the segregation of the additive and non-additive soft-sphere mixtures, which have the purely repulsive interactions, on the relative range of temperature, the cross-interaction between unlike species, the buoyant mass, and the layer numbers. The results show that the most segregation is found at m2/m1 = 1 and a low temperature, where mi is the mass of species i. The crossover point corresponding to the mixing phase is shifted toward a large mass ratio with increasing the temperature. For the non-additive soft sphere mixture, the crossover point is shifted toward a small mass ratio with increasing the cross-interaction between unlike species. The increase of gravitational strength drives the larger particles sinking to the bottom. The pressure at height z has been calculated from the force balance on a slab of fluids adjacent to the wall. The pressure at the bottom decreases with decreasing the temperature, whereas the pressure at a high altitude increases because of the large particles at the top. For the mixing phase, the large pressure discontinuity is found at z = σ1 because of the density difference between two particles. Through this work, we show that the center of mass of the species, < zi >, is a proper factor for studying the particle segregation.