A mathematical model considering mass and momentum transfer was developed for simulation of ethanol dewatering via pervaporation process. The process involves removal of water from a water/ethanol liquid mixture using a dense polymeric membrane. The model domain was divided into two compartments including feed and membrane. For a description of water transport in ...

The Maxwell equations contain a dielectric permittivity e that describes the particular media. For homogeneous materials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between...

We present a numerical method to solve the Vlasov–Maxwell equations for spin-1/2 particles, in semiclassical approximation where orbital motion is treated classically while spin variable fully quantum. Unlike spinless case, phase-space distribution function $2\times 2$ matrix, which can also be represented, Pauli basis, as one scalar $f_0$ and three-component vector $\boldsymbol f$ . The relati...