A two-dimensional two-phase lattice-Boltzmann model is presented and used for the study of interfacial phenomena under static and flow conditions. The model is based on the nonideal lattice-Boltzmann model proposed originally by Swift, Osborn, and Yeomans [Phys. Rev. Lett. 75, 830 (1995)] and makes it possible to couple a prescribed equation of state with the pressure tensor at the interface and the excess free-energy density formalism. The characteristic feature of the present model is that Galilean invariance is restored in the presence of interfaces without sacrificing any of the merits of the original model and, hence, the Navier-Stokes equation is adequately (to second order) recovered. The fluid properties can be prescribed in a thermodynamically consistent manner, which remains accurate at states close to the critical point. The model is first validated through static equilibrium tests and then applied to flow systems. It is shown that the simulator can reproduce some known two-phase flow configurations, like the motion of deformable droplets under the action of an external flow field. The simulator can also capture some interesting events during jet breakup and can be useful for the parametric study of the process in the two-dimensional case.

Monte Carlo computations of transmission probabilities of test molecules and the mean-square displacement of a large number of molecules in finite pore network samples are used to compute effective Knudsen diffusivities in two- and three-dimensional parallel random pore structures (consisting of two or three mutually perpendicular bundles of parallel capillaries), and in structures of randomly oriented pores. The orientationally averaged effective diffusivities, which are obtained either directly from the mean-square displacement method or indirectly by orientational averaging of the transmission probability results, are found to be practically independent of the orientational distribution of the pores, that is, of whether the pores are randomly distributed or grouped into one, two or three bundles of parallel capillaries, in the major part of the porosity range.

The problem of potential flow inside an evaporating liquid line, shaped as an infinitely long cylindrical segment lying on a flat surface, is considered and an analytical solution is obtained for any contact angle in $(0,\pi )$. In this way, microflow details inside linear liquid bodies evaporating on hydrophilic, hydrophobic, and strongly hydrophobic substrates can now be obtained. The mathematical formulation employs the velocity potential and stream function formulations in bipolar coordinates and the solution is obtained using the technique of Fourier transform. Both pinned and depinned contact lines are considered. The solution is applicable to any evaporation mechanism but for illustration purposes numerical results are presented here for the particular case of kinetically controlled evaporation. For hydrophilic substrates, the flow inside the evaporating liquid line is directed towards the edges for pinned contact lines, thus, promoting a coffee stain effect. The opposite flow direction is observed for depinned contact lines. However, for strongly hydrophobic substrates, flow is directed outwards for both pinned and depinned contact lines, but owing to its low magnitude compared to that on hydrophilic substrates, a craterlike colloidal deposit should be expected rather than a ringlike deposit, in agreement with experimental observations.