Capillary penetration of a wetting liquid in a microtomographic image of paper board, whose linear dimension was close to the average length of wood fibers, was simulated by the lattice-Boltzmann method. In spite of the size of the system not being large with respect to the size of structural inhomogeneities in the sample, for unidirectional penetration the simulated behavior was described well by that of the Lucas-Washburn equation, while for radial penetration a radial capillary equation described the behavior. In both cases the average penetration depth of the liquid front as a function of time followed a power law over many orders of magnitude. Capillary penetration of small droplets of liquid was also simulated in the same three-dimensional image of paper. In this case the simulation results could be described by a generalized form of the radial-penetration equation.

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The behaviour of liquid droplets on inclined heterogeneous surfaces was simulated by the lattice-Boltzmann method using the Shan-Chen multiphase model. The effect of topography of the surface on the contact angle hysteresis was investigated. It is shown in particular, by using anisotropic rough surfaces, how surface topography and thereby the continuity of the three-phase contact line, affect this hysteresis. Our results clearly indicate that the superhydrophobicity of a surface cannot be judged by the contact angle alone.

A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the characteristic cluster size deduced from the kinetic clustering model. For Re(p) approximately 1, clustering is maximal, but the simple kinetic model becomes inapplicable presumably due to onset of instabilities. In this transition regime viscosity begins to increase. For Re(p) greater than or approximately equal 10, inertial effects become important, clusters begin to breakup, and suspension displays shear thickening. This phenomenon may be attributed to enhanced contribution of solid phase in the total shear stress.

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The saturation curve of a sample of paper board was measured with mercury-intrusion porosimetry, and the three-dimensional structure of its pore space was determined by x-ray tomographic imaging. Ab initio numerical simulation of intrusion on the tomographic reconstruction, based on the lattice-Boltzmann method, was in excellent agreement with the measured saturation curve. A numerical invasion-percolation simulation in the same tomographic reconstruction showed good agreement with the lattice-Boltzmann simulation. The access function of the sample, determined from the saturation curve and the pore-throat distribution determined from the tomographic reconstruction, indicated that the ink-bottle effect is significant in paperlike materials.