The motion of an air-fluid interface through an irregularly coated capillary is studied by analysing the Lucas-Washburn equation with a random capillary force. The pinning probability goes from zero to a maximum value, as the interface slows down. Un
der a critical velocity, the distribution of waiting times $tau$ displays a power-law tail $sim tau^{-2}$ which corresponds to a strongly intermittent dynamics, also observed in experiments. We elaborate a procedure to predict quantities of experimental interest, such as the average interface trajectory and the distribution of pinning lengths.
The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated, both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven osc
illator, an analytical criterion for front pinning is derived, under the condition of diluteness of the coating spots. The criterion is tested against two dimensional Lattice Boltzmann simulations, and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.
We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changi
ng the ratio the typical size of the capillary, H, and the wettability of walls. Numerical results yield quantitative agreement with the Washburn law in all cases, provided the channel lenght is sufficiently larger then the interface width. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling. Finally, at variance with multiphase LB simulations, velocity and pressure profiles evolve under the sole effect of capillary drive all along the channel.
Numerical simulations of two-dimensional capillary filling using the pseudo-potential lattice Boltzmann model for multiphase fluids are presented, with special emphasis on the role of finite-vapour density effects. It is shown that whenever the densi
ty of the light-phase exceeds about ten percent of the dense phase, the front motion proceeds through a combined effect of capillary advection and condensation. As a result, under these conditions, the front proceeds at a higher speed as compared to the Washburn prediction. It is suggested that such an acceleration effect might be observed in experiments performed sufficiently close to critical conditions
