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We present a systematic study of capillary filling for a binary fluid byusing mesoscopic a lattice Boltzmann model describing a diffusive interfacemoving at a given contact angle with respect to the walls. We compare thenumerical results at changing the ratio the typical size of the capillary, H,and the wettability of walls. Numerical results yield quantitative agreementwith the Washburn law in all cases, provided the channel lenght is sufficientlylarger then the interface width. We also show that in the initial stage of thefilling process, transient behaviour induced by inertial effects are undercontrol in our lattice Boltzmann equation and in good agreement with thephenomenology of capillary filling. Finally, at variance with multiphase LBsimulations, velocity and pressure profiles evolve under the sole effect ofcapillary drive all along the channel.

Capillary filling using Lattice Boltzmann Equations: the case of multi-component fluids