Eur. Phys. J. E (2008) 27: 99-106
https://doi.org/10.1140/epje/i2008-10369-4

Capillary filling with pseudo-potential binary Lattice-Boltzmann model

¹ Istituto per le Applicazioni del Calcolo CNR, Viale del Policlinico 137, 00161, Roma, Italy
² Dipartimento di Ingegneria Meccaninca, Università di Roma Tor Vergata, 00133, Roma, Italy

^* e-mail: chibbaro@iac.rm.cnr.it

Received: 9 March 2008
Revised: 22 June 2008
Published online: 26 August 2008

Abstract

We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn’s law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.