Lattice Boltzmann simulations of apparent slip in hydropho- bic microchannels

– Various experiments have found a boundary slip in hydrophobic microchannel flows, but a consistent understanding of the results is still lacking. While Molecular Dynamics (MD) simulations cannot reach the low shear rates and large system sizes of the experiments, it is often impossible to resolve the needed details with macroscopic approaches. We model the interaction between hydrophobic channel walls and a fluid by means of a multi-phase lattice Boltzmann model. Our mesoscopic approach overcomes the limitations of MD simulations and can reach the small flow velocities of known experiments. We reproduce results from experiments at small Knudsen numbers and other simulations, namely an increase of slip with increasing liquid-solid interactions, the slip being independent of the flow velocity, and a decreasing slip with increasing bulk pressure. Within our model we develop a semi-analytic approximation of the dependence of the slip on the pressure. During the last century it was widely assumed that the velocity of a Newtonian liquid at a surface is always identical to the velocity of the surface. However, in recent years well controlled experiments have shown a violation of the no-slip boundary condition in sub-micron sized geometries. Since then, experimental [1] and theoretical works [2], as well as computer simulations [3–9] have tried to improve our understanding of boundary slip. The complex behavior of a fluid close to a solid interface involves the interplay of many physical and chemical properties. These include the wettability of the solid, shear rate, pressure, surface charge, surface roughness, as well as impurities and dissolved gas. Since all those quantities have to be determined very precisely, it is not surprising that our understanding of the phenomenon is still unsatisfactory. Due to the large number of different parameters, a significant dispersion of the results can be observed for ostensibly similar systems [1], e.g. observed slip lengths vary between nanometres [10] and micrometers [11] and while some authors find a dependence of the slip on the flow velocity [12], others do not [11, 13]. Most computer simulations apply Molecular Dynamics (MD) and report increasing slip with decreasing liquid density [6, 7] or liquid-solid interactions [8,14], while slip decreases with increasing pressure [4]. These simulations are usually limited to some tens of thousands of particles, lengths scales of nanometres and timescales of nanoseconds. Also, shear rates are orders of magnitude higher than in any experiment [1]. We overcome these limitations using the lattice Boltzmann (LB) algorithm –