Dynamics of liquid penetration into capillary tubes.

The dynamics of penetration is considered in the case where inertia effects are small. The effect of the contact line speed on the dynamic contact angle is taken into consideration. Analytical solutions are obtained for short and large times, and are found to cover together most of the time domain. The results obtained numerically show good agreement with the asymptotic solutions. The large-time solutions are valid in the case of penetration into horizontal capillaries. The large-time asymptotic solution shows a correction term compared to the Lucas-Washburn equation, which is found to be a limiting case valid for very large times (horizontal capillaries case). The analysis shows how to include gravity effects in the case of penetration into vertical tubes. Excellent agreement is found with available published experimental data.