Capillary penetration into inclined circular glass tubes

The spontaneous penetration of a wetting liquid into a vertical tube against the force of gravity and the imbibition of the same liquid into a horizontal tube (or channel) are both driven by capillary forces and described by the same fundamental equations. However, there have been few experimental studies of the transition from one orientation to the other. We report systematic measurements of capillary penetration of polydimethylsiloxane oils of viscosities 9.6, 19.2 and 48.0 mPas into glass capillary tubes. We first report the effect of tube radii R between 140 μm and 675 μm on the dynamics of spontaneous imbibition We show that the data can be fitted using the exact numerical solution to the governing equations and that these are similar to fits using the analytical visco-gravitational approximation. However, larger diameter tubes show a rate of penetration slower than expected using an equilibrium contact angle and the known value of liquid viscosity. To account for the slowness, an increase in viscosity by a factor (η/ρ)scaling is needed. We show full agreement with theory requires the ratio R/κ -1 ∼0.1 or less, where κ -1 is the capillary length. In addition, we propose an experimental method that enables the determination of the dynamic contact angle during imbibition, which gives values that agree with the literature values. We then report measurements of dynamic penetration into the tubes of R=190 μm and 650 μm for a range of inclination angles to the horizontal, ϕ, from 5o to 90o. We show that capillary penetration can still be fitted using the visco-gravitational solution, rather than the Bosanquet solution which describes imbibition without gravity, even for inclination angles as low as 10o. Moreover, at these low angles, the effect of the tube radius is found to diminish and this appears to relate to an effective capillary length, κ–1(φ)=(γLV/ρg sin φ)1/2