title: Capillary Penetration into Inclined Circular Glass Tubes.
abstract: 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 mPa·s into glass capillary tubes. We first report the effect of tube radii R between 140 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 viscogravitational 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 and 650 μm for a range of inclination angles to the horizontal, φ, from 5 to 90°. We show that capillary penetration can still be fitted using the viscogravitational solution, rather than the Bosanquet solution which describes imbibition without gravity, even for inclination angles as low as 10°. 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) = (γ(LV)/ρg sin φ)(1/2).
authors.affiliation: School of Science and Technology, Nottingham Trent University , Clifton Lane, Nottingham NG11 8NS, U.K.
authors.forename: Christophe L
authors.initials: CL
authors.lastname: Trabi
authors.affiliation: School of Science and Technology, Nottingham Trent University , Clifton Lane, Nottingham NG11 8NS, U.K.
authors.forename: F Fouzia
authors.initials: FF
authors.lastname: Ouali
authors.affiliation: Faculty of Engineering & Environment, Northumbria University , Ellison Place, Newcastle upon Tyne NE1 8ST, U.K.
authors.forename: Glen
authors.initials: G
authors.lastname: McHale
authors.affiliation: School of Science and Technology, Nottingham Trent University , Clifton Lane, Nottingham NG11 8NS, U.K.
authors.forename: Haadi
authors.initials: H
authors.lastname: Javed
authors.affiliation: School of Science and Technology, Nottingham Trent University , Clifton Lane, Nottingham NG11 8NS, U.K.
authors.forename: Robert H
authors.initials: RH
authors.lastname: Morris
authors.affiliation: School of Science and Technology, Nottingham Trent University , Clifton Lane, Nottingham NG11 8NS, U.K.
authors.forename: Michael I
authors.initials: MI
authors.lastname: Newton