Journal of Fluid Mechanics
Capillarity, Microfluidics, Fluid dynamics
The problem of low-gravity isothermal capillary ﬂow along interior corners that are rounded is revisited analytically in this work. By careful selection of geometric length scales and through the introduction of a new geometric scaling parameter Tc, the Navier–Stokes equation is reduced to a convenient∼O(1) form for both analytic and numeric solutions for all values of corner half-angle α and corner roundedness ratio λ for perfectly wetting ﬂuids. The scaling and analysis of the problem captures much of the intricate geometric dependence of the viscous resistance and signiﬁcantly reduces the reliance on numerical data compared with several previous solution methods and the numerous subsequent studies that cite them. In general, three asymptotic regimes may be identiﬁed from the large second-order nonlinear evolution equation: (I) the 'sharp-corner' regime, (II) the narrow-corner 'rectangular section' regime, and (III) the 'thin ﬁlm' regime. Flows are observed to undergo transition between regimes, or they may exist essentially in a single regime depending on the system. Perhaps surprisingly, for the case of imbibition in tubes or pores with rounded interior corners similarity solutions are possible to the full equation, which is readily solved numerically. Approximate analytical solutions are also possible under the constraints of the three regimes, which are clearly identiﬁed. The general analysis enables analytic solutions to many rounded-corner ﬂows, and example solutions for steady ﬂows, perturbed inﬁnite columns, and imbibing ﬂows over initially dry and prewetted surfaces are provided.
YONGKANG CHEN, MARK M. WEISLOGEL and CORY L. NARDIN (2006). Capillary-driven flows along rounded interior corners. Journal of Fluid Mechanics, 566, pp 235-271 doi:10.1017/S0022112006001996