Saturated imbibition under the influence of gravity and geometry

Hypothesis: The effect of gravity was generally neglected in the classical imbibition law for one dimensional geometries. Following researches complemented the classical Lucas-Washburn law with consideration of gravity, but no examination of geometries under influence of gravity has been done, while geometry was shown to yield different scaling law for the imbibition process. Hence, it is possible to discover new time exponents for imbibition length in two dimensional and three dimensional imbibition process under gravity. Methods: Through theoretical analysis and numerical simulations, the size of wetted region under three gravitational scenarios (zero gravity, acceleration and deceleration) in three geometries (one dimensional, two dimensional radial and three dimensional radial) are determined quantitatively. Findings: New time exponents other than classic 1/2 are identified under different directions of gravity in two dimensional radial and three dimensional radial imbibition, and symmetry of time exponents due to different directions of gravity is discovered. A new time exponent of 1 for the acceleration case in one dimensional imbibition is found. The flow field in the wetted region is also determined from simulations. Discoveries in this paper show that new physical laws for imbibition length exist at the intersection of gravity and geometry. (C) 2018 Elsevier Inc. All rights reserved.