Saturated imbibition under the influence of gravity and geometry

Junfeng Xiao; Jianchao Cai; Jianfeng Xu

doi:10.1016/j.jcis.2018.03.050

Saturated imbibition under the influence of gravity and geometry

J Colloid Interface Sci. 2018 Jul 1:521:226-231. doi: 10.1016/j.jcis.2018.03.050. Epub 2018 Mar 15.

Authors

Junfeng Xiao¹, Jianchao Cai², Jianfeng Xu³

Affiliations

¹ School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: xiaojf@hust.edu.cn.
² Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China. Electronic address: caijc@cug.edu.cn.
³ School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: jfxu@hust.edu.cn.

PMID: 29571104
DOI: 10.1016/j.jcis.2018.03.050

Abstract

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.

Keywords: Capillarity; Geometry; Gravity; Imbibition; Time exponent.