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.

中文翻译：

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重力和几何形状影响下的饱和吸水

假设

在经典的吸水定律中，对于一维几何形状，重力的影响通常被忽略。后续研究在考虑重力的情况下补充了经典的“卢卡斯-瓦斯本定律”，但没有对重力影响下的几何形状进行检查，而几何形状对于吸水过程产生了不同的比例定律。因此，有可能在重力作用下的二维和三维吸收过程中发现吸收长度的新的时间指数。

方法

通过理论分析和数值模拟，定量确定了三种几何形状（一维，二维径向和三维径向）在三种重力情况下（零重力，加速度和减速度）的润湿区域的大小。

发现

在二维径向吸收和三维径向吸收中，在不同的重力方向上确定了经典1/2以外的新时间指数，并发现了由于重力不同而引起的时间指数的对称性。对于一维吸收，加速情况下的新时间指数为1。润湿区域中的流场也由模拟确定。本文的发现表明，在重力和几何形状的交点处存在新的吸收长度物理定律。