Kornev Konstantin G., Neimark Alexander V.
TRI/Princeton, 601 Prospect Avenue, Princeton, New Jersey, 08542
J Colloid Interface Sci. 2001 Mar 1;235(1):101-113. doi: 10.1006/jcis.2000.7347.
A critical review of the problem of spontaneous penetration of a wetting liquid into pore channels shows that no theory exists to quantitatively predict the initial stage of imbibition. Since C. H. Bosanquet (1923, Phil. Mag. 45, 525), the theory operates with an universal velocity U(Bosanquet)=(2gammacosstraight thetarhor(1/2), with gamma being the surface tension, straight theta the contact angle, r the capillary/pore radius, and rho the fluid density. It is assumed that the initial impulse of the liquid entering the pore is insignificant for the penetration dynamics. Though the importance of the outside flow pattern has been noted in many papers, a thorough mathematical analysis of this effect is lacking in the literature. We derived a generalized equation of the fluid front motion by averaging the Euler equations of flow inside and outside the pore space. This analysis shows the significance of the flow patterns at the pore entrance. The initial stage of liquid imbibition is studied in the inviscid approximation using the methods of dynamic systems. The phase portrait of the dynamic system reveals a multiplicity of penetration regimes. Remarkably, the Bosanquet solution represents a particular regime, with the apparent mass being set zero. The Bosanquet trajectory refers to a separatrix of the phase portrait. It is shown that the initial conditions affect the rate of uptake significantly. The initial conditions stem from the prehistory of the fluid motion outside the pores prior to the liquid-solid contact. The phase portrait method allows us to distinguish two groups of solutions for the capillary rise dynamics of an inviscid fluid. The first group of trajectories corresponds to the liquid front rebound; the second group includes cyclic trajectories which correspond to the periodic regimes with liquid front oscillations at the equilibrium position. The upper estimate of the oscillation amplitude is found. Copyright 2001 Academic Press.
对润湿液体自发渗入孔隙通道问题的批判性综述表明，不存在能够定量预测吸渗初始阶段的理论。自C. H. 博赞奎特（1923年，《哲学杂志》45卷，525页）以来，该理论采用通用速度U(博赞奎特)=(2γcosθ/ρr)^(1/2)，其中γ为表面张力，θ为接触角，r为毛细管/孔隙半径，ρ为流体密度。假定液体进入孔隙的初始冲量对渗透动力学而言微不足道。尽管许多论文中已指出外部流动模式的重要性，但文献中缺乏对此效应的全面数学分析。我们通过对孔隙空间内外的流动欧拉方程进行平均，推导出了流体前沿运动的广义方程。该分析表明了孔隙入口处流动模式的重要性。利用动态系统方法，在无粘近似下研究了液体吸渗的初始阶段。动态系统的相图揭示了多种渗透模式。值得注意的是，博赞奎特解代表了一种特殊模式，表观质量被设为零。博赞奎特轨迹指的是相图的一条分界线。结果表明，初始条件对吸收速率有显著影响。初始条件源于液体与固体接触之前孔隙外部流体运动的历史。相图方法使我们能够区分无粘流体毛细管上升动力学的两组解。第一组轨迹对应液体前沿反弹；第二组包括循环轨迹，它们对应于平衡位置处液体前沿振荡的周期性模式。找到了振荡幅度的上限。版权所有2001年学术出版社。
