Scaling at the selective withdrawal transition

Comment on ``Force Balance at the Transition from Selective Withdrawal to Viscous Entrainment

Comment on paper by Blanchette and Zhang, Phys. Rev. Lett. 102, 144501 (2009).

Predicting transition from selective withdrawal to entrainment in two fluid stratified systems

Selective withdrawal is a desired phenomenon in transferring oil from large caverns in US Strategic petroleum reserve, because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. In order to predict a critical submergence depth at a critical flow rate, a selective withdrawal experiment at a high Reynolds Number was conducted. A tube was positioned through a liquid-liquid interface that draws the lower liquid upwards. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted …

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates …

Liquid interfaces in viscous straining flows: Numerical studies of the selective withdrawal transition

This paper presents a numerical analysis of the transition from selective withdrawal to viscous entrainment. In our model problem, an interface between two immiscible layers of equal viscosity is deformed by an axisymmetric withdrawal flow, which is driven by a point sink located some distance above the interface in the upper layer. We find that steady-state hump solutions, corresponding to selective withdrawal of liquid from the upper layer, cease to exist above a threshold withdrawal flux, and that this transition corresponds to a saddle-node bifurcation for the hump solutions. Numerical res…

统一粘性毛细和惯性 regime 在选择性撤回中

Unifying Viscocapillary and Inertial Regimes in Selective Withdrawal

本研究提出了一种统一框架，通过Moody图类型表示连接粘性毛细、剪切控制和惯性掺入，适用于牛顿和广义牛顿双层系统。

基于广义分流量理论和非玻尔兹曼变换的自发渗吸建模与标度

Modeling and scaling spontaneous imbibition with generalized fractional flow theory and non-Boltzmann transformation

本研究提出基于Hausdorff分形导数的广义分流量理论与非玻尔兹曼标度，用于建模自发渗吸，通过分形指数alpha调整幂律关系，在多种多孔介质数据上验证了其优于传统方法，可更准确预测渗吸速率。