Control of Pressure Gradient-Driven Spatio-temporal Patterns in Strongly Correlated Soft Materials

Saffinan-Taylor不稳定性，即从Saffinan-Taylor到尖端分裂模式的指法模式的变化首次发生的起始施加剪切速率2V_f/b，与位移强相关软材料（如聚合物溶液、悬浊液和乳液）的流变性能表现出非牛顿行为的情况很好地一致，而与材料无关。手指生长的平均速度几乎与修正的达西定律一致，其中粘度被剪切速率相关的粘度所取代，而与注入的流体和Hele-Shaw细胞无关。因此，可以得到软质材料中手指生长的粘性指法的基本方程，并对其粘性指法结果进行进一步的理论研究和计算机模拟。由于HPMC层吸附在空气-水界面处的粘弹性特性，气泡运动由单调振动转变为经过阻尼的直线运动。当Strouhal数为0.2时，在上升气泡后的尾迹中可见卡门涡街，而当Strouhal数为0.2时，尾迹结构与卡门涡街不同。这种差异应归因于从卡门流到湍流的流动变化。

The onset imposed shear rate 2V_f/b at which the Saffinan-Taylor instability, namely changes in the fingering pattern from the Saffinan-Taylor to the tip splitting ones occur for the first time, is in good agreement with that where the rheological properties of the displaced strongly correlated soft materials, such as polymer solutions, suspensions, and emulsions show non-Newtonian behavior irrespective of the material. The average velocity of the finger growth is almost coincident with that of the modified Darcy's law, in which the viscosity is displaced by the shear rate dependent viscosity, irrespective of the injected fluid and the Hele-Shaw cell. Therefore, the fundamental equation of viscous fingering in the soft materials can be obtained for the finger growth and it seems to be useful further to develop theoretical works and computer simulations for their viscous fingering results.The bubble motion is changed from monotonous vibration to straight paths through damped one, due to the viscoelastic properties of the HPMC layer adsorbed at the air-water interface. Below the Strouhal number of 0.2, the Karman vortex street is observed in the wake behind rising bubbles, whereas above the Strouhal number of 0.2, the wake structures are different from the Karman vortex street. The difference should be attributed to changes in flow from the Karman to turbulent flow.