Droplet motion on inclined heterogeneous substrates
Droplet motion on inclined heterogeneous substrates
复制标题
DOI：
10.1017/jfm.2013.201
复制
发表时间：
2013-05
影响因子：
3.7
通讯作者：
N. Savva;S. Kalliadasis
中科院分区：
文献类型：
--
作者：
N. Savva;S. Kalliadasis
摘要本文研究二维液滴在倾斜异质衬底上的静态和动态行为。我们利用的液滴厚度的长波近似的斯托克斯方程在存在滑移的基础上的演化方程。通过奇异摄动方法，在准静态动力学假设下得到了两个运动锋位置的演化方程。推导出的方程，这是验证了直接比较数值解的控制方程，在各种动态和平衡设置仔细检查。例如，我们证明了粘滑动力学，基板引起的滞后，足够强的化学梯度的液滴的上坡运动的可能性和存在的临界倾角超过该液滴可以不再支持在平衡。在可能的情况下，获得各种感兴趣的量的解析表达式，这也通过适当的数值实验进行验证。
Abstract We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasi-static dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick–slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.