Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers
Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers
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DOI：
10.1017/s0022112008000190
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发表时间：
2008-03-25
影响因子：
3.7
通讯作者：
Spelt, Peter D. M.
中科院分区：
文献类型：
--
作者：
Ding, Hang;Spelt, Peter D. M.
本文研究了中等雷诺数下剪切流中三维液滴贴壁运动的临界条件。为此目的，使用扩散界面方法，其也避免了在移动接触线处的应力奇异性，并且该方法允许流体之间的密度和粘度对比。接触角滞后由后退接触角θ（R）和前进接触角值θ（A）的规定表示。通过跟踪液滴的运动和变形来确定临界条件（最初是具有均匀接触角θ（0）的球冠）。在足够低的韦伯数，我们（基于所施加的剪切速率和液滴体积）的值，液滴变形和平移一段时间，但随后达到一个固定的位置，并达到稳态形状。在足够大的We值时，没有发现这样的稳定状态。我们给出了接触角θ（0）= θ（R）和θ（0）= θ（A）的情况下，We临界值作为雷诺数Re的函数的结果。一个缩放参数的基础上的力平衡下降所示的结果非常准确。计算结果还包括临界状态下的静态形状、瞬态运动和流动结构。结果表明，在低Re下，我们的结果与Dimitrakopoulos和Higdon（1998，J.Fluid Mech.vol.377，p.189）的结果一致（有一些限制）。总的来说，结果表明，我们的临界值是受惯性效应在中等雷诺数显着，而稳定的液滴形状仍然显示出一些相似之处，以前获得的蠕动流条件。最后，本文研究了液滴后定常尾迹的复杂结构和液滴上游侧驻点的出现。
We investigate the critical conditions for the onset of motion of a three-dimensional droplet on a wall in shear flows at moderate Reynolds number. A diffuse-interface method is used for this purpose, which also circumvents the stress singularity at the moving contact line, and the method allows for a density and viscosity contrast between the fluids. Contact-angle hysteresis is represented by the prescription of a receding contact angle theta(R) and an advancing contact angle value theta(A). Critical conditions are determined by tracking the motion and deformation of a droplet (initially a spherical cap with a uniform contact angle theta(0)). At sufficiently low values of a Weber number, We (based on the applied shear rate and the drop volume), the drop deforms and translates for some time, but subsequently reaches a stationary position and attains a steady-state shape. At sufficiently large values of We no such steady state is found. We present results for the critical value of We as a function of Reynolds number Re for cases with the initial value of the contact angle theta(0) = theta(R) as well as for theta(0) = theta(A). A scaling argument based on a force balance on the drop is shown to represent the results very accurately. Results are also presented for the static shape, transient motion and flow structure at criticality. It is shown that at low Re our results agree (with some qualifications) with those of Dimitrakopoulos & Higdon (1998, J. Fluid Mech. vol. 377, p. 189). Overall, the results indicate that the critical value of We is affected significantly by inertial effects at moderate Reynolds numbers, whereas the steady shape of droplets still shows some resemblance to that obtained previously for creeping flow conditions. The paper concludes with an investigation into the complex structure of a steady wake behind the droplet and the occurrence of a stagnation point at the upstream side of the droplet.