University of Dayton Research Institute.
Langmuir. 2010 Aug 17;26(16):13272-86. doi: 10.1021/la101557p.
A comprehensive numerical and experimental investigation on micrometer-sized water droplet impact dynamics and evaporation on an unheated, flat, dry surface is conducted from the standpoint of spray-cooling technology. The axisymmetric time-dependent governing equations of continuity, momentum, energy, and species are solved. Surface tension, wall adhesion effect, gravitational body force, contact line dynamics, and evaporation are accounted for in the governing equations. The explicit volume of fluid (VOF) model with dynamic meshing and variable-time stepping in serial and parallel processors is used to capture the time-dependent liquid-gas interface motion throughout the computational domain. The numerical model includes temperature- and species-dependent thermodynamic and transport properties. The contact line dynamics and the evaporation rate are predicted using Blake's and Schrage's molecular kinetic models, respectively. An extensive grid independence study was conducted. Droplet impingement and evaporation data are acquired with a standard dispensing/imaging system and high-speed photography. The numerical results are compared with measurements reported in the literature for millimeter-size droplets and with current microdroplet experiments in terms of instantaneous droplet shape and temporal spread (R/D(0) or R/R(E)), flatness ratio (H/D(0)), and height (H/H(E)) profiles, as well as temporal volume (inverted A) profile. The Weber numbers (We) for impinging droplets vary from 1.4 to 35.2 at nearly constant Ohnesorge number (Oh) of approximately 0.025-0.029. Both numerical and experimental results show that there is air bubble entrapment due to impingement. Numerical results indicate that Blake's formulation provides better results than the static (SCA) and dynamic contact angle (DCA) approach in terms of temporal evolution of R/D(0) and H/D(0) (especially at the initial stages of spreading) and equilibrium flatness ratio (H(E)/D(0)). Blake's contact line dynamics is dependent on the wetting parameter (K(W)). Both numerical and experimental results suggest that at 4.5 < We < 11.0 the short-time dynamics of microdroplet impingement corresponds to a transition regime between two different spreading regimes (i.e., for We < or = 4.5, impingement is followed by spreading, then contact line pinning and then inertial oscillations, and for We > or = 11.0, impingement is followed by spreading, then recoiling, then contact line pinning and then inertial oscillations). Droplet evaporation can be satisfactorily modeled using the Schrage model, since it predicts both well-defined transient and quasi-steady evaporation stages. The model compares well with measurements in terms of flatness ratio (H/H(E)) before depinning occurs. Toroidal vortices are formed on the droplet surface in the gaseous phase due to buoyancy-induced Rayleigh-Taylor instability that enhances convection.
对非加热、平面、干燥表面上微米级水滴冲击动力学和蒸发进行了全面的数值和实验研究，从喷雾冷却技术的角度出发。求解了轴对称时变连续、动量、能量和物种控制方程。控制方程考虑了表面张力、壁面附着力、重力体力、接触线动力学和蒸发。使用显式体积分数（VOF）模型，在串行和并行处理器中采用动态网格和变时间步长方法，以捕获整个计算域内随时间变化的液-气界面运动。数值模型包括温度和物种依赖的热力学和输运特性。使用 Blake 的和 Schrage 的分子动力学模型分别预测接触线动力学和蒸发率。进行了广泛的网格独立性研究。使用标准分配/成像系统和高速摄影术获得液滴冲击和蒸发数据。数值结果与文献中报道的毫米级液滴的测量值以及当前微液滴实验的测量值进行了比较，比较内容包括瞬时液滴形状和时间扩展（R/D(0) 或 R/R(E)）、平坦度比（H/D(0)）和高度（H/H(E)）轮廓以及时间体积（倒置 A）轮廓。冲击液滴的韦伯数（We）在近似为 0.025-0.029 的常 Ohnesorge 数（Oh）范围内从 1.4 变化到 35.2。数值和实验结果均表明，由于冲击，会产生气泡捕获。数值结果表明，与静态（SCA）和动态接触角（DCA）方法相比，Blake 公式在 R/D(0) 和 H/D(0) 的时间演化（尤其是在扩展的初始阶段）和平衡平坦度比（H(E)/D(0)）方面提供了更好的结果。Blake 的接触线动力学取决于润湿参数（K(W)）。数值和实验结果均表明，在 4.5 < We < 11.0 时，微液滴冲击的短时间动力学对应于两种不同扩展状态之间的过渡状态（即，对于 We < = 4.5，冲击后是扩展，然后是接触线钉扎，然后是惯性振动，对于 We > = 11.0，冲击后是扩展，然后是回弹，然后是接触线钉扎，然后是惯性振动）。使用 Schrage 模型可以很好地模拟液滴蒸发，因为它可以很好地预测瞬态和准稳态蒸发阶段。在解钉之前，模型在平坦度比（H/H(E)）方面与测量值吻合良好。由于浮力诱导的瑞利-泰勒不稳定性引起的涡旋在气体相中形成，从而增强了对流。
