A wetting boundary condition for handling contact line dynamics on three-dimensional curved geometries is developed in the lattice Boltzmann color-gradient framework. By combining the geometrical formation and the prediction-correction wetting scheme, the present wetting boundary condition is able to avoid the necessity to select an appropriate interface normal vector from its multiple solutions in the previous prediction-correction method. The effectiveness and accuracy of the wetting boundary condition are first validated by several benchmark cases, namely a droplet resting on a flat surface and on a solid sphere, and the spontaneous imbibition into a cylindrical tube. We then use the color-gradient model equipped with the developed wetting boundary condition to study the trapping behavior of a confined droplet in a microchannel with a cylindrical hole on the top surface, in which the effects of the hole radius and the droplet radius are identified for varying capillary numbers. Results show that the simulated critical capillary numbers, below which the droplet would be anchored by the hole, and the steady-state shapes of the anchored droplet generally match well with their theoretical solutions. The critical capillary number is found to decrease by either decreasing the hole radius or increasing the droplet radius, which is attributed to the weakened anchoring surface energy gradient and the enhanced driving force from outer flow, respectively. In addition, we show that the previous theoretical solutions are valid only when the initial droplet radius is greater than twice the height of the channel.

中文翻译：

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格子玻尔兹曼颜色梯度模型中三维弯曲几何的润湿边界条件

在格子玻尔兹曼颜色梯度框架中开发了用于处理三维弯曲几何上的接触线动力学的润湿边界条件。通过将几何结构与预测校正润湿方案相结合，本润湿边界条件能够避免先前预测校正方法中从多个解中选择合适的界面法向量的必要性。润湿边界条件的有效性和准确性首先通过几个基准案例进行验证，即液滴停留在平坦表面和实心球上，以及自发吸入到圆柱形管中。然后，我们使用配备开发的润湿边界条件的颜色梯度模型来研究顶部表面具有圆柱形孔的微通道中受限液滴的捕获行为，其中确定了孔半径和液滴半径的影响对于不同的毛细管数。结果表明，模拟的临界毛细管数（低于该数，液滴将被孔锚定）以及锚定液滴的稳态形状与理论解总体吻合良好。发现临界毛细管数通过减小孔半径或增加液滴半径而减小，这分别归因于锚定表面能梯度的减弱和外流驱动力的增强。此外，我们还表明，只有当初始液滴半径大于通道高度的两倍时，先前的理论解才有效。