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A consistent energy integral model for a film over a substrate featuring topographies
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-08-21 , DOI: 10.1002/fld.5040 S. K. Pal 1 , Y. V. S. S. Sanyasiraju 1 , R. Usha 1
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-08-21 , DOI: 10.1002/fld.5040 S. K. Pal 1 , Y. V. S. S. Sanyasiraju 1 , R. Usha 1
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A depth-averaged model, based on energy integral method (EIM) has been employed to capture the steady-state free surface profiles in a gravity-driven thin film flow of a viscous, incompressible fluid over inclined substrates with topographical features. The model incorporates inertial effects, energy balance and is consistent up to , where , is the film thickness parameter. The governing equations are solved using a meshless numerical scheme based on radial basis functions. The predictions of the effects of inertia, inclination of the substrate, and aspect ratio of the topographical features are compared with the available finite-element solutions and experimental observations. The steady-state profiles generated using the EIM equations are in close agreement with the experimental observations. Being a consistent model, EIM model predictions are expected to be more reliable and accurate than the results based on the depth averaged form of the momentum equations, which are known to be not consistent. This feature is the motivating factor for the present work which is also a first attempt in implementing the meshless numerical scheme to free surface problems. The analysis paves a way for similar investigations on three-dimensional flows related to film flow over chemically patterned substrates.
中文翻译：
具有形貌特征的基材上薄膜的一致能量积分模型
已采用基于能量积分法 (EIM) 的深度平均模型来捕获具有地形特征的倾斜基板上的粘性不可压缩流体的重力驱动薄膜流中的稳态自由表面轮廓。该模型结合了惯性效应、能量平衡，并且在， 在哪里 , 是膜厚参数。使用基于径向基函数的无网格数值方案求解控制方程。惯性效应的预测、基底的倾斜度和地形特征的纵横比与可用的有限元解决方案和实验观察进行了比较。使用 EIM 方程生成的稳态曲线与实验观察结果非常一致。作为一个一致的模型，EIM 模型预测预计比基于动量方程的深度平均形式的结果更可靠和准确，而众所周知，后者是不一致的。这一特征是当前工作的推动因素，这也是实现无网格数值方案以解决自由表面问题的第一次尝试。
更新日期：2021-08-21
中文翻译：
具有形貌特征的基材上薄膜的一致能量积分模型
已采用基于能量积分法 (EIM) 的深度平均模型来捕获具有地形特征的倾斜基板上的粘性不可压缩流体的重力驱动薄膜流中的稳态自由表面轮廓。该模型结合了惯性效应、能量平衡，并且在， 在哪里 , 是膜厚参数。使用基于径向基函数的无网格数值方案求解控制方程。惯性效应的预测、基底的倾斜度和地形特征的纵横比与可用的有限元解决方案和实验观察进行了比较。使用 EIM 方程生成的稳态曲线与实验观察结果非常一致。作为一个一致的模型，EIM 模型预测预计比基于动量方程的深度平均形式的结果更可靠和准确，而众所周知，后者是不一致的。这一特征是当前工作的推动因素，这也是实现无网格数值方案以解决自由表面问题的第一次尝试。
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