標題: A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant
作者: Chen, Kuan-Yu
Lai, Ming-Chih
應用數學系
數學建模與科學計算所(含中心)
Department of Applied Mathematics
Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
關鍵字: A conservative scheme;Interfacial flow;Soluble surfactant;Adsorption-desorption process;Immersed boundary method
公開日期: 15-一月-2014
摘要: Many physical problems arising in biological or material sciences involve solving partial differential equations in deformable interfaces or complex domains. For instance, the surfactant (an amphiphilic molecular) which usually favors the presence in the fluid interface may couple with the surfactant soluble in one of bulk domains through adsorption and desorption processes. Thus, it is important to accurately solve coupled surface-bulk convection-diffusion equations especially when the interface is moving. In this paper, we first rewrite the original bulk concentration equation in an irregular domain (soluble region) into a regular computational domain via the usage of the indicator function so that the concentration flux across the interface due to adsorption and desorption processes can be termed as a singular source in the modified equation. Based on the immersed boundary formulation, we then develop a new conservative scheme for solving this coupled surface-bulk concentration equations which the total surfactant mass is conserved in discrete sense. A series of numerical tests has been conducted to validate the present scheme. As an application, we extend our previous work [M.-C. Lai, Y.-H. Tseng, H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, J. Comput. Phys. 227 (2008) 7279-7293] to the soluble case. The effects of solubility of surfactant on drop deformations in a quiescent and shear flow are investigated in detail. (C) 2013 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jcp.2013.10.003
http://hdl.handle.net/11536/23189
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2013.10.003
期刊: JOURNAL OF COMPUTATIONAL PHYSICS
Volume: 257
Issue: 
起始頁: 1
結束頁: 18
顯示於類別:期刊論文


文件中的檔案:

  1. 000327483200001.pdf