An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid
An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid
复制标题
DOI：
10.1016/j.jcp.2021.110851
复制
发表时间：
2021-11
期刊：
影响因子：
--
通讯作者：
Lei Li;Jiaqi Zhang;Zelai Xu;Y. Young;James J. Feng;P. Yue
中科院分区：
文献类型：
--
作者：
Lei Li;Jiaqi Zhang;Zelai Xu;Y. Young;James J. Feng;P. Yue
水凝胶是用水性溶剂溶胀的交联聚合物网络，并且在生物微流体装置中发挥核心作用。在这样的应用中，凝胶通常与流动的流体接触，从而建立流体-水凝胶两相系统。使用最近提出的模型（Young等人。[41] 2019），我们将水凝胶视为由Saint Venant-Kirchhoff聚合物网络和牛顿粘性溶剂组成的多孔弹性材料，并开发了一种有限元方法来计算涉及流体-水凝胶界面的流动。使用固定网格的任意拉格朗日-欧拉方法，将接口映射到一个参考配置的接口跟踪。界面变形与流体和固体的控制方程耦合成一个整体的算法，使用有限元库deal。该代码进行了验证，在几个非平凡的流动问题的分析解决方案：一维压缩的凝胶层的均匀流动，两层剪切流，和达西凝胶颗粒在平面拉伸流的变形。在所有情况下，数值解与解析解都非常吻合。数值试验表明，二阶收敛相对于网格细化，和一阶收敛相对于时间步长细化。
Hydrogels are crosslinked polymer networks swollen with an aqueous solvent, and play central roles in biomicrofluidic devices. In such applications, the gel is often in contact with a flowing fluid, thus setting up a fluid-hydrogel two-phase system. Using a recently proposed model (Young et al. [41] 2019), we treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian viscous solvent, and develop a finite-element method for computing flows involving a fluid-hydrogel interface. The interface is tracked by using a fixed-mesh arbitrary Lagrangian-Eulerian method that maps the interface to a reference configuration. The interfacial deformation is coupled with the fluid and solid governing equations into a monolithic algorithm using the finite-element library deal.II. The code is validated against available analytical solutions in several non-trivial flow problems: one-dimensional compression of a gel layer by a uniform flow, two-layer shear flow, and the deformation of a Darcy gel particle in a planar extensional flow. In all cases, the numerical solutions are in excellent agreement with the analytical solutions. Numerical tests show second-order convergence with respect to mesh refinement, and first-order convergence with respect to time-step refinement.