摘要
Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures.In contrast,Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation.In modeling complex fluids,the extra stress from the non-Newtonian contribution must be included in the governing equations.In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluidstructure interaction in an immersed boundary framework.The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models.For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results.The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters.A regridding algorithm is introduced for the Lagrangian mesh model.We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldfoyd-B model.
基金
We would like to thank Isaac Klapper for many helpful discussions about Lagrangian mesh rheometry.Z.Zhuo was supported in part by NSF grant DMS-0652535
R.Dillon was supported in part by NSF grants DMS-0652535 and DMS-1317671.
