We consider the extended Doimodel for nematic liquid crystalline polymers in-planar shear flow,which is inhomogeneous in shear direction.We study the formation of microstructure and the dynamics of defects.We discreti...We consider the extended Doimodel for nematic liquid crystalline polymers in-planar shear flow,which is inhomogeneous in shear direction.We study the formation of microstructure and the dynamics of defects.We discretize the Fokker-Plank equation using the spherical harmonic spectralmethod.Five in-plane flow modes and eight out-of-plane flow modes are replicated in our simulations.In order to demonstrate the validity of our method in simulating liquid crystal dynamics,we replicated weak shear limit results and detected defects.We also demonstrate numerically that the Bingham closure model,which maintains energy dissipation,is a reliable closure model.展开更多
This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constraine...This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constrained in the shear plane.The modified Crank-Nicolson finite difference scheme satisfying a discrete energy law will be developed.By using this scheme,it is observed numerically that the direction of the molecules will tumble from the boundary layer and later on the inner layer with a much longer time period.This is consistent with the theoretical prediction.Moreover,we find some complex phenomena,where the tumbling rises from boundary layer and is then embedded into the interior area more clearly when the viscosity coefficientµof the macro flow has a larger value.The norm of the molecular director d will endure greater change as well.This implies that the viscosity of flow plays the role of an accelerator in the whole complex fluids.Comparing these results with the theoretical analysis,we can find that the gradient of the velocity has direct impact on the tumbling phenomena.These results show that the proposed scheme is capable of exploring some physical phenomena embedded in the macro-micro model.展开更多
基金The authors would like to thank Prof.Sharon Murrel for her help in revising the En-glish.Guanghua Ji is partially supported by the National Science Foundation of China 10726015Pingwen Zhang is partially supported by the special funds for Major State Research Projects 2005CB321704National Science Foundation of China for Distin-guished Young Scholars 10225103 and 20490222.
文摘We consider the extended Doimodel for nematic liquid crystalline polymers in-planar shear flow,which is inhomogeneous in shear direction.We study the formation of microstructure and the dynamics of defects.We discretize the Fokker-Plank equation using the spherical harmonic spectralmethod.Five in-plane flow modes and eight out-of-plane flow modes are replicated in our simulations.In order to demonstrate the validity of our method in simulating liquid crystal dynamics,we replicated weak shear limit results and detected defects.We also demonstrate numerically that the Bingham closure model,which maintains energy dissipation,is a reliable closure model.
基金Hui Zhang’s research is partially supported by the Key Basic Research Project of the Ministry of Education of China under Grant No.107016the State Key Basic Research Project of China under Grant No.2005CB321704.
文摘This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constrained in the shear plane.The modified Crank-Nicolson finite difference scheme satisfying a discrete energy law will be developed.By using this scheme,it is observed numerically that the direction of the molecules will tumble from the boundary layer and later on the inner layer with a much longer time period.This is consistent with the theoretical prediction.Moreover,we find some complex phenomena,where the tumbling rises from boundary layer and is then embedded into the interior area more clearly when the viscosity coefficientµof the macro flow has a larger value.The norm of the molecular director d will endure greater change as well.This implies that the viscosity of flow plays the role of an accelerator in the whole complex fluids.Comparing these results with the theoretical analysis,we can find that the gradient of the velocity has direct impact on the tumbling phenomena.These results show that the proposed scheme is capable of exploring some physical phenomena embedded in the macro-micro model.
