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Single Particle DPD: Algorithms and Applications Single Particle DPD: Algorithms and Applications by Wenxiao Pan M.S., Applied Mathematics, Brown University, USA, 2007 M.S., Mechanics and Engineering Science, Peking University, China, 2003 B.S., Mechanics and Engineering Science, Peking University, China, 2000 Thesis Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in the Division of Applied Mathematics at Brown University May 2010 Abstract of “Single Particle DPD: Algorithms and Applications,” by Wenxiao Pan, Ph.D., Brown University, May 2010 This work presents the new single particle dissipative particle dynamics (DPD) model for flows around bluff bodies that are represented by single DPD particles. This model leads to an accurate representation of the hydrodynamics and allows for economical exploration of the properties of complex fluids. The new DPD formulation introduces a shear drag coeffi- cient and a corresponding term in the dissipative force that, along with a rotational force, incorporates non-central shear forces between particles and preserves both linear and angu- lar momenta. First, we simulated several prototype Stokes flows to verify the performance of the proposed formulation. Next, we demonstrated that, in colloidal suspensions, the suspended spherical colloidal particles can effectively be modeled as single DPD particles. In particular, we investigated the rheology, microstructure and shear-induced migration of a monodisperse colloidal suspension in plane shear flows. The simulation results agree well with both experiments and simulations by the Stokesian Dynamics. Then, we devel- oped a new low-dimensional red blood cell (LD-RBC) model based on this single particle DPD algorithm. The LD-RBC model is constructed as a closed-torus-like ring of 10 DPD particles connected by wormlike chain springs combined with bending resistance. The LD- RBC model is able to capture the linear and non-linear elastic deformations for healthy and malaria-infected cells. Also, it reproduces the key features of blood flow in vessels such as the cell free layer, the Fahraeus effect and the Fahraeus-Lindqvist effect, except for capillaries of sizes comparable to the cell diameter. The discrepancy is caused by the simplified representation of the RBC 3D structure, which becomes more critical for blood flow in small tubes. Finally, we examined the effect of aggregation of RBCs on the blood rheology. To reproduce the tendency of RBCs to form structures known as “rouleaux”, a weak anisotropic attractive interaction derived from the Morse potential is included with each RBC. A reversible rouleau formation is reproduced. The presence of rouleaux causes a great increase in the low-shear-rate viscosity of the suspensions, and a non-zero yield stress. Both are consistent with experimental studies. °c Copyright 2010 by Wenxiao Pan This dissertation by Wenxiao Pan is accepted in its present form by the Division of Applied Mathematics as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date......................... ..................................................... George Em Karniadakis, Director Recommended to the Graduate Council Date......................... ..................................................... Bruce Caswell, Reader Date......................... ..................................................... Martin Maxey, Reader Approved by the Graduate Council Date......................... ..................................................... Sheila Bonde Dean of the Graduate School iii The Vita of Wenxiao Pan Education May 2010 Ph.D. in Applied Mathematics, Brown University, USA Advisors: George E. Karniadakis & Bruce Caswell May 2007 M.S. in Applied Mathematics, Brown University, USA Advisor: George E. Karniadakis July 2003 M.S. in Mechanics and Engineering Science, Peking University, China July 2000 B.S. with Honor in Mechanics and Engineering Science, Peking University, China Awards and fellowships Sep 2009 - Dec 2009 Simon Ostrach disertation fellowship, Brown University Sep 2005 - May 2006 Academic fellowship, Brown University Teaching experience Sep 2006 - Dec 2006 Teaching Assistant, Division of Applied Mathematics, Brown University, Course: Statistical Inference II Jan 2007 - May 2007 Teaching Assistant, Division of Applied Mathematics, Brown University, Course: Essential Statistics Research interests • Molecular and coarse-grained molecular simulations • Rheology and dynamics of complex fluids and biological systems • Mesoscopic simulations of Multiphase flow Publications Articles in peer-reviewed journals 1. W. Pan, B. Caswell and G. E. Karniadakis, “A low-dimensional model for the red blood cell”, Soft Matter, submitted. 2. W. Pan, D. A. Fedosov, B. Caswell and G. E. Karniadakis, “A comparison of multi- scale and low-dimensional models of red blood cells”, Microvascular Research, submit- ted. iv 3. W. Pan, B. Caswell and G. E. Karniadakis, “Rheology, Microstructure and Migration in Brownian Colloidal Suspensions”, Langmuir, 26(1), 133-142, 2010. 4. W. Pan, D. A. Fedosov, B. Caswell and G. E. Karniadakis, “Hydrodynamic Interac- tions for Single DPD Particles, and their Clusters and Filaments”, Physical Review E, 78(4), 046706, 2008. 5. W. Pan, I. V. Pivkin, and G. E. Karniadakis, “Single-particle hydrodynamics in DPD: A new formulation”, Europhysics Letters, 84, 10012, 2008. 6. Samuel CW Tan*, Wen X Pan*, Gang Ma, Ning Cai, Kam W Leong and Kin Liao, “Viscoelastic behaviour of human mesenchymal stem cells”, BMC Cell Biology, 9(40), 2008. *contributed equally 7. WC Tan, WX Pan, and MY Xu, “A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates”, International Journal of Non-linear Mechanics, 38, 645-650, 2003. 8. Pan WX, and Tan WC, “An unsteady flow of a viscoelastic fluid with the fractional Maxwell model between two parallel plates”, Mechanics in Engineering, 25(1), 19-22, 2003. Articles in conference proceedings 1. Pan, Wenxiao, Petersen, Erik and Cai, Ning and Ma, Gang and Lee, Jian Run and Feng, Zhiqin and Liao, Kin and Leong, Kam W., ”Viscoelastic properties of human mesenchymal stem cells”, Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, 7S, 4854-4857, 2005. Conference Presentation • 2008 Society for Industrial and Applied Mathematics (SIAM) Annual meeting (AN08), San Diego, California U.S.A, July 2008. • Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics–Focus: Ad- vances in CFD, Massachusetts Institute of Technology, Cambridge, MA U.S.A., June 2009. v • 13th IACIS International Conference on Surface and Colloid Science and the 83rd ACS Colloid & Surface Science Symposium, Columbia University, New York U.S.A, June 2009. • Society of Rheology 81st Annual Meeting, Madison, Wisconsin U.S.A, Oct 2009. • American Physical Society 62nd Annual Meeting, Division of Fluid Dynamics, Min- neapolis, Minnesota, Nov 2009. vi To My parents My husband vii Acknowledgments First of all, I want to give my deepest thanks to my primary dissertation advisor, Professor George Karniadakis. I am deeply impressed by Professor Karniadakis’ broad specialty and perceptive insight in areas ranging from mathematics and numerical analysis to physics, biology and engineering. This greatly inspires my scientific curiosity in these fields. I feel so lucky to have the chance to study and work under his guidance in this CRUNCH group. I learned how to think, before starting anything new and when problems appeared. This is absolutely unprecedentedly valuable to my future career. Professor Karniadakis is not only my advisor, but also my good friend. He was always trying to encourage me when I was frustrated facing any challenges in my projects. This means a lot to me and motivates me to move forward. I’ll remember for ever all the help he gives to me during the whole time of my PhD pursuit. I feel honored to have Professor Bruce Caswell as my second dissertation advisor. Al- though he started to co-direct my research from the third year of my graduate study, I cannot forget at all the countless help and timely advice from him. He never hesitated to share with me his rich knowledge and experience in mathematics, fluid dynamics and rheol- ogy of complex fluids. This contributes a great deal to my academic progress and helps to mature myself scientifically. Also, I want to thank Professor Martin Maxey for him agreeing to be my thesis committee member and devoting time for suggestions and comments. The discussions with him deepened my understandings of the science behind. His strict attitude towards science provides a model to me that helps shape up mine. I am feeling lucky to work in this energetic research group with the many energetic members. They are confident, hardworking and friendly. Everyone is ready to help. The active interactions between them make this group an pleasant and attactive one. I’ll re- member all these lovely people. Let me write down their names: Igor Pivkin, Xiaoliang Wan, Guang Lin, Hyoungsu Baek, Dmitry Fedosov, Huan Lei, Kyongmin Yeo, Zhongqiang Zhang, Minseok Choi, Yue Yu, Chao Li, Xiu Yang, etc. I also want to thank my friends for their encouragements and their prayers for me, which makes my life much easier. They are: Rev. Tin-Yau Wong, Deacon. Ching Chuen Wong, Mrs. Wong, Deacon. Jian-Ren Song, Deacon. Zi-Ping Wu, Hyoungsu Baek, Haejong Lee, Shih-Hsiu Huang, David Lau, Irene Yang, etc. viii Finally, I want to give my very special thanks to my husband, Xiaoliang Wei. He is my tremendous support during
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