화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.20, No.3, 143-152, September, 2008
Export Citation
Concentration distributions during flow of confined flowing polymer solutions at finite concentration: slit and grooved channe
Juan P. Hernandez-Ortiz1, 2, Hongbo Ma1, Juan J. de Pablo1, and Michael D. Graham1, †
  • 1Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691, USA
  • 2Departamento de Materiales, Universidad Nacional de Colombia, Sede Medellin, Kra 80 # 65-223, Bloque M3-050, USA
E-mail:
Simulations of solutions of flexible polymer molecules during flow in simple or complex confined geometries are performed. Concentrations from ultradilute up to near the overlap concentration are considered. As concentration increases, the hydrodynamic migration effects observed in dilute solution unidirectional flows (Couette flow, Poiseuille flow) become less prominent, virtually vanishing as the overlap concentration is approached. In a grooved channel geometry, the groove is almost completely depleted of polymer chains at high Weissenberg number in the dilute limit, but at finite concentration this depletion effect is dramatically reduced. Only upon inclusion of hydrodynamic interactions can these phenomena be properly captured.
Keywords:microfluidics;polymer migration;Brownian dynamics;hydrodynamic interactions
  1. Agarwal US, Dutta A, Mashelkar RA, Chem. Eng. Sci., 49(11), 1693 (1994)
  2. Banchio AJ, Brady JF, J. Chem. Phys., 118(22), 10323 (2003)
  3. Batchelor G, 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge
  4. Bird RB, Curtiss C, Armstrong FRC, Hassager O, 1987, Dynamics of Polymer Liquids: Kinetic Theory, vol. 2, John Wiley & Sons, New York, 2nd Edition
  5. Chan EY, Goncalves NM, Haeusler RA, Hatch AJ, Larson JW, Maletta AM, Yantz GR, Carstea ED, Fuchs M, Wong GG, Gullans SR, Gilmanshin R, Genome Res., 14, 1137 (2004)
  6. Demmel JW, Eisenstat SC, Gilbert JR, Li XS, Liu JWH, SIAM J. Matrix Analysis and Applications, 20, 720 (1999)
  7. Deserno M, Holm C, J. Chem. Phys., 109(18), 7678 (1998)
  8. Dimalanta ET, Lim A, Runnheim R, Lamers C, Churas C, Forrest DK, de Pablo JJ, Graham MD, Coppersmith SN, Goldstein S, Schwartz D, Anal. Chem., 76, 5293 (2004)
  9. Fixman M, J. Chem. Phys., 69, 1527 (1978)
  10. Fixman M, Macromolecules, 19, 1204 (1986)
  11. Frigo M, Johnson SG, 1997, Tech. Rep. MIT-LCS-TR-728, Massachusetts Institute of Technology, Boston
  12. Frigo M, Johnson SG, Proceedings of the IEEE, 93, 216 (2005)
  13. Gardiner C, 1985, Handbook of Stochastic Methods, Springer, Berlin
  14. Grassia P, Hinch E, Nitsche L, J. Fluid. Mech., 282, 373 (1995)
  15. Han J, Craighead HG, Science, 288, 1026 (2000)
  16. Hasimoto H, J. Fluid Mech., 5, 317 (1959)
  17. Hernandez-Ortiz JP, Ma H, de Pablo JJ, Graham MD, Phys. Fluids, 18, 123101 (2006)
  18. Hernandez-Ortiz JP, de Pablo JJ, Graham MD, J. Chem. Phys., 125, 164906 (2006)
  19. Hernandez-Ortiz JP, de Pablo JJ, Graham MD, Phys. Rev. Lett., 98, 140602 (2007)
  20. Hockney RW, Eastwood JW, 1988, Computer Simulation Using Particles, Taylor & Francis, Bristol
  21. Jendrejack RM, Graham MD, de Pablo JJ, J. Chem. Phys., 113(7), 2894 (2000)
  22. Jendrejack RM, de Pablo JJ, Graham MD, J. Chem. Phys., 16, 7752 (2002)
  23. Jendrejack RM, Schwartz DC, Graham MD, de Pablo JJ, J. Chem. Phys., 119(2), 1165 (2003)
  24. Jendrejack RM, Dimalanta ET, Schwartz DC, Graham MD, de Pablo JJ, Phys. Rev. Lett., 91, 038102 (2003)
  25. Jendrejack RM, Schwartz DC, de Pablo JJ, Graham MD, J. Chem. Phys., 120(5), 2513 (2004)
  26. Jing J, Reed J, Huang J, Hu X, Clarke V, Edington J, Housman D, Anantharaman T, Huff E, Mishra B, Porter B, Shenker A, Wolfson E, Hiort C, Kantor R, Aston C, Schwartz D, Proc. Natl. Acad. Sci. U.S.A., 95, 8046 (1998)
  27. Kan CW, Fredlake CP, Doherty EAS, Barron AE, Electrophoresis, 25(21-22), 3564 (2004)
  28. Landau L, Lifshitz S, 1987, Fluid Mechanics, Butterworth Heinemann, Oxford, 2nd Edition
  29. Ma H, Graham MD, Phys. Fluids, 17, 083103 (2005)
  30. Mucha PY, Tee SY, Weitz DA, Shraiman BI, Brenner MP, J. Fluid Mech., 501, 71 (2004)
  31. Ottinger HC, 2005, Beyond Equilibrium Thermodynamics, Wiler-Interscience, New York
  32. Ottinger HC, 1996, Stochastic Processes in Polymeric Fluids, Springer, Berlin
  33. Power H, Wrobel LC, 1995, Boundary Integral Methods in Fluid Mechanics, Computational Mechanics Publications, Southampton
  34. Pozrikidis C, 1992, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, Cambridge
  35. Press WH, Teukolsky SA, Vetterling WT, Flannery BP, 1992, Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, 2nd Edition
  36. Reichl L, 1998, A Modern Course in Statistical Physics, Wiley-Interscience, New York 2nd Edition
  37. Risken H, 1989, The Fokker-Planck Equation, Springer, Berlin, 2nd Edition
  38. Roper MG, Easley CJ, Landers JP, Anal. Chem., 77, 3887 (2005)
  39. Stoltz C, de Pablo JJ, Graham MD, J. Rheol., 50(2), 137 (2006)
  40. Storm AJ, Chen JH, Zandbergen HW, Dekker CD, Phys. Rev. E, 71, 051903 (2006)
  41. Streek M, Schmid F, Duong TT, Anselmetti D, Ros A, Physical Rev. E, 71, 011905 (2005)
  42. Zwanzig R, 2001, Nonequilibrium Statistical Mechanics, Oxford University Press, Oxford