Smoothed dissipative particle dynamics model for polymer molecules in suspension

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 6, 2008, Pages

  Litvinov, Sergey ^a   Ellero, Marco ^a,b   Hu, Xiangyu ^a   Adams, Nikolaus A ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMATIONS; DYNAMICS; FLUID DYNAMICS; FLUID MECHANICS; FUNCTION EVALUATION; GALLIUM ALLOYS; MECHANICS; MICROFLUIDICS; MOLECULAR STRUCTURE; MOLECULES; MULTIPHASE FLOW; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; POLYMERS; SEDIMENTATION; TWO DIMENSIONAL;

(MIN ,MAX ,+) FUNCTIONS; AMERICAN PHYSICAL SOCIETY (APS); ANALYTICAL THEORY; CONFORMATIONAL PROPERTIES; DISSIPATIVE PARTICLE DYNAMICS (DPD); ELASTIC INTERACTIONS; FLUCTUATION-DISSIPATION THEOREM (FDT); GYRATION RADIUS; IN ORDER; MESOSCOPIC; MICRO CHANNELS; MULTI-PHASE; NAVIER STOKES EQUATIONS; POLYMER CHAINS; POLYMER MOLECULES; SMOOTHED PARTICLE HYDRODYNAMICS (SPH); STATIC AND DYNAMIC; THERMAL FLUCTUATIONS; TWO-DIMENSIONAL (2D); UNIVERSAL BEHAVIORS;

CHEMICALS;

EID: 45149118679     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.066703     Document Type: Article

References (60)

1. G. E. Karniadakis and A. Beskok, Micro Flows, Fundamentals and Simulations (Springer, New York, 2002).
2. S. C. Glotzer and W. Paul, Annu. Rev. Mater. Res. ARMRCU 1531-7331 10.1146/annurev.matsci.32.010802.112213 32, 401 (2002).
3. A. Uhlherr and D. N. Theodorou, Curr. Opin. Solid State Mater. Sci. COSSFX 1359-0286 10.1016/S1359-0286(98)80023-5 3, 544 (1998).
4. H. A. Stone and S. Kim, AIChE J. AICEAC 0001-1541 10.1002/aic.690470602 47, 1250 (2001).
5. M. Mertig, L. Colombi, R. Seidel, W. Pompe, and A. De Vita, Nano Lett. NALEFD 1530-6984 10.1021/nl025612r 2, 841 (2002).
6. S. Diez, C. Reuther, C. Dinu, R. Seidel, M. Mertig, W. Pompe, and J. Howard, Nano Lett. 3, 1251 (2003). 1530-6984
7. M. Mertig, L. Colombi, A. Benke, A. Huhle, J. Opitz, R. Seidel, H. K. Schackert, and W. Pompe, in Foundations of Nanoscience: Self-Assembled Architectures and Devices, edited by, J. Reif, (Science Technica, Snowbird, Utah, 2004), p. 132.
8. L. D. Landau and E. M. Lifschitz, Fluid Mechanics (Pergamon Press, New York, 1959).
9. B. Dünweg and K. Kremer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.465445 99, 6983 (1993).
10. C. Aust, M. Kröger, and S. Hess, Macromolecules MAMOBX 0024-9297 10.1021/ma981683u 32, 5660 (1999).
11. J. M. Polson and J. P. Gallant, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2194903 124, 184905 (2006).
12. R. Jendrejack, D. C. Schwartz, M. D. Graham, and J. J. de Pablo, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1575200 119, 1165 (2003).
13. K. Mussawisade, M. Ripoll, R. G. Winkler, and G. Gomper, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2041527 123, 144905 (2005).
14. P. Ahlrichs and B. Dünweg, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.480156 111, 8225 (1999).
15. P. J. Hoogerbrugge and J. Koelman, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/19/3/001 19, 155 (1992).
16. P. Español and P. Warren, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/30/4/001 30, 191 (1995).
17. N. A. Spenley, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00183-2 49, 534 (2000).
18. W. Jiang, J. Huang, Y. Wang, and M. Laradji, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2428307 126, 044901 (2007).
19. V. Symeonidis, G. E. Karniadakis, and B. Caswell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.076001 95, 076001 (2005).
20. Y. Kong, C. W. Manke, W. G. Madden, and A. G. Schlijper, Tribol. Lett. 3, 133 (1997). 1023-8883
21. S. Chen, N. Phan-Thien, X.-J. Fan, and B. C. Khoo, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2004.02.005 118, 65 (2004).
22. X. Fan, N. Phan-Thien, and S. Chen, Phys. Fluids PHFLE6 1070-6631 10.1063/1.2206595 18, 063102 (2006).
23. X. Fan, N. Phan-Thien, and T. Ng, Phys. Fluids 15, 11 (2003). 1070-6631
24. The use of soft two-body potentials in DPD may allow for chain crossing (violating topological constraints) as well as particle penetration to the walls in problems involving confined situations.
25. P. Español and M. Revenga, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.026705 67, 026705 (2003).
26. J. J. Monaghan, Annu. Rev. Astron. Astrophys. ARAAAJ 0066-4146 10.1146/annurev.astro.30.1.543 30, 543 (1992).
27. R. A. Gingold and J. J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977). 0035-8711
28. L. B. Lucy, Astron. J. ANJOAA 0004-6256 10.1086/112164 82, 1013 (1977).
29. J. M. Vianney and A. Koelman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1915 64, 1915 (1990).
30. B. Maier and J. O. Rädler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1911 82, 1911 (1999).
31. R. Azuma and H. Takayama, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.480206 111, 8666 (1999).
32. S. R. Shannon and T. C. Choy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.1455 79, 1455 (1997).
33. E. Falck, O. Punkkinen, I. Vattulainen, and T. Ala-Nissila, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.050102 68, 050102 (R) (2003).
34. O. Punkkinen, E. Falck, I. Vattulainen, and T. Ala-Nissila, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1855876 122, 094904 (2005).
35. A. Milchev and K. Binder, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1996165 6, 21 (1996).
36. Y. Kong, C. W. Manke, W. G. Madden, and A. G. Schlijper, Int. J. Thermophys. IJTHDY 0195-928X 10.1007/BF01458818 15 (6), 1093 (1994).
37. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
38. J. P. Morris, P. J. Fox, and Y. Zhu, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1997.5776 136, 214 (1997).
39. J. P. Morris, Int. J. Numer. Methods Fluids IJNFDW 0271-2091 10.1002/1097-0363(20000615)33:3<333::AID-FLD11>3.0.CO;2-7 33, 333 (2000).
40. X. Y. Hu and N. A. Adams, J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2005.09.001 213, 844 (2006).
41. Note that, unlike DPD, SDPD repulsive interparticle forces have a multibody character due to the dependency of the pressure term Pi on the local value of the particle density ρi = j mj Wij. This is a remarkable property of the method which prevents particle crossing for monomers and confining walls.
42. E. G. Flekkøy, P. V. Coveney, and G. de Fabritiis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.2140 62, 2140 (2000).
43. J. Bonet and T.-S. L. Lok, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/S0045-7825(99)00051-1 180, 97 (1999).
44. M. Ellero, P. Español, and E. G. Flekkøy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.041504 68, 041504 (2003).
45. M. Grmela and H. C. Öttinger, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.6620 56, 6620 (1997).
46. H. C. Öttinger and M. Grmela, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.6633 56, 6633 (1997).
47. P. Español, M. Serrano, and H. C. Öttinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4542 83, 4542 (1999).
48. P. W. Randles and L. D. Libersky, Mech. Eng. 139, 375 (1996). 0025-6501
49. H. Takeda, S. M. Miyama, and M. Sekiya, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.92.939 92, 939 (1994).
50. M. Ellero, M. Kröger, and S. Hess, Multiscale Model. Simul. MMSUBT 1540-3459 10.1137/060651367 5, 759 (2006).
51. P. Español (private communication).
52. Notice that the FENE polymer molecule introduces an additional length in the model. The contour length is an appropriate parameter to estimate this molecular size. According to, if Lc denotes one segment of the molecular chain, its average value is of the order of R02 / (b+5), where b=K R02 / (kB T) is a dimensionless parameter approximately equal to 95 in our simulations. This gives Lc 6.6× 10-2 μm. The polymer contour length will be therefore L=N Lc and assumes values ranging from 1.3 μm (N=20) to 7 μm (N=100) consistent with the contour lengths of λ -DNA molecules.
53. M. Ellero, M. Kröger, and S. Hess, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(02)00059-9 105, 35 (2002).
54. M. Ellero and R. I. Tanner, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2005.08.012 132, 61 (2005).
55. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
56. P. Cifra and T. Bleha, Macromol. Theory Simul. MTHSEK 1022-1344 10.1002/(SICI)1521-3919(19991101)8:6<603::AID-MATS603>3.3.CO;2-B 8, 603 (1999).
57. R. Jendrejack, D. C. Schwartz, M. D. Graham, and J. J. de Pablo, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1637331 120, 2513 (2004).
58. E. A. J. F. Peters, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004- 10010-4 66, 311 (2004).
59. S. C. Whitehouse, M. R. Bate, and J. J. Monaghan, Mon. Not. R. Astron. Soc. 364, 1367 (2005). 0035-8711
60. T. Shardlow, SIAM J. Sci. Comput. 24, 1267 (2003). 1064-8275