Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 17, Issue 3-4, 2016, Pages 175-183

  Müller, Thomas ^a,b   Arosio, Paolo ^a   Rajah, Luke ^a   Cohen, Samuel I A ^a   Yates, Emma V ^a   Vendruscolo, Michele ^a   Dobson, Christopher M ^a   Knowles, Tuomas P J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b FLUIDIC ANALYTICS LTD   (United Kingdom)

Author keywords

convection; diffusion; microchannel; steady state mass transport

Indexed keywords

EID: 84979302775     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/ijnsns-2015-0056     Document Type: Article

References (30)

1. A. E. Kamholz, B. H. Weigl, B. A. Finlayson, and P. Yager, Quantitative analysis of molecular interaction in a microfluidic channel: the T-sensor, Anal. Chem. 71 (1999), 5340.
2. R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesides, and H. A. Stone, Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels, Appl. Phys. Lett. 76 (2000), 2376.
3. C. D. Costin and R. E. Synovec, A Microscale-molecular weight sensor: probing molecular diffusion between adjacent laminar flows by refractive index gradient detection, Anal. Chem. 74 (2002), 4558.
4. C. D. Costin, R. K. Olund, B. A. Staggemeier, A. K. Torgerson, and R. E. Synovec, Diffusion coefficient measurement in a microfluidic analyzer using dual-beam microscale-refractive index gradient detection application to on-chip molecular size determination, J. Chromatogr. A 1013 (2003), 77.
5. T. M. Squires and S. R. Quake, Microfluidics: fluid physics at the nanoliter scale, Rev. Mod. Phys. 77 (2005), 977.
6. E. V. Yates, T. Müller, L. Rajah, E. J. De Genst, P. Arosio, S. Linse, M. Vendruscolo, C. M. Dobson, and T. P. J. Knowles, Latent analysis of unmodified biomolecules and their complexes in solution with attomole detection sensitivity, Nat. Chem. 7 (2015), 802.
7. P. Arosio, T. Müller, L. Rajah, E. V. Yates, F. A. Aprile, Y. Zhang, S. I. A. Cohen, D. A. White, T. W. Herling, E. J. De Genst, S. Linse, M. Vendruscolo, C. M. Dobson, and T. P. J. Knowles, Microfluidic diffusion analysis of the sizes and interactions of proteins under native solution conditions, ACS Nano. 10 (2016), 333.
8. P. Arosio, K. Hu, F. A. Aprile, T. Müller, and T. P. J. Knowles, Microfluidic diffusion viscometer for rapid analysis of complex solutions, Anal. Chem. 88 (2016), 3488-3493.
9. M. Spiga and G. L. Morini, A Symmetric solution for velocity profile in laminar flow through rectangular ducts, Int. Commun. Heat Mass Transfer 21 (1994), 469.
10. G. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. A 219 (1953), 186.
11. A. E. Kamholz and P. Yager, Theoretical analysis of molecular diffusion in pressure-driven laminar flow in microfluidic channels, Biophys. J. 80 (2001), 155.
12. Z. Wu and N. T. Nguyen, Hydrodynamic focusing in microchannels under consideration of diffusive dispersion: theories and experiments, Sens. Actuators B 107 (2005), 965.
13. M. J. Kennedy, H. D. Ladouceur, T. Moeller, D. Kirui, and C. A. Batt, Analysis of a laminar-flow diffusional mixer for directed self-assembly of liposomes , Biomicrofluidics 6 (2012), 044119.
14. M. R. Schure, Digital simulation of sedimentation field-flow fractionation, Anal. Chem. 60 (1988), 1109.
15. Z. Li and G. Drazer, Separation of suspended particles by arrays of obstacles in microfluidic devices, Phys. Rev. Lett. 98 (2007), 050602.
16. A. Fokker, Die mittlere energie rotierender elektrischer dipole im strahlungsfeld, Ann. Phys. 348 (1914), 810.
17. M. von Smoluchowski, Über Brownsche Molekularbewegung unter Einwirkung äußerer Kräfte und deren Zusammenhang mit der verallgemeinerten Diffusionsgleichung, Ann. Phys. 48 (1915), 1103.
18. M. Planck, Über einen satz der statistischen dynamik und seine erweiterung in der quantentheorie, Sitzber. Preuss. Akad. Wiss. (1917), 324.
19. H. Risken, The Fokker-Planck Equation, Springer, Berlin, 1989.
20. P. Langevin, Sur la théorie du mouvement brownien, C. R. Acad Sci. 146 (1908), 530.
21. G. Segré and A. Silberberg, Behaviour of macroscopic rigid spheres in poiseuille flow part 2. experimental results and interpretation, J. Fluid Mech. 14 (1962), 136.
22. J. Rotne and S. Prager, Variational treatment of hydrodynamic interaction in polymers, J. Chem. Phys. 50 (1969), 4831.
23. E. C. Eckstein, D. G. Bailey, and A. H. Shapiro, Self-diffusion of particles in shear flow of a suspension, J. Fluid Mech. 79 (1977), 191.
24. C. W. J. Beenakker, Ewald sum of the rotne-prager tensor, J. Chem. Phys. 85 (1986), 1581.
25. D. Leighton and A. Acrivos, Measurement of shear-induced self-diffusion in concentrated suspensions of spheres, J. Fluid Mech. 177 (1987), 109.
26. F. R. da Cunha and E. J. Hinch, Shear-induced dispersion in a dilute suspension of rough spheres, J. Fluid Mech. 309 (1996), 211
27. Y. Wang, R. Mauri, and A. Acrivos, Transverse shear-induced gradient diffusion in a dilute suspension of spheres, J. Fluid Mech. 327 (1996), 255.
28. A. Hatch, A. E. Kamholz, K. R. Hawkins, M. S. Munson, E. A. Schilling, B. H. Weigl, and P. Yager, A rapid diffusion immunoassay in a T-sensor, Nat. Biotechnol. 19 (2001), 461.
29. D. Bedeaux and P. Mazur, Brownian motion and fluctuating hydrodynamics, Physica 76 (1974), 247.
30. D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, Rapid prototyping of microfluidic systems in poly (dimethylsiloxane), Anal. Chem. 70 (1998), 4974.