Abstract
Using our generalized Fick-Jacobs approach [1, 2] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coefficient on the channel height. In particular, we observe a giant suppression of the effective diffusivity in thin channels; four orders of magnitude compared to the bulk value.
Similar content being viewed by others
References
S. Martens, A.V. Straube, G. Schmid, L. Schimansky-Geier, P. Hänggi, Phys. Rev. Lett. 110, 010601 (2013)
S. Martens, G. Schmid, A.V. Straube, L. Schimansky-Geier, P. Hänggi, Eur. Phys. J. Special Topics 222, 2453 (2013)
P.S. Dittrich, A. Manz, Nat. Rev. Drug. Discov. 5, 210 (2006)
F.J. Keil, R. Krishna, M.-O. Coppens, Rev. Chem. Eng. 16, 71 (2000)
A.M. Berezhkovskii, S.M. Bezrukov, Biophys. J. 88, L17 (2005)
A.M. Berezhkovskii, S.M. Bezrukov, Phys. Rev. Lett. 100, 038104 (2008)
M. Firnkes, D. Pedone, J. Knezevic, M. Döblinger, U. Rant, Nano Lett. 10, 2162 (2010)
J. Voldman, Annu. Rev. Biomed. Eng. 8, 425 (2006)
P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)
D. Reguera, A. Luque, P.S. Burada, G. Schmid, J.M. Rubí, P. Hänggi, Phys. Rev. Lett. 108, 020604 (2012)
R. Harrison, P. Todd, S. Rudge, D. Petrides, Bioseparations Science and Engineering (Oxford University Press, USA, 2002)
K.D. Dorfman, Rev. Mod. Phys. 82, 2903 (2010)
G. Giupponi, I. Pagonabarraga, Phys. Rev. Lett. 106, 248304 (2011)
M. MacDonald, G. Spalding, K. Dholakia, Nature 426, 421 (2003)
L. Bogunovic, R. Eichhorn, J. Regtmeier, D. Anselmetti, P. Reimann, Soft Matter 8, 3900 (2012)
C. Kettner, P. Reimann, P. Hänggi, F. Müller, Phys. Rev. E 61, 312 (2000)
X.T. Zheng, J.C. Wu, B.Q. Ai, F.G. Li, Eur. Phys. J. B 86, 479 (2013)
V.Y. Zitserman, A.M. Berezhkovskii, A.E. Antipov, Y.A. Makhnovskii, J. Chem. Phys. 135, 121102 (2011)
L. Dagdug, I. Pineda, J. Chem. Phys. 137, 024107 (2012)
T. Motz, G. Schmid, P. Hänggi, D. Reguera, J.M. Rubí, J. Chem. Phys. 141, 074104 (2014)
D. Reguera, G. Schmid, P.S. Burada, J.M. Rubí, P. Reimann, P. Hänggi, Phys. Rev. Lett. 96, 130603 (2006)
P. Burada, P. Hänggi, F. Marchesoni, G. Schmid, P. Talkner, Chem. Phys. Chem. 10, 45 (2009)
J.M. Rubí, D. Reguera, Chem. Phys. 375, 518 (2010)
P.K. Ghosh, P. Hänggi, F. Marchesoni, S. Martens, F. Nori, L. Schimansky-Geier, G. Schmid, Phys. Rev. E 85, 011101 (2012)
S.L. Dettmer, S. Pagliara, K. Misiunas, U.F. Keyser, Rev. Sci. Instrum. 85, 023708 (2014)
S.L. Dettmer, S. Pagliara, K. Misiunas, U.F. Keyser, Phys. Rev. E 98, 062305 (2014)
M. Jacobs, Diffusion Processes, 2nd edn. (Springer, New York, 1967)
R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)
D. Reguera, J.M. Rubí, Phys. Rev. E 64, 061106 (2001)
P. Kalinay, J.K. Percus, Phys. Rev. E 74, 041203 (2006)
P. Kalinay, Phys. Rev. E 84, 011118 (2011)
S. Martens, G. Schmid, L. Schimansky-Geier, P. Hänggi, Phys. Rev. E 83, 051135 (2011)
S. Martens, G. Schmid, L. Schimansky-Geier, P. Hänggi, Chaos 21, 047518 (2011)
S. Martens, I.M. Sokolov, L. Schimansky-Geier, J. Chem. Phys. 136, 111102 (2012)
P.K. Ghosh, P. Hänggi, F. Marchesoni, F. Nori, G. Schmid, Phys. Rev. E 86, 021112 (2012)
P.K. Ghosh, P. Hänggi, F. Marchesoni, F. Nori, G. Schmid, Europhys. Lett. 98, 50002 (2012)
M. Schindler, P. Talkner, M. Kostur, P. Hänggi, Physica A 385, 46 (2007)
G. Volpe, I. Buttinoni, D. Vogt, H.-J. Kummerer, C. Bechinger, Soft Matter 7, 8810 (2011)
C. Scholz, F. Wirner, J. Götz, U. Rüde, G.E. Schröder-Turk, K. Mecke, C. Bechinger, Phys. Rev. Lett. 109, 264504 (2012)
C. Scholz, F. Wirner, Y. Li, C. Bechinger, Exp. Fluids 53, 1327 (2012b)
B.Q. Ai, Y.F. He, F.G. Li, W.R. Zhong, J. Chem. Phys. 138, 154107 (2013)
F.G. Li, B.Q. Ai, J. Stat. Mech. Theor. Exp. 2014, P04027 (2014)
M. Tarama, A.M. Menzel, H. Löwen, Phys. Rev. E 90, 032907 (2014)
J.C.T. Eijkel, A. van den Berg, Microfluid. Nanofluid. 1, 249 (2005)
J. Happel, H. Brenner, Low Reynolds number hydrodynamics: with special applications to particulate media (Prentice-Hall, Inc., Engelwood Cliffs, N.J., 1965)
M.R. Maxey, J.J. Riley, Phys. Fluids 26, 883 (1983)
H. Bhatia, G. Norgard, V. Pascucci, P.-T. Bremer, IEEE Trans. Visual. Comput. Graphics 19, 1386 (2013)
A.V. Straube, J. Phys. Condens. Matter 23, 184122 (2011)
N. Laachi, M. Kenward, E. Yariv, K.D. Dorfman, Europhys. Lett. 80, 50009 (2007)
P.S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, J.M. Rubí, BioSystems 93, 16 (2008)
I.M. Sokolov, Eur. Phys. J. 31, 1353 (2010)
H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008)
E. Lauga, A.D. Stroock, H.A. Stone, Phys. Fluids 16, 3051 (2004)
G. Taylor, Phil. Trans. R. Soc. Lond. A 219, 186 (1953)
R. Aris, Phil. Trans. R. Soc. Lond. A 235, 67 (1956)
A. Zöttl, H. Stark, Eur. Phys. J. E 36, 4 (2013)
D. Di Carlo, D. Irimia, R.G. Tompkins, M. Toner, Proc. Nat. Ac. Sc. USA 104, 18892 (2007)
N. Liron, S. Mochon, J. Eng. Math. 10, 287 (1976)
S. Reddig, H. Stark, J. Chem. Phys. 138, 234902 (2013)
P. Hänggi, H. Thomas, Phys. Rep. 88, 207 (1982)
H. Risken, The Fokker-Planck Equation, 2nd edn. (Springer, Berlin, 1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Martens, S., Straube, A.V., Schmid, G. et al. Giant enhancement of hydrodynamically enforced entropic trapping in thin channels. Eur. Phys. J. Spec. Top. 223, 3095–3111 (2014). https://doi.org/10.1140/epjst/e2014-02321-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02321-9