Abstract
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly interacting Brownian particles. Dynamical density functional theory (DDFT) for classical Brownian particles represents an ideal tool for this purpose. After outlining the basic ingredients to DDFT we show that it can be readily applied to flowing suspensions with time-dependent particle sources. Particle interactions lead to considerable layering in the mean density profiles, a feature that is absent in the trivial case of noninteracting, freely diffusing particles. If the particle injection rate varies periodically in time with a suitable frequency, a resonance in the layering of the mean particle density profile is predicted.
Similar content being viewed by others
References
P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)
C. Lutz, M. Kollmann, C. Bechinger, Phys. Rev. Lett. 93, 026001 (2004)
C. Kreuter, U. Siems, P. Nielaba, P. Leiderer, A. Erbe, Eur. Phys. J. Special Topics 222, 2923 (2013)
M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)
J. Hansen, I. McDonald, Theory of Simple Liquids, third edition (Academic Press, 2005)
Y. Tsori, P.-G. de Gennes, EPL 66, 599 (2004)
A. Sengupta, T. Kruppa, H. Löwen, Phys. Rev. E 83, 031914 (2011)
A.J. Archer, R. Evans, J. Chem. Phys. 121, 4246 (2004)
N.D. Mermin, Phys. Rev. 137, A1441 (1965)
P. Español, H. Löwen, J. Chem. Phys. 131, (2009)
H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G.I. Tóth, G. Tegze, L. Gránásy, Adv. Phys. 61, 665 (2012)
P. Zhang, L. Cai, Z.-J. Lian, X.-Y. Pan, Chin. Phys. Lett. 27, 080504 (2010)
H. Löwen, Phys. Rep. 237, 249 (1994)
M.H. Yamani, M. Oettel, Phys. Rev. E 88, 022301 (2013)
J. Reinhardt, F. Weysser, J.M. Brader, EPL 102, 28011 (2013)
T. Neuhaus, M. Schmiedeberg, H. Löwen, New J. Phys. 15, 073013 (2013)
I. Santamaría-Holek, Z. Grzywna, J. Rubi, Eur. Phys. J. Special Topics 222, 129 (2013)
A.J. Archer, P. Hopkins, M. Schmidt, Phys. Rev. E 75, 040501 (2007)
A.L. Yarin, Annu. Rev. Fluid Mech. 38, 159 (2006)
M.C. Jenkins, S.U. Egelhaaf, J. Phys.: Condens. Matter 20, 404220 (2008)
J.K. Percus, G.J. Yevick, Phys. Rev. 110, 1 (1958)
M. Heinen, E. Allahyarov, H. Löwen, J. Comput. Chem. 35, 275 (2014)
R.D. Rohrmann, A. Santos, Phys. Rev. E 76, 051202 (2007)
M. Adda-Bedia, E. Katzav, D. Vella, J. Chem. Phys. 129, 144506 (2008)
M. Plischke, D. Henderson, J. Chem. Phys. 84, 2846 (1986)
R. Kjellander, S. Sarman, Mol. Phys. 74, 665 (1991)
A. Ivlev, H. Löwen, G. Morfill, C.P. Royall, Complex Plasmas and Colloidal Dispersions: Particle-resolved Studies of Classical Liquids and Solids, Vol. 5, Series in Soft Condensed Matter (World Scientific, Singapore [u.a.], 2012)
K. Nygård, R. Kjellander, S. Sarman, S. Chodankar, E. Perret, J. Buitenhuis, J.F. van der Veen, Phys. Rev. Lett. 108, 037802 (2012)
M. Engel, J.A. Anderson, S.C. Glotzer, M. Isobe, E.P. Bernard, W. Krauth, Phys. Rev. E 87, 042134 (2013)
J. Kolafa, M. Rottner, Mol. Phys. 104, 3435 (2006)
T. Franosch, S. Lang, R. Schilling, Phys. Rev. Lett. 109, 240601 (2012)
A. Reinmüller, E.C. Oğuz, R. Messina, H. Löwen, H.J. Schöpe, T. Palberg, J. Chem. Phys. 136, 164505 (2012)
A. Sengupta, S. van Teeffelen, H. Löwen, Phys. Rev. E 80, 031122 (2009)
K. Lichtner, S.H.L. Klapp, EPL 92, 40007 (2010)
D. Takagi, J. Palacci, A.B. Braunschweig, M.J. Shelley, J. Zhang, Soft. Matter 10, 1784 (2014)
M. Rex, H. Löwen, Phys. Rev. Lett. 101, 148302 (2008)
M. Rex, H. Löwen, Eur. Phys. J. E 28, 139 (2009)
J.-L. Barrat, H. Xu, J. Phys.-Condes. Matter 2, 9445 (1990)
H. Xu, M. Baus, J. Phys.-Condes. Matter 2, 5885 (1990)
S. van Teeffelen, C. N. Likos, H. Löwen, Phys. Rev. Lett. 100, 108302 (2008)
T. Neuhaus, A. Härtel, M. Marechal, M. Schmiedeberg, H. Löwen, Eur. Phys. J. Special Topics 223, 373 (2014)
K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88, 245701 (2002)
K. Lichtner, A.J. Archer, S.H.L. Klapp, J. Chem. Phys. 136, 024502 (2012)
M. Rex, H.H. Wensink, H. Löwen, Phys. Rev. E 76, 021403 (2007)
R. Wittkowski, H. Löwen, H.R. Brand, Phys. Rev. E 82, 031708 (2010)
R. Wittkowski, H. Löwen, H.R. Brand, Phys. Rev. E 84, 041708 (2011)
H. Löwen, J. Phys.: Condens. Matter 22, 364105 (2010)
R. Wittkowski, H. Löwen, Molec. Phys. 109, 2935 (2011)
R. Wittkowski, H. Löwen, H.R. Brand, J. Chem. Phys. 137, 224904 (2012)
P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)
H.H. Wensink, H. Löwen, Phys. Rev. E 78, 031409 (2008)
A.M. Menzel, H. Löwen, Phys. Rev. Lett. 110, 055702 (2013)
F. Kümmel, B. ten Hagen, R. Wittkowski, I. Buttinoni, R. Eichhorn, G. Volpe, H. Löwen, C. Bechinger, Phys. Rev. Lett. 110, 198302 (2013)
X. Zheng, B. ten Hagen, A. Kaiser, M. Wu, H. Cui, Z. Silber-Li, H. Löwen, Phys. Rev. E 88, 032304 (2013)
S. van Teeffelen, H. Löwen, Phys. Rev. E 78, 020101 (2008)
M.B. Wan, C.J. Olson Reichhardt, Z. Nussinov, C. Reichhardt, Phys. Rev. Lett. 101, 018102 (2008)
C.A. Brackley, M.E. Cates, D. Marenduzzo, Phys. Rev. Lett. 109, 168103 (2012)
P.K. Ghosh, V.R. Misko, F. Marchesoni, F. Nori, Phys. Rev. Lett. 110, 268301 (2013)
M. Enculescu, H. Stark, Phys. Rev. Lett. 107, 058301 (2011)
H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. 109, 14308 (2012)
I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Phys. Rev. Lett. 108, 268303 (2012)
I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013)
J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)
J. Bialké, H. Löwen, T. Speck, EPL 103, 30008 (2013)
J. Bialké, T. Speck, H. Löwen, Phys. Rev. Lett. 108, 168301 (2012)
I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013)
J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)
J. Bialké, H. Löwen, T. Speck, EPL 103, 30008 (2013)
J. Bialké, T. Speck, H. Löwen, Phys. Rev. Lett. 108, 168301 (2012)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Löwen, H., Heinen, M. Dynamical density functional theory for the diffusion of injected Brownian particles. Eur. Phys. J. Spec. Top. 223, 3113–3127 (2014). https://doi.org/10.1140/epjst/e2014-02322-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02322-8