7 tion which is opposite to the applied force. The inset of Fig. 5 illustrates this by showing the total displacement of the chain’s center of mass for the salt concentration ρ$_{s}$ = 0 . 05625 σ − 3 and various slip lengths. In nearly all cases except δ$_{B}$ ≈ 0, the total mobility of the polyelec- trolyte is negative. To summarize this section, both the assumptions and the predictions of section II are supported by our numer- ical results. The total mobility of the polyelectrolyte can therefore be adequately described by Eqs. (7) and (13). ing mobility µ$_{e}$ oppose each other, i.e. , if the effective charges on the polyelectrolyte and the walls have the same sign, the mobility may even become negative. As mentioned in the introduction, this effect has also been observed experimentally $^{4}$. In the other case, where the sign of the charges on the polyelectrolyte and the wall are opposite, the main effect of slip is to enhance the total mobility of the polyelectrolyte. In summary, the total mobility of polyelectrolytes in microchannels results from an interplay of electroos- motic, electrophoretic, electrostatic and slippage effects. The latter have a particularly strong influence and can be used to design channels with improved properties. For example, the characteristics of the channel walls could be designed to tune effective slip lengths 27 and hence flow velocities, which offers the possibility to optimize the time which is needed for polymer migration or sep- aration techniques. This could be an important aspect for future applications in microchannels or micropumps to accelerate measuring times. We have presented mesoscopic DPD simulations of polyelectrolyte electrophoresis in narrow microchannels, taking full account of hydrodynamic and electrostatic in- teractions. A particular focus was put on studying the effects of the hydrodynamic boundary conditions at the channel walls on the electroosmotic flow and on the net electrophoretic mobility of the polyelectrolyte. We have shown that they can be incorporated into a single dimen- sionless parameter (1 + κ δ$_{B}$ ), where δ$_{B}$ is the slip length and κ the (local) inverse screening length of the charge distribution at the wall. This was derived analytically and supported by our numerical data. It remained valid even for very narrow channels, where the chain confor- mations were affected by the confinement. We have shown that wall slip massively enhances the EOF and hence influences the total mobility of the poly- electrolyte. If the EOF mobility µ$_{EOF}$ and the free drain- We thank Christian Holm, Burkhard D¨ unweg, Ulf D. Schiller, Marcello Sega and Kai Grass for nice and fruitful discussions and the Arminius PC 2 Cluster at Paderborn University, HLRS Stuttgart and NIC J¨ ulich for comput- ing time. J. S. especially thanks Stefanie G¨ urtler and Theodor A. Smiatek. Financial funding from the Volk- swagen Stiftung is gratefully acknowledged. Acknowledgments V. CONCLUSIONS ∗ Electronic address: jens.smiatek@uni-muenster.de † Electronic address: Friederike.Schmid@Uni-Mainz.DE 1 Viovy, J.-L. Rev. Mod. Phys. 2000 , 72 , 813. 2 Iki, N.; Kim, Y.; Yeung, E. S. Anal. Chem. 1996 , 68 , 4321. 3 Roeraade, M.; Stjernstr¨ om, M. International Patent WO/1997/26531, 1997 , avaible at http://www.wipo.int . 4 Mathe, J.; Di Meglio, J.-M.; Tinland, B. J. Colloid Inter- face Sci. 2007 , 316 , 831. 5 Effenhauser, C. S.; Bruin, G. J. M.; Paulus, A. Elec- trophoresis 1997 , 18 , 2203. 6 Bader, J. S.; Hammond, R. W.;, Henck, S. A.; Deem, M. W.; McDermott, G. A.; Bustillo, J. M.; Simpson, J. W.; Rothberg, J. M. PNAS 1999 , 96 13165. 7 Han, J.; Craighead, G. Science 2000 , 288 , 1026. 8 Han, J.; Turner, S. W.; Craighead, G. Phys. Rev. Lett. 2002 , 83 , 1688. 9 Huang, L. R.; Tegenfeldt, J. O.; Kraeft, J. J.; Sturm, J. C.; Austin, R. H.; Cox, E. C. Nature Biotechnology 2002 , 20 , 1048. 10 Duong, T. T.; Ros, R.; Streek, M.; Schmid, F.; Brugger, J.; Anselmetti, D.; Ros, A. Microelectronic Engineering 2003 , 67-68 , 905. 11 Ros, A.; Hellmich, W.; Duong, T. T.; Anselmetti, D. J. Biotechnology 2004 , 112 , 65. 12 Manning, G. S. J. Phys. Chem. 1981 , 85 , 1506. 13 Barrat, J.-L.; Joanny, J. F. J. F. Adv. Chem. Phys. 1996 , XCIV , 1. 14 Streek, M.; Schmid, F.; Duong, T. T.; Ros, A. J. Biotech- nology 2004 , 112 , 79. 15 Streek, M.; Schmid, F.; Duong, T. T.; Ros, A. Phys. Rev. E 2005 , 71 , 11905. 16 Duong-Hong, D.; Han, J.; Wang, J. S.; Hadjiconstantinou, N. G.; Chen, Y. Z.; Liu, G. R. Electrophoresis 2008 , 29 , 4880. 17 Slater, G. W.; Holm, C.; Chubynsky, M. V.; de Haan, H. W.; Dube, A.; Grass, K.; Hickey, O. A.; Kingsburry, C.; Sean, D.; Shendruk, T. N.; Nhan, L. X. Electrophoresis 2009 , 30 , 792. 18 Long, D.; Viovy, J.-L.; Ajdari, A. Phys. Rev. Lett. 1996 , 76 , 3858. 19 Grass, K.; B¨ ohme, U.; Scheler, U.; Cottet, H.; Holm, C. Phys. Rev. Lett. 2008 , 100 , 096104. 20 Frank, S.; Winkler, R. G. Europhys. Lett. 2008 , 83 , 38004. 21 Cummings, E. B.; Griffiths, S. K.; Nilson, R. H.; Paul, P. H. Anal. Chem. 2000 , 72 , 2526. 22 We note that it is always possible to separate a steady ve- locity field v ( r ) into an EOF component v$_{EOF}$ ( r ) which satisfies the EOF boundary conditions, and a residual (e.g., Poiseuille flow) component with no-slip boundary condi- tions at the wall and arbitrary boundary conditions at the