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Molecular simulations of electroosmotic flows in rough nanochannels. (English) Zbl 1197.78017

Summary: A highly efficient molecular dynamics algorithm for micro and nanoscale electrokinetic flows is developed. The long-range Coulomb interactions are calculated using the Particle-Particle Particle-Mesh (P\(^3\)M) approach. The Poisson equation for the electrostatic potential is solved in physical space using an iterative multi-grid technique. After validation, the method is used to study electroosmotic flow in nanochannels with regular or random roughness on the walls. The results show that roughness reduces the electroosmotic flow rate dramatically even though the roughness is very small compared to the channel width. The effect is much larger than for pressure driven flows because the driving force is localized near the walls where the charge distribution is high. Non-Newtonian behavior is also observed at much lower flow rates. Systematic investigation of the effect of surface charge density and random roughness will help to better understand the mechanism of electrokinetic transport in rough nanochannels and to design and optimize nanofluidic devices.

MSC:

78A30 Electro- and magnetostatics
78A45 Diffraction, scattering
76W05 Magnetohydrodynamics and electrohydrodynamics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
76A05 Non-Newtonian fluids

Software:

Wesseling
Full Text: DOI

References:

[1] Sharp, K. A.; Honig, B., Electrostatic interactions in macromolecules: theory and applications, Annu. Rev. Biophys. Biophys. Chem., 19, 310-332 (1990)
[2] Honig, B.; Nicholls, A., Classical electrostatics in biology and chemistry, Science, 268, 1144-1149 (1995)
[3] Yang, C.; Li, D. Q., Analysis of electrokinetic effects on liquid flow in rectangular microchannels, Colloids Surf. A, 143, 339-353 (1998)
[4] Li, D. Q., Electro-viscous effects on pressure-driven liquid flow in microchannels, Colloids Surf. A, 195, 35-57 (2001)
[5] Li, D. Q., Electrokinetics in Microfluidics (2004), Academic: Academic Oxford
[6] Hu, Y. D.; Werner, C.; Li, D. Q., Electrokinetic transport through rough microchannels, Anal. Chem., 75, 5747-5758 (2003)
[7] Hu, Y. D.; Werner, C.; Li, D. Q., Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels, J. Colloid Interf. Sci., 280, 527-536 (2004)
[8] Wang, J. K.; Wang, M.; Li, Z. X., Lattice Boltzmann simulations of mixing enhancement by the electro-osmotic flow in microchannels, Mod. Phys. Lett. B, 19, 1515-1518 (2005) · Zbl 1096.76044
[9] Guo, Z. L.; Zhao, T. S.; Shi, Y., A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices, J. Chem. Phys., 112, 14, 144907 (2005)
[10] Wang, J. K.; Wang, M.; Li, Z. X., Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels, J. Colloid Interf. Sci., 296, 2, 729-736 (2006)
[11] Wang, M.; Wang, J. K.; Chen, S. Y., Roughness and cavitations effects on electro-osmotic flows in rough microchannels using lattice Poisson-Boltzmann methods, J. Comput. Phys., 226, 836-851 (2007) · Zbl 1310.76148
[12] Qiao, R.; Aluru, N. R., Ion concentrations and velocity profiles in nanochannel electroosmotic flows, J. Chem. Phys., 118, 10, 4692-4701 (2003)
[13] Thompson, A. P., Nonequilibrium molecular dynamics simulation of electro-osmotic flow in a charged nanopore, J. Chem. Phys., 119, 14, 7503-7511 (2003)
[14] Kim, D.; Darve, E., Molecular dynamics simulation of electro-osmotic flows in rough wall nanochannels, Phys. Rev. E, 73, 051203 (2006)
[15] Wang, M.; Liu, J.; Chen, S. Y., Similarity of electroosmotic flows in nanochannels, Mol. Simul., 33, 239-244 (2007)
[16] Wang, M.; Liu, J.; Chen, S. Y., Electric potential distribution in nanoscale electroosmosis: from molecules to continuum, Mol. Simul., 33, 1273-1277 (2007)
[17] Qiao, R., Effects of molecular level surface roughness on electroosmotic flow, Microfluid. Nanofluid., 3, 33-38 (2007)
[18] Toukmaji, A. Y.; Board, J. A., Ewald summation techniques in perspective: a survey, Comput. Phys. Commun., 95, 73-92 (1996) · Zbl 0923.65090
[19] Ewald, P., Evaluation of optical and electrostatic lattice potentials, Ann. Phys., 64, 253-287 (1921) · JFM 48.0566.02
[20] Perram, J. W.; Petersen, H. G.; de Leeuw, S. W., An algorithm for simulation of condensed matter which grows as the 3/2 power of the number of particles, Mol. Phys., 65, 875-889 (1988)
[21] Darden, T.; York, D.; Pedersen, L., Particle mesh Ewald: an \(N\)·log \((N)\) method for Ewald sums in large systems, J. Chem. Phys., 98, 10089-10092 (1993)
[22] Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J. Comput. Phys., 73, 325-348 (1987) · Zbl 0629.65005
[23] Pollock, E. L.; Glosli, J., Comments on \(P^3\) M, FMM, and the Ewald method for large periodic Coulombic systems, Comput. Phys. Commun., 95, 93-110 (1996) · Zbl 0921.65081
[24] Beckers, J. V.L.; Lowe, C. P.; de Leeuw, S. W., An iterative PPPM method for simulating Coulombic systems on distributed memory parallel computers, Mol. Simul., 20, 369-383 (1998) · Zbl 0961.81500
[25] Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1981), McGraw-Hill: McGraw-Hill New York · Zbl 0662.76002
[26] Luty, B. A.; van Gunsteren, W. F., Calculating electrostatic interactions using the Particle-Particle Particle-Mesh method with nonperiodic long-range interactions, J. Phys. Chem., 100, 2581-2587 (1996)
[27] Allen, M. P.; Tildesley, D. J., Computer Simulation of Liquids (1987), Clarendon Press: Clarendon Press Oxford · Zbl 0703.68099
[28] Grest, G. S.; Kremer, K., Molecular dynamics simulation for polymers in the presence of a heat bath, Phys. Rev. A, 33, 3628-3631 (1986)
[29] Shan, Y.; Klepeis, J. L.; Eastwood, M. P.; Dror, R. O.; Shaw, D. E., Gaussian split Ewald: a fast Ewald mesh method for molecular simulation, J. Chem. Phys., 122, 054101 (2005), 1-13
[30] Aboud, S.; Marreiro, D.; Saraniti, M.; Eisenberg, R., A Poisson \(P^3\) M force field scheme for particle-based simulations of ionic liquids, J. Comput. Electron., 3, 117-133 (2004)
[31] Hackbush, W., Multi-Grid Methods and Applications (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0595.65106
[32] Wesseling, P., An Introduction to Multigrid Methods (1991), J. Wiley: J. Wiley New York
[33] Xu, J., Iterative methods by space decomposition and subspace correction, SIAM Rev., 34, 581-613 (1992) · Zbl 0788.65037
[34] Shu, S.; Sun, D.; Xu, J., An algebraic multigrid method for higher-order finite element discretizations, Computing, 77, 347-377 (2006) · Zbl 1127.65092
[35] Parry, D. E., The electrostatic potential in the surface region of an ionic crystal, Surf. Sci., 49, 433-440 (1975)
[36] Liem, S. Y.; Clarke, J. H.R., Calculation of Coulomb interactions in two-dimensionally periodic systems, Mol. Phys., 92, 19-25 (1997)
[37] Widmann, A. H.; Adolf, D. B., A comparison of Ewald summation techniques for planar surfaces, Comput. Phys. Commun., 107, 167-186 (1997) · Zbl 0939.81525
[38] Spohr, E., Effect of electrostatic boundary conditions and system size on the interfacial properties of water and aqueous solutions, J. Chem. Phys., 107, 6342-6348 (1997)
[39] Yeh, I.; Berkowitz, M. L., Ewald summation for systems with slab geometry, J. Chem. Phys., 111, 3155-3162 (1999)
[40] Karniadakis, G. E.; Beskok, A., Micro Flows (2002), Springer-Verlag: Springer-Verlag Berlin · Zbl 0998.76002
[41] Nie, X. B.; Chen, S. Y.; E, W.; Robbins, M. O., A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow, J. Fluid Mech., 500, 55-64 (2004) · Zbl 1059.76060
[42] Liu, J.; Chen, S. Y.; Nie, X. B.; Robbins, M. O., A continuum-atomistic simulation of heat transfer in micro- and nano-flows, J. Comput. Phys., 227, 279-291 (2007) · Zbl 1130.80010
[43] Thompson, P. A.; Robbins, M. O., Shear flow near solids: epitaxial order and flow boundary conditions, Phys. Rev. A, 41, 6830-6837 (1990)
[44] Thompson, P. A.; Troian, S. M., A general boundary condition for liquid flow at solid surfaces, Nature, 389, 360-363 (1997)
[45] Liu, J.; Chen, S. Y.; Nie, X. B.; Robbins, M. O., A continuum-atomistic multi-timescale algorithm for micro/nano flows, Commun. Comput. Phys., 4, 1279-1291 (2008)
[46] Wang, M.; Kang, Q., Electrokinetic transport in microchannels with random roughness, Anal. Chem., 81, 2953-2961 (2009)
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