Lattice evolution solution for the nonlinear Poisson–Boltzmann equation in confined domains

Journal of Colloid and Interface Science

Chen

2007

Self Cite

121

Electroosmosis in homogeneously charged micro-and nanoscale random porous media has been numerically investigated using mesoscopic simulation methods which involve a random generation-growth method for reproducing three-dimensional random microstructures of porous media and a high-efficiency lattice Poisson-Boltzmann algorithm for solving the strongly nonlinear governing equations of electroosmosis in three-dimensional porous media. The numerical modeling and predictions of EOF in micro-and nanoscale random porous media indicate: the electroosmotic permeability increases monotonically with the porosity of porous media and the increasing rate rises with the porosity as well; the electroosmotic permeability increases with the average solid particle size for a given porosity and with the bulk ionic concentration as well; the proportionally linear relationship between the electroosmotic permeability and the zeta potential on solid surfaces breaks down for high zeta potentials. The present predictions agree well with the available experimental data while some results deviate from the predictions based on the macroscopic theories.

Section: Lattice Poisson-boltzmann Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electroosmosis in homogeneously charged micro- and nanoscale random porous media

Journal of Colloid and Interface Science

Chen

2007

Self Cite

121

“…Electric charge conversation can be considered as an additional restrict for certain solution under the Neumann boundary condition, which brings a big additional computational cost as well. Recent investigations show a lattice evolution method can deal with this problem easily [26]. [Insert Figure 1 here]…”

Section: Continuum Modelsmentioning

confidence: 99%

Electric potential distribution in nanoscale electroosmosis: from molecules to continuum

Liu

Chen

2008

Molecular Simulation

Electric potential distribution in nanoscale electroosmosis has been investigated using the nonequilibrium molecular dynamics (NEMD), whose results are compared with the continuum based Poisson-Boltzmann (PB) theory. If the bin size of the MD simulation is no smaller than a molecular diameter and the focusing region is limited to the diffusion layer, the ionic density profiles on the bins of the MD results agree well with the predictions based on the Poisson-Boltzmann theory for low and moderate bulk ionic concentrations. The PB equation breaks down at high bulk ionic concentrations, which is also consistent with the macroscopic description.

“….~ C g where c g IS the lattice speed for the electric potential propagation 41 The dimensionless relaxation time is (29) It has been proved that c!' can be any positive number only ensuring the value of Til: within 0.5 and 2 41,42. After evolving on the discrete lattices, the macroscopic electric potential can be calculated using a…”

Section: Fig 4 the Lattice Direction System (A) For D3q 15 Modelmentioning

confidence: 99%

Electrokinetic Transport in Microchannels with Random Roughness

Kang

2009

Anal. Chem.

Self Cite

I Email address: mwang(a),lanl.!!ov (M.W.); gkang@lanLgov (Q.K) Electrokinetic tr"t1'~n{',rt In microchannels Abstract: We present a numerical framework to model the electrokinetic transport in microchannels with random roughness. The three-dimensional microstructure of the rough channel is generated by a random generation-growth method with three statistical parameters to control the number density, the total volume fraction and anisotropy characteristics of roughness elements. The governing equations for the electrokinetic transport are solved by a high efficiency lattice Poisson-Boltzmann method in complex geometries. The effects from the geometric characteristics of roughness on the electrokinetic transport in microchannels are therefore modeled and analyzed. For a given total roughness volume fraction, a higher number density leads to a lower fluctuation due to the random factors. The electroosmotic permeability increases with the roughness number density nearly at a logarithmic law for a given volume fraction of roughness, but decreases with the volume fraction of roughness for a given roughness number density. When both the volume fraction and the number density of roughness are given, the electroosmotic permeability is enhanced by increases of the characteristic length along the external electric field direction or decreases of the length of the direction of across the channel.For a given microstructure of rough microchannel, the electroosmotic permeability decreases with the Debye length. Compared with the corresponding flows in a smooth channel, the rough surface may enhance the electrokinetic transport when the Debye length is smaller than the roughness characteristic height under the assumption of constant zeta potential for all surfaces.The present results may improve the understanding of the electrokinetic transport characteristics in microchannels.