{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:11:30Z","timestamp":1772295090753,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,1,28]],"date-time":"2014-01-28T00:00:00Z","timestamp":1390867200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s10915-014-9820-6","type":"journal-article","created":{"date-parts":[[2014,1,27]],"date-time":"2014-01-27T08:24:34Z","timestamp":1390811074000},"page":"222-238","source":"Crossref","is-referenced-by-count":40,"title":["A Coupled Lattice Boltzmann Method to Solve Nernst\u2013Planck Model for Simulating Electro-osmotic Flows"],"prefix":"10.1007","volume":"61","author":[{"given":"Xuguang","family":"Yang","sequence":"first","affiliation":[]},{"given":"Baochang","family":"Shi","sequence":"additional","affiliation":[]},{"given":"Zhenhua","family":"Chai","sequence":"additional","affiliation":[]},{"given":"Zhaoli","family":"Guo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,28]]},"reference":[{"key":"9820_CR1","volume-title":"The MEMS Handbook","author":"M Gad-el-Hak","year":"2002","unstructured":"Gad-el-Hak, M.: The MEMS Handbook. CRC Press, Boca Raton, FL (2002)"},{"key":"9820_CR2","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1146\/annurev.fluid.36.050802.122124","volume":"36","author":"HA Stone","year":"2004","unstructured":"Stone, H.A., Stroock, A.D., Ajdari, A.: Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381\u2013411 (2004)","journal-title":"Annu. Rev. Fluid Mech."},{"key":"9820_CR3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.physleta.2006.12.006","volume":"364","author":"ZH Chai","year":"2007","unstructured":"Chai, Z.H., Shi, B.C.: Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method. Phys. Lett. A 364, 183\u2013188 (2007)","journal-title":"Phys. Lett. A"},{"issue":"7","key":"9820_CR4","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1142\/S0129183107011200","volume":"18","author":"ZH Chai","year":"2007","unstructured":"Chai, Z.H., Shi, B.C., Zheng, L.: Lattice Boltzmann simulation of viscous dissipation in electro-osmotic flow in microchannels. Int. J. Mod. Phys. C 18(7), 1119\u20131131 (2007)","journal-title":"Int. J. Mod. Phys. C"},{"issue":"2","key":"9820_CR5","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/S0021-9797(02)00078-4","volume":"258","author":"LM Fu","year":"2003","unstructured":"Fu, L.M., Lin, J.Y., Yang, R.J.: Analysis of electroosmotic flow with step change in zeta potential. J. Colloid Interface Sci. 258(2), 266\u2013275 (2003)","journal-title":"J. Colloid Interface Sci."},{"issue":"2","key":"9820_CR6","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.jcis.2007.07.007","volume":"315","author":"HM Park","year":"2007","unstructured":"Park, H.M., Lee, J.S., Kim, T.W.: Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels. J. Colloid Interface Sci. 315(2), 731\u2013739 (2007)","journal-title":"J. Colloid Interface Sci."},{"issue":"1\u20133","key":"9820_CR7","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.colsurfa.2009.02.017","volume":"339","author":"S Bhattacharyya","year":"2009","unstructured":"Bhattacharyya, S., Nayak, A.K.: Electroosmotic flow in micro\/nanochannels with surface potential heterogeneity: An analysis through the Nernst-Planck model with convection effect. Colloid Surf. A 339(1\u20133), 167\u2013177 (2009)","journal-title":"Colloid Surf. A"},{"issue":"1","key":"9820_CR8","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1006\/jcis.2001.7847","volume":"224","author":"RJ Yang","year":"2001","unstructured":"Yang, R.J., Fu, L.M., Hwang, C.C.: Electro-osmotic entry flow in a microchannel. J. Colloid Interface Sci. 224(1), 173\u2013179 (2001)","journal-title":"J. Colloid Interface Sci."},{"issue":"7","key":"9820_CR9","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1002\/nme.1965","volume":"71","author":"EYK Ng","year":"2007","unstructured":"Ng, E.Y.K., Tan, S.T.: Study of EDL effect on 3-D developing flow in microchannel with Poisson-Boltzmann and Nernst-Planck models. Int. J. Numer. Methods Eng. 71(7), 818\u2013836 (2007)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"10","key":"9820_CR10","doi-asserted-by":"crossref","first-page":"A1576","DOI":"10.1149\/1.1789154","volume":"151","author":"Z Chen","year":"2004","unstructured":"Chen, Z.: Comparison of the mobile charge distribution models in mixed ionic-electronic conductors. J. Electrochem. Soc. 151(10), A1576\u2013A1583 (2004)","journal-title":"J. Electrochem. Soc."},{"key":"9820_CR11","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0370-1573(92)90090-M","volume":"222","author":"R Benzi","year":"1992","unstructured":"Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145\u2013197 (1992)","journal-title":"Phys. Rep."},{"key":"9820_CR12","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1146\/annurev-fluid-121108-145519","volume":"42","author":"CK Aidun","year":"2010","unstructured":"Aidun, C.K., Clausen, J.R.: Lattice Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439\u2013472 (2010)","journal-title":"Annu. Rev. Fluid Mech."},{"issue":"9","key":"9820_CR13","doi-asserted-by":"crossref","first-page":"4492","DOI":"10.1063\/1.1644107","volume":"120","author":"S Melchionna","year":"2004","unstructured":"Melchionna, S., Succi, S.: Electrorheology in nanopores via lattice Boltzmann simulation. J. Chem. Phys. 120(9), 4492\u20134497 (2004)","journal-title":"J. Chem. Phys."},{"issue":"5","key":"9820_CR14","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1002\/fld.765","volume":"46","author":"D Hlushkou","year":"2004","unstructured":"Hlushkou, D., Kandhai, D., Tallarek, U.: Coupled lattice-Boltzmann and finite-difference simulation of electroosmosis in microfluidic channels. Int. J. Numer. Methods Fluids 46(5), 507\u2013532 (2004)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"1\u20133","key":"9820_CR15","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/S0010-4655(00)00103-X","volume":"129","author":"X He","year":"2000","unstructured":"He, X., Li, N.: Lattice Boltzmann simulation of electrochemical systems. Comput. Phys. Commun. 129(1\u20133), 158\u2013166 (2000)","journal-title":"Comput. Phys. Commun."},{"issue":"3","key":"9820_CR16","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1016\/j.jcp.2009.10.006","volume":"229","author":"MR Wang","year":"2010","unstructured":"Wang, M.R., Kang, Q.J.: Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods. J. Comput. Phys. 229(3), 728\u2013744 (2010)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"9820_CR17","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1209\/0295-5075\/17\/6\/001","volume":"17","author":"YH Qian","year":"1992","unstructured":"Qian, Y.H., d\u2019Humi\u00e9res, D., Lallemand, P.: Lattice BGK model for Navier-Stokes equations. Europhys. Lett. 17(6), 479\u2013484 (1992)","journal-title":"Europhys. Lett."},{"issue":"6","key":"9820_CR18","doi-asserted-by":"crossref","first-page":"6546","DOI":"10.1103\/PhysRevE.61.6546","volume":"61","author":"P Lallemand","year":"2000","unstructured":"Lallemand, P., Luo, L.S.: Theory of the Lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61(6), 6546 (2000)","journal-title":"Phys. Rev. E"},{"issue":"3","key":"9820_CR19","doi-asserted-by":"crossref","first-page":"036707","DOI":"10.1103\/PhysRevE.77.036707","volume":"77","author":"ZL Guo","year":"2008","unstructured":"Guo, Z.L., Zheng, C.G., Shi, B.C.: Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Phys. Rev. E 77(3), 036707 (2008)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"9820_CR20","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1016\/j.physleta.2006.07.074","volume":"359","author":"R Du","year":"2006","unstructured":"Du, R., Shi, B.C., Chen, X.W.: Multi-relaxation-time lattice Boltzmann model for incompressible flow. Phys. Lett. A 359(6), 564\u2013572 (2006)","journal-title":"Phys. Lett. A"},{"issue":"4","key":"9820_CR21","doi-asserted-by":"crossref","first-page":"046308","DOI":"10.1103\/PhysRevE.65.046308","volume":"65","author":"ZL Guo","year":"2002","unstructured":"Guo, Z.L., Zheng, C.G., Shi, B.C.: Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65(4), 046308 (2002)","journal-title":"Phys. Rev. E"},{"issue":"10","key":"9820_CR22","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1016\/j.apm.2007.06.033","volume":"32","author":"ZH Chai","year":"2008","unstructured":"Chai, Z.H., Shi, B.C.: A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32(10), 2050\u20132058 (2008)","journal-title":"Appl. Math. Model."},{"issue":"1","key":"9820_CR23","doi-asserted-by":"crossref","first-page":"016701","DOI":"10.1103\/PhysRevE.79.016701","volume":"79","author":"BC Shi","year":"2009","unstructured":"Shi, B.C., Guo, Z.L.: Lattice Boltzmann model for nonlinear convection\u2013diffusion equations. Phys. Rev. E 79(1), 016701 (2009)","journal-title":"Phys. Rev. E"},{"issue":"7","key":"9820_CR24","doi-asserted-by":"crossref","first-page":"1568","DOI":"10.1016\/j.camwa.2007.08.016","volume":"55","author":"BC Shi","year":"2008","unstructured":"Shi, B.C., Deng, B., Du, R., Chen, X.W.: A new scheme for source term in LBGK model for convection\u2013diffusion equation. Comput. Math. Appl. 55(7), 1568\u20131575 (2008)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"9820_CR25","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1088\/1009-1963\/11\/4\/310","volume":"11","author":"ZL Guo","year":"2002","unstructured":"Guo, Z.L., Zheng, C.G., Shi, B.C.: Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11(4), 366 (2002)","journal-title":"Chin. Phys."},{"key":"9820_CR26","doi-asserted-by":"crossref","unstructured":"Tian, F., Li, B., Kwok, D.Y.: Lattice Boltzmann Simulation of Electroosmotic Flows in Micro- and Nanochannels. International Conference on MEMS, NANO, and Smart Systems (ICMENS) of 2004, Banff, Alberta, Canada, 294 (2004)","DOI":"10.1115\/ICMM2004-2435"},{"issue":"1\u20132","key":"9820_CR27","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1014510704701","volume":"107","author":"W Miller","year":"2002","unstructured":"Miller, W., Succi, S.: A lattice Boltzmann model for anisotropic crystal growth from melt. J. Stat. Phys. 107(1\u20132), 173\u2013186 (2002)","journal-title":"J. Stat. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9820-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/article\/10.1007\/s10915-014-9820-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9820-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T02:16:24Z","timestamp":1688955384000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/10.1007\/s10915-014-9820-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,28]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["9820"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/s10915-014-9820-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,28]]}}}