Lattice Boltzmann method (LBM) is used to model the hydrogen production by splitting water by incident sunlight over Si nanorods. The purpose of this study is to investigate the transport and the formation of the hydrogen bubbles by electrochemical reactions with a 2D and a 3D numerical model using LBM. An ordered array of nanorods is created where each rod is 10 μm in high and 10 nm in diameter. The numerical models are simulated using MATLAB and parallel computing with the program Palabos. A reaction–advection–diffusion transport for two components is analyzed with electrochemical reactions. This process is further coupled with the momentum transport. The effect of different bond numbers and contact angels on the simulation results are analyzed. It has here been shown that LBM can be used to evaluate the transport processes at microscale and it is possible to include the effect of electrochemical reactions on the transport processes. An increased Bond number increases the bubble flow through the nanorod domain. A decreased contact angle facilitates the disconnection of the bubble to the nanorod at the top surface. The collection of the hydrogen bubbles at the top surface of the nanorods will be facilitated by an easy disconnection of the bubbles.
LBM, bubble flow, microscale, mass diffusion, electrochemical reactions, bond number, contact angle
 Momirlan, M. & Veziroglu, T.N., Current status of hydrogen energy. Renewable and Sustainable Energy Reviews, 6, pp. 141–179, 2002. doi: http://dx.doi.org/10.1016/S1364-0321(02)00004-7
 Walter, M.G., Warren, E.L., McKone, J.R., Boettcher, S.W., Mi, Q., Santori, E.A. & Lewis, N.S., Solar water splitting cells. Chemical Review, 110, pp. 6446–6473, 2010. doi: http://dx.doi.org/10.1021/cr1002326
 Reyes Gil, K.R., Spurgeon, J.M. & Lewis, N.S., Silicon and tungsten oxide nanostructures for water splitting. Proceedings of SPIE Solar Hydrogen and Nanotechnology IV, ed. F.E. Osterloth, Vol. 7404, 74080S-1–74080S-11, 2009. doi: http://dx.doi.org/10.1117/12.825545
 Dawson, S.P., Chen, S. & Doolen, G.D., Lattice Boltzmann computations for reaction–diffusion equations. Journal of Chemical Physics, 98, pp. 1514–1523, 1993. doi: http://dx.doi.org/10.1063/1.464316
 Xu, Y.-S., Zhong, Y.-J. & Huang, G.-X., Lattice Boltzmann method for diffusion–reaction–transport processes in heterogeneous porous media. Chinese Physics Letters, 21(7), 2004.
 Clift, R., Grace, J.R. & Weber, M., Bubbles, Drops and Particles, Academic Press: New York, USA, 1978.
 Haussener, S., Xiang, C., Spurgeon, J.M., Ardo, S., Lewis, N.S. & Weber, A.Z., Modeling, simulation, and design criteria for photoelectrochemical water-splitting systems. Energy & Environmental Science, 5, pp. 9922–9935, 2012. doi: http://dx.doi.org/10.1039/c2ee23187e
 Leenheer, A.J. & Atwater, H.A., Water-splitting photoelectrolysis reaction rate via microscopic imaging of evolved oxygen bubbles. Journal of Electrochemical Society, 157, pp. B1290–B1294, 2010. doi: http://dx.doi.org/10.1149/1.3462997
 Joshi, A.S., Peracchio, A.A., Grew, K.N. & Chiu, W.K.S., Lattice Boltzmann method for multi-component, non-continuum mass diffusion. Journal of Physics D: Applied Physics, 40, pp. 7593–7600, 2007. doi: http://dx.doi.org/10.1088/0022-3727/40/23/053
 Sukop, M.C. & Thorne, D.J. Jr., Lattice Boltzmann Modeling – An Introduction for Geoscientists and Engineers, Springer: New York, USA, 2007.
 Latt, J., Hydrodynamic limit of the lattice Boltzmann equations. PhD Thesis, University of Geneva, 2007.
 Chen, S., Dawson, S.P., Doolen, G.D., Janecky, D.R. & Lawniczak, A., Lattice methods and their applications to reacting systems. Computers and Chemical Engineering, 19, pp. 617–646, 1995. doi: http://dx.doi.org/10.1016/0098-1354(94)00072-7
 Kang, Q.J., Lichtner, P.C. & Janecky,D.R., Lattice Boltzmann method for reacting flows in porous media. Advances in Applied Mathematics and Mechanics, 5, pp. 545–563, 2010.
 Shan, X. & Doolen, G., Diffusion in a multi-component lattice Boltzmann equation model. Technical Report, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, 2002.
 He, X. & Li, N., Lattice Boltzmann simulation of electrochemical systems. Computer Physics Communications, 129, pp. 158–166, 2000. doi: http://dx.doi.org/10.1016/S0010-4655(00)00103-X
 Thürey, N., Physically based animation of free surface fl ows with the lattice Boltzmann method. Doctoral Thesis, Der Technischen Fakultät, Universität Erlangen-Nürnberg, Erlangen-Nürnberg, Germany, 2007.
 Pohl, T., High performance simulation of free surface fl ows using the lattice Boltzmann method, Der Technischen Fakultät, Universität Erlangen-Nürnberg, Erlangen- Nürnberg, Germany, 2008.