Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-07-11T17:32:14Z No. of bitstreams: 1 JulyHerbertDaSilvaMariano_DISSERT.pdf: 1467170 bytes, checksum: 580209f3bb69ab431e0c78eef36c48f4 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-07-15T21:55:59Z (GMT) No. of bitstreams: 1 JulyHerbertDaSilvaMariano_DISSERT.pdf: 1467170 bytes, checksum: 580209f3bb69ab431e0c78eef36c48f4 (MD5) / Made available in DSpace on 2016-07-15T21:55:59Z (GMT). No. of bitstreams: 1 JulyHerbertDaSilvaMariano_DISSERT.pdf: 1467170 bytes, checksum: 580209f3bb69ab431e0c78eef36c48f4 (MD5) Previous issue date: 2015-11-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Nesta disserta??o de mestrado, propomos uma modelagem computacional multiescala de fen?menos eletrocin?ticos em meios poroso carregados eletricamente. Consideramos um meio poroso r?gido e incompress?vel saturado por uma solu??o eletrol?tica contendo quatro solutos i?nicos monovalentes totalmente dilu?dos no solvente.Inicialmente, desenvolvemos a modelagem da dupla camada el?trica com a inten??o de computar o potencial el?trico, densidade superficial de cargas el?tricas e, considerando duas rea??es qu?micas, propomos um modelo 2-pK para calcular as adsor??es qu?micas que ocorrem no dom?nio da dupla camada el?trica. De posse do modelo nanosc?pico, desenvolvemos um modelo na microescala, onde as adsor??es eletroqu?micas de ?ons no dom?nio da camada dupla, rea??es de protona??o/deprotona??o e potencial zeta obtidos na escala nanosc?pica, s?o incorporados ao modelo na escala microsc?pica atrav?s das condi??es de interface fluido/s?lido do problema de Stokes e no transporte dos ?ons, modelado pelas equa??es de Nerst-Planck. Usando a t?cnica de homogeneiza??o de estrutura peri?dicas juntamente com a hip?tese de periodicidade do meio, deduzimos um modelo na escala macrosc?pica com respectivos problemas de c?lulas para os par?metros efetivos das equa??es macrosc?picas.Finalmente, fazendo uso do modelo 2-pK, simulamos os fen?menos de adsor??es eletroqu?micas em uma caulinita saturada por uma solu??o aquosa na micro escala. Em seguida fazemos duas simula??es macrosc?picas em regimes ?cidos e b?sico com a intens?o de observar a influ?ncia dos fen?menos na escala nano/microsc?pica sobre a macroescala. / In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.