{"id":10907,"date":"2024-01-01T18:27:28","date_gmt":"2024-01-01T18:27:28","guid":{"rendered":"http:\/\/lequia-udg.com\/2024\/01\/01\/investigating-the-impact-of-adsorbent-particle-size-on-column-adsorption-kinetics-through-a-mathematical-model\/"},"modified":"2024-03-20T17:02:07","modified_gmt":"2024-03-20T17:02:07","slug":"investigating-the-impact-of-adsorbent-particle-size-on-column-adsorption-kinetics-through-a-mathematical-model","status":"publish","type":"post","link":"https:\/\/lequia-udg.com\/ca\/2024\/01\/01\/investigating-the-impact-of-adsorbent-particle-size-on-column-adsorption-kinetics-through-a-mathematical-model\/","title":{"rendered":"Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"10907\" class=\"elementor elementor-10907 elementor-5834\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3b9c6acc ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3b9c6acc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-779604b8 ts-bg-color-over-image\" data-id=\"779604b8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-628701ff ts-align-left elementor-widget elementor-widget-ts_heading\" data-id=\"628701ff\" data-element_type=\"widget\" data-widget_type=\"ts_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t<div class=\"ts-heading-subheading ts-reverse-heading-yes animation-style4\"><h4 class=\"ts-custom-heading ts-custom-subtitle\">\r\n\t\t\t\r\n\t\t\t\tAuthors: Valverde, Abel; Cabrera-Codony, Alba; Calvo-Schwarzwalder, Marc; Myers, Timothy G.                                                                                                         \r\n\t\t\t\r\n\t\t\t<\/h4>\r\n\t\t<h2 class=\"ts-custom-heading ts-custom-heading-title\">\r\n\t\t\t\r\n\t\t\t\tInvestigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model\r\n\t\t\t\r\n\t\t\t<\/h2>\r\n\t\t<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b30bf09 ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b30bf09\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3f1dcf32 ts-bg-color-over-image\" data-id=\"3f1dcf32\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5fd8f604 elementor-widget-tablet__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"5fd8f604\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Experimental data demonstrates that the breakthrough curves of column adsorption exhibit qualitative differences related to the size of the adsorbent particles. Standard models do not account for particle size, consequently, in this paper we develop a new formulation that incorporates the diffusion of the adsorbate into the adsorbent particles. Two kinetic models are considered, Langmuir adsorption and a linear driving force. Approximate analytical solutions are developed for these two models coupled to mass flow and intra-particle diffusion equations. The accuracy of the analytical solutions is verified through comparison with numerical solutions of the full mathematical model. Comparison with experimental data confirms that the new analytical solutions show better agreement than previous models. However, in certain cases, neither form of model predicts the behaviour suggesting a combination of different effects contribute to the breakthrough form.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-32900d78 ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"32900d78\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-469beba3 ts-bg-color-over-image\" data-id=\"469beba3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1d1d17af elementor-widget elementor-widget-accordion\" data-id=\"1d1d17af\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-4881\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-4881\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-plus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-minus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Informaci\u00f3 addicional<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-4881\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-4881\"><table style=\"border: hidden;\">\n<tbody>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Any:<\/strong><\/td>\n<td>2024<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Autors:<\/strong><\/td>\n<td>Valverde, Abel; Cabrera-Codony, Alba; Calvo-Schwarzwalder, Marc; Myers, Timothy G.<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong><span class=\"catItemExtraFieldsLabel\">Refer\u00e8ncia<\/span>:<\/strong><\/td>\n<td>International Journal of Heat and Mass Transfer, 218, 124724<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Enlla\u00e7:<\/strong><\/td>\n<td><a href=\"http:\/\/dx.doi.org\/10.1016\/j.ijheatmasstransfer.2023.124724\" target=\"_blank\" rel=\"noopener\">http:\/\/dx.doi.org\/10.1016\/j.ijheatmasstransfer.2023.124724<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5eaf7970 elementor-widget elementor-widget-spacer\" data-id=\"5eaf7970\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Authors: Valverde, Abel; Cabrera-Codony, Alba; Calvo-Schwarzwalder, Marc; Myers, Timothy G. Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model Experimental data demonstrates that the breakthrough curves of column adsorption exhibit qualitative differences related to the size of the adsorbent particles. Standard models do not account for particle size, consequently, &hellip; <a href=\"https:\/\/lequia-udg.com\/ca\/2024\/01\/01\/investigating-the-impact-of-adsorbent-particle-size-on-column-adsorption-kinetics-through-a-mathematical-model\/\" class=\"more-link\" title=\"Continue reading <span class=\"screen-reader-text\">Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model<\/span>&#8220;>Continue reading <span class=\"screen-reader-text\">Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[64],"tags":[],"class_list":["post-10907","post","type-post","status-publish","format-standard","hentry","category-articles-ca"],"_links":{"self":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/10907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/comments?post=10907"}],"version-history":[{"count":1,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/10907\/revisions"}],"predecessor-version":[{"id":10908,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/10907\/revisions\/10908"}],"wp:attachment":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/media?parent=10907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/categories?post=10907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/tags?post=10907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}