{"id":14536,"date":"2025-07-17T13:39:03","date_gmt":"2025-07-17T13:39:03","guid":{"rendered":"https:\/\/lequia-udg.com\/2025\/07\/17\/an-analytical-model-for-column-adsorption-with-two-competing-contaminants\/"},"modified":"2025-08-28T08:41:02","modified_gmt":"2025-08-28T08:41:02","slug":"an-analytical-model-for-column-adsorption-with-two-competing-contaminants","status":"publish","type":"post","link":"https:\/\/lequia-udg.com\/ca\/2025\/07\/17\/an-analytical-model-for-column-adsorption-with-two-competing-contaminants\/","title":{"rendered":"An analytical model for column adsorption with two competing contaminants"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"14536\" class=\"elementor elementor-14536 elementor-14530\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ef6a9fc ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ef6a9fc\" 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-79cef1b6 ts-bg-color-over-image\" data-id=\"79cef1b6\" 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-6431c80 ts-align-left elementor-widget elementor-widget-ts_heading\" data-id=\"6431c80\" 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:   M. Calvo-Schwarzwalder, T.G. Myers, A. Cabrera-Codony, A. Valverde                                                                                                      \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\tAn analytical model for column adsorption with two competing contaminants\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-3f6e8280 ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3f6e8280\" 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-1926538b ts-bg-color-over-image\" data-id=\"1926538b\" 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-4d0e8ee8 elementor-widget-tablet__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"4d0e8ee8\" 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>We develop a mathematical model to describe an adsorption process where two contaminants are simultaneously removed from a fluid mixture as it flows through a packed column. Both species compete to occupy the available sites, including displacing previously attached molecules. The system of governing equations involves mass balances for the two species coupled to an attachment model. In the common situation, where one contaminant is more strongly adsorbed than the other, the analysis may be split between two distinct regions \u2014 one where competition dominates the adsorption process and all of the first contaminant is eventually captured and a second region, ahead of the first, where only the weaker contaminant remains and so is able to be adsorbed without being displaced. In both regions, it is possible to find travelling waves which may be used to construct an analytical expression for the breakthrough curves. To verify this, a numerical solution is developed and compared with the approximate analytical solutions. The model results are then verified against experimental data for the capture of siloxanes, toluene and n-decane on activated carbon, obtaining excellent agreement with R2&gt; 0.98<span id=\"MathJax-Element-1-Frame\" class=\"MathJax_SVG\" style=\"box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.4px; font-size-adjust: none; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;msup is=&quot;true&quot;&gt;&lt;mrow is=&quot;true&quot; \/&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mn is=&quot;true&quot;&gt;2&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;mo linebreak=&quot;goodbreak&quot; linebreakstyle=&quot;after&quot; is=&quot;true&quot;&gt;&amp;gt;&lt;\/mo&gt;&lt;mn is=&quot;true&quot;&gt;0&lt;\/mn&gt;&lt;mo is=&quot;true&quot;&gt;.&lt;\/mo&gt;&lt;mn is=&quot;true&quot;&gt;98&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><\/span>\u00a0in the cases examined.<\/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-58cf4c4e ts-col-stretched-none ts-bg-color-over-image elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58cf4c4e\" 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-49bb33c6 ts-bg-color-over-image\" data-id=\"49bb33c6\" 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-12e90b69 elementor-widget elementor-widget-accordion\" data-id=\"12e90b69\" 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-3171\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-3171\" 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-3171\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-3171\"><table style=\"border: hidden;\">\n<tbody>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Year:<\/strong><\/td>\n<td>2025<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Authors:<\/strong><\/td>\n<td>M. Calvo-Schwarzwalder, T.G. Myers, A. Cabrera-Codony, A. Valverde<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Reference:<\/strong><\/td>\n<td>International Journal of Heat and Mass Transfer, Volume 245, 2025, 127004<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #efefef;\">\n<td align=\"right\" width=\"200\"><strong>Link:<\/strong><\/td>\n<td><a href=\"https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2025.127004\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2025.127004<\/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-17d8e22e elementor-widget elementor-widget-spacer\" data-id=\"17d8e22e\" 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: M. Calvo-Schwarzwalder, T.G. Myers, A. Cabrera-Codony, A. Valverde An analytical model for column adsorption with two competing contaminants We develop a mathematical model to describe an adsorption process where two contaminants are simultaneously removed from a fluid mixture as it flows through a packed column. Both species compete to occupy the available sites, including &hellip; <a href=\"https:\/\/lequia-udg.com\/ca\/2025\/07\/17\/an-analytical-model-for-column-adsorption-with-two-competing-contaminants\/\" class=\"more-link\" title=\"Continue reading <span class=\"screen-reader-text\">An analytical model for column adsorption with two competing contaminants<\/span>&#8220;>Continue reading <span class=\"screen-reader-text\">An analytical model for column adsorption with two competing contaminants<\/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-14536","post","type-post","status-publish","format-standard","hentry","category-articles-ca"],"_links":{"self":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/14536","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=14536"}],"version-history":[{"count":1,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/14536\/revisions"}],"predecessor-version":[{"id":14537,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/posts\/14536\/revisions\/14537"}],"wp:attachment":[{"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/media?parent=14536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/categories?post=14536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lequia-udg.com\/ca\/wp-json\/wp\/v2\/tags?post=14536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}