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<p>This paper presents a novel mathematical and numerical framework for atmospheric water harvesting using porous desiccant materials. Our comprehensive model integrates relative humidity dynamics, water content variation, thermodynamic isotherms, multi-phase diffusion mechanisms, heat transfer, and phase change phenomena. We employ the Method of Lines with Galerkin discretization to solve the resulting coupled nonlinear equations. Validation against experimental data for three distinct desiccant salts (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40899_2025_1244_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CuCl}_2\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40899_2025_1244_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {MgSO}_4\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40899_2025_1244_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CuSO}_4\)</EquationSource> </InlineEquation>) demonstrates accuracy within 0.7–2%. The analysis reveals that <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40899_2025_1244_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CuCl}_2\)</EquationSource> </InlineEquation> achieves approximately 95% moisture uptake efficiency at 60–70% relative humidity, while <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40899_2025_1244_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {MgSO}_4\)</EquationSource> </InlineEquation> maintains about 78% effectiveness under similar conditions. Our research identifies critical relationships where humidity directly modulates diffusion rates while temperature simultaneously alters sorption capacity and phase-change kinetics. Under cyclic environmental conditions, each salt exhibits distinctive performance signatures that establish definitive selection criteria for specific applications. These findings enable precise design optimization of atmospheric water harvesting systems across diverse climatic conditions, addressing global water scarcity challenges with enhanced efficiency.</p>

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Numerical modeling with thermodynamic aspects of harvesting atmospheric water using porous desiccant materials

  • 期刊论文

  • 发表日期：

    2025年5月31日

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  • Narjisse Kabbaj,
  • Mohamed F. El-Amin

摘要

This paper presents a novel mathematical and numerical framework for atmospheric water harvesting using porous desiccant materials. Our comprehensive model integrates relative humidity dynamics, water content variation, thermodynamic isotherms, multi-phase diffusion mechanisms, heat transfer, and phase change phenomena. We employ the Method of Lines with Galerkin discretization to solve the resulting coupled nonlinear equations. Validation against experimental data for three distinct desiccant salts ( \(\hbox {CuCl}_2\) , \(\hbox {MgSO}_4\) , \(\hbox {CuSO}_4\) ) demonstrates accuracy within 0.7–2%. The analysis reveals that \(\hbox {CuCl}_2\) achieves approximately 95% moisture uptake efficiency at 60–70% relative humidity, while \(\hbox {MgSO}_4\) maintains about 78% effectiveness under similar conditions. Our research identifies critical relationships where humidity directly modulates diffusion rates while temperature simultaneously alters sorption capacity and phase-change kinetics. Under cyclic environmental conditions, each salt exhibits distinctive performance signatures that establish definitive selection criteria for specific applications. These findings enable precise design optimization of atmospheric water harvesting systems across diverse climatic conditions, addressing global water scarcity challenges with enhanced efficiency.