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(PDF) Diffusion in pore fractals: A review of linear response models | Ramachandran Muralidhar - Academia.edu

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window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":114898331,"created_at":"2024-02-14T07:24:38.671-08:00","from_world_paper_id":249843287,"updated_at":"2024-11-24T01:56:55.803-08:00","_data":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"A major aspect of describing transport in heterogeneous media has been that of relating effective diffusivities to the topological properties of the medium. While such effective transport coefficients may be useful for mass fractals or under steady state conditions, they are not adequate under transient conditions for self-similar pore fractal media. In porous formations without scale, diffusion is anomalous with the mean-squared displacement of a particle proportional to time raised to a fractional exponent less than unity. The objective of this review is to investigate the nature of the laws of diffusion in fractal media using the framework of linear response theory of nonequilibrium statistical mechanics. A Langevin/Fokker-Planck approach reveals that the particle diffusivity depends on its age defined as the time spent by the particle since its entry into the medium. An analysis via generalized hydrodynamics describes fractal diffusion with a frequency and wave number dependent diffusivity.","publication_date":"1993,,","publication_name":"Transport in Porous Media","grobid_abstract_attachment_id":"111464438"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Diffusion in pore fractals: A review of linear response models","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [196476842]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div 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Understanding flow</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A general fractal model of flow and solute transport in randomly heterogeneous porous media&quot;,&quot;attachmentId&quot;:42295738,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/17183710/A_general_fractal_model_of_flow_and_solute_transport_in_randomly_heterogeneous_porous_media&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17183710/A_general_fractal_model_of_flow_and_solute_transport_in_randomly_heterogeneous_porous_media"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="23946331" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23946331/Fractal_Structure_of_Hydrodynamic_Dispersion_in_Porous_Media">Fractal Structure of Hydrodynamic Dispersion in Porous Media</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38272870" href="https://independent.academia.edu/TorsteinJ%C3%B8ssang">Torstein Jøssang</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1988</p><div 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