{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21585"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21585","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Mechanics of polydisperse suspensions","abstract":"This work describes the results of numerical simulations for polydisperse sedimentation of equal sized spheres, e.g. particles of different density. Using the stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particle species may be expressed (4.39) in terms of two scalar functions of total volume fraction. These are the self mobility M$\\sb{\\rm o}$ (eq. short time self diffusion coefficient) and the interaction mobility M$\\sb{\\rm I}$. This latter tensor is related to the velocity of a force free tracer particle in a suspension of identical particle subjected to a unit force. Numerical values for M$\\sb{\\rm o}$ and M$\\sb{\\rm I}$ are calculated for a range of volume fractions from $\\phi$ = 0.025 to 0.55. All results show excellent agreement with the dilute theory of Batchelor (1982). Simple algebraic expressions are given which well correlate the numerical results.","abstract_html":"This work describes the results of numerical simulations for polydisperse sedimentation of equal sized spheres, e.g. particles of different density. Using the stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particle species may be expressed (4.39) in terms of two scalar functions of total volume fraction. These are the self mobility M$\\sb{\\rm o}$ (eq. short time self diffusion coefficient) and the interaction mobility M$\\sb{\\rm I}$. This latter tensor is related to the velocity of a force free tracer particle in a suspension of identical particle subjected to a unit force. Numerical values for M$\\sb{\\rm o}$ and M$\\sb{\\rm I}$ are calculated for a range of volume fractions from $\\phi$ = 0.025 to 0.55. All results show excellent agreement with the dilute theory of Batchelor (1982). Simple algebraic expressions are given which well correlate the numerical results.","abstract_has_math":true,"creators":["Revay, Joseph Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Higdon, Jonathan J.L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:13:02Z","date_published":"2011-05-07T13:13:02Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Engineering, Chemical"],"languages":["eng"],"rights":["Copyright 1992 Revay, Joseph Michael"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9215876","(UMI)AAI9215876"],"render_values":[{"text":"AAI9215876","href":null,"code":true},{"text":"(UMI)AAI9215876","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21585","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Higdon, Jonathan J.L."]},{"key":"dc:creator","label":"Author","values":["Revay, Joseph Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:13:02Z","10000-01-01","1992"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Chemical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1992 Revay, Joseph Michael"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9215876","(UMI)AAI9215876","http://hdl.handle.net/2142/21585"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This work describes the results of numerical simulations for polydisperse sedimentation of equal sized spheres, e.g. particles of different density. Using the stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particle species may be expressed (4.39) in terms of two scalar functions of total volume fraction. These are the self mobility M$\\sb{\\rm o}$ (eq. short time self diffusion coefficient) and the interaction mobility M$\\sb{\\rm I}$. This latter tensor is related to the velocity of a force free tracer particle in a suspension of identical particle subjected to a unit force. Numerical values for M$\\sb{\\rm o}$ and M$\\sb{\\rm I}$ are calculated for a range of volume fractions from $\\phi$ = 0.025 to 0.55. All results show excellent agreement with the dilute theory of Batchelor (1982). Simple algebraic expressions are given which well correlate the numerical results.","\"To study the streaming phenomenon that may occur in suspensions of two types of particles we employed average mass and momentum equations which describe the fluid and particle motion as though they were interpenetrating media. Solution of these equations allows investigation of the evolution of convective streams or blobs of particles from a bidisperse suspension subject to an initial random disturbance. Here we follow the evolution of the initial disturbance through the exponential growth period. At relatively short times, t $\\ll$ 1, locally periodic concentration patterns developed which resulted in a flow field characterized by centers of circulation. Following this exponential growth period, the resulting bulk flow became strong relative to the particle velocities, \"\"freezing\"\" any structure present in the suspension. These structures were then convected throughout the cell for the remainder of the simulation. The results indicate that the bulk flow field is defined by the largest length scale given by the size of the cell, while the concentration field chose the smallest length scale determined by the number of Fourier modes. This combination did not allow for complete lateral segregation of the individual particle species or the formation of convective vertical streams that have been observed experimentally.\"","Made available in DSpace on 2011-05-07T13:13:02Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9215876.pdf: 12036093 bytes, checksum: c21bb93a236278483745436692e15d26 (MD5) Previous issue date: 1992","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:46Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:23:48-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Mechanics of polydisperse suspensions"]}]}],"canonical_facts":{"dc:contributor":["Higdon, Jonathan J.L."],"dc:creator":["Revay, Joseph Michael"],"dc:date":["2011-05-07T13:13:02Z","10000-01-01","1992"],"dc:description":["This work describes the results of numerical simulations for polydisperse sedimentation of equal sized spheres, e.g. particles of different density. Using the stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particle species may be expressed (4.39) in terms of two scalar functions of total volume fraction. These are the self mobility M$\\sb{\\rm o}$ (eq. short time self diffusion coefficient) and the interaction mobility M$\\sb{\\rm I}$. This latter tensor is related to the velocity of a force free tracer particle in a suspension of identical particle subjected to a unit force. Numerical values for M$\\sb{\\rm o}$ and M$\\sb{\\rm I}$ are calculated for a range of volume fractions from $\\phi$ = 0.025 to 0.55. All results show excellent agreement with the dilute theory of Batchelor (1982). Simple algebraic expressions are given which well correlate the numerical results.","\"To study the streaming phenomenon that may occur in suspensions of two types of particles we employed average mass and momentum equations which describe the fluid and particle motion as though they were interpenetrating media. Solution of these equations allows investigation of the evolution of convective streams or blobs of particles from a bidisperse suspension subject to an initial random disturbance. Here we follow the evolution of the initial disturbance through the exponential growth period. At relatively short times, t $\\ll$ 1, locally periodic concentration patterns developed which resulted in a flow field characterized by centers of circulation. Following this exponential growth period, the resulting bulk flow became strong relative to the particle velocities, \"\"freezing\"\" any structure present in the suspension. These structures were then convected throughout the cell for the remainder of the simulation. The results indicate that the bulk flow field is defined by the largest length scale given by the size of the cell, while the concentration field chose the smallest length scale determined by the number of Fourier modes. This combination did not allow for complete lateral segregation of the individual particle species or the formation of convective vertical streams that have been observed experimentally.\"","Made available in DSpace on 2011-05-07T13:13:02Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9215876.pdf: 12036093 bytes, checksum: c21bb93a236278483745436692e15d26 (MD5) Previous issue date: 1992","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:46Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:23:48-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9215876","(UMI)AAI9215876","http://hdl.handle.net/2142/21585"],"dc:language":["eng"],"dc:rights":["Copyright 1992 Revay, Joseph Michael"],"dc:subject":["Engineering, Chemical"],"dc:title":["Mechanics of polydisperse suspensions"],"dc:type":["text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:18Z"}