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window.loswp.work = {"work":{"id":27321534,"created_at":"2016-07-27T18:39:18.846-07:00","from_world_paper_id":155955512,"updated_at":"2024-11-13T13:53:13.913-08:00","_data":{"grobid_abstract":"In this paper the problem of calculating the liquid flow force on a particle in interaction with an air bubble with a mobile surface in flotation as a function of the separation distance was solved. The force equation was obtained by first deriving the disturbed flow confined between the surfaces. The model for the force includes the separation distance between the bubble and the particle, the particle size, the bubble's Reynolds number, the bubble rise velocity, and the polar position of the particle on the bubble surface. The proposed equations provide an exact solution to the situation where the particle and the bubble are very close together. The attractive flow force and the surface forces are of similar orders of magnitude.","publication_date":"2002,,","publication_name":"Journal of Colloid and Interface Science","grobid_abstract_attachment_id":"47577722"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"The Liquid Flow Force on a Particle in the Bubble–Particle Interaction in Flotation","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [132470]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; 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 class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":47577722,"attachmentType":"pdf"}"><img alt="First page of “The Liquid Flow Force on a Particle in the Bubble–Particle Interaction in Flotation”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/47577722/mini_magick20190206-17449-m9el95.png?1549473516" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">The Liquid Flow Force on a Particle in the Bubble–Particle Interaction in Flotation</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="132470" href="https://newcastle-au.academia.edu/GeoffreyEvans"><img alt="Profile image of Geoffrey Evans" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/132470/106438756/95648776/s65_geoffrey.evans.png" />Geoffrey Evans</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2002, Journal of Colloid and Interface Science</p></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In this paper the problem of calculating the liquid flow force on a particle in interaction with an air bubble with a mobile surface in flotation as a function of the separation distance was solved. The force equation was obtained by first deriving the disturbed flow confined between the surfaces. The model for the force includes the separation distance between the bubble and the particle, the particle size, the bubble's Reynolds number, the bubble rise velocity, and the polar position of the particle on the bubble surface. The proposed equations provide an exact solution to the situation where the particle and the bubble are very close together. The attractive flow force and the surface forces are of similar orders of magnitude.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":47577722,"attachmentType":"pdf","workUrl":"https://www.academia.edu/27321534/The_Liquid_Flow_Force_on_a_Particle_in_the_Bubble_Particle_Interaction_in_Flotation"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":47577722,"attachmentType":"pdf","workUrl":"https://www.academia.edu/27321534/The_Liquid_Flow_Force_on_a_Particle_in_the_Bubble_Particle_Interaction_in_Flotation"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="47577722" data-landing_url="https://www.academia.edu/27321534/The_Liquid_Flow_Force_on_a_Particle_in_the_Bubble_Particle_Interaction_in_Flotation" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="21355060" 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/21355060/Bubble_particle_attachment_and_detachment_in_flotation">Bubble–particle attachment and detachment in flotation</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="42445107" href="https://independent.academia.edu/DanielFornasiero">Daniel Fornasiero</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Mineral Processing, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">The mechanism by which particles and bubbles interact captures many of the central concepts of colloid science and hydrodynamics and is an example of heterocoagulation. Hydrodynamics, Ž . interfacial including capillary forces, particle and bubble behaviour and solution chemistry are all interwoven. The processes of attachment and detachment are focused upon here. We deal with the identification of a flotation 'domain', the deformation of a bubble surface upon interaction with a solid surface, the kinetics of three phase contact line expansion and the determination of attachment efficiencies through to the direct measurement of bubble-particle interaction forces. The results, concepts and implications of this work are discussed. q 1999 Elsevier Science B.V. All rights reserved. 0301-7516r99r$ -see front matter q 1999 Elsevier Science B.V. All rights reserved.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Bubble–particle attachment and detachment in flotation","attachmentId":41830723,"attachmentType":"pdf","work_url":"https://www.academia.edu/21355060/Bubble_particle_attachment_and_detachment_in_flotation","alternativeTracking":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/21355060/Bubble_particle_attachment_and_detachment_in_flotation"><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="1" data-entity-id="80404691" 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/80404691/The_role_of_hydrodynamic_and_surface_forces_in_bubble_particle_interaction">The role of hydrodynamic and surface forces in bubble–particle interaction</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="45124351" href="https://independent.academia.edu/YoonRoeHoan">Roe-Hoan Yoon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Mineral Processing, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">In modeling flotation, the process of bubble-particle interaction is usually divided into three subprocesses, including collision, adhesion and detachment. Of these, the hydrodynamics of bubble-particle collision has been studied most extensively by many investigators, and the results are useful for the design and scale-up of flotation cells. The process of adhesion, on the other hand, is least understood because it is essentially controlled by the chemistry of the system, which is complex and difficult to model mathematically. However, it is possible to determine the probability of the bubble-particle adhesion from the induction times that can be measured experimentally under different chemical environments. Furthermore, the new information reported in the literature on the hydrophobic forces of both particles and bubbles allow prediction of adhesion probabilities using various surface chemistry parameters. Consideration of both the hydrodynamic and surface force parameters is essential in predicting flotation rates from first principles.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The role of hydrodynamic and surface forces in bubble–particle interaction","attachmentId":86797471,"attachmentType":"pdf","work_url":"https://www.academia.edu/80404691/The_role_of_hydrodynamic_and_surface_forces_in_bubble_particle_interaction","alternativeTracking":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/80404691/The_role_of_hydrodynamic_and_surface_forces_in_bubble_particle_interaction"><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="2" data-entity-id="21190091" 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/21190091/Particle_bubble_interaction_and_attachment_in_flotation">Particle–bubble interaction and attachment in flotation</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="42349095" href="https://monash.academia.edu/PeterTLKoh">Peter T.L. Koh</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chemical Engineering Science, 2011</p><p class="ds-related-work--abstract ds2-5-body-sm">Flotation is an important unit operation in the minerals industry, among others. Current state-of-theart flotation modelling combines computational fluid dynamics (CFD) with user-defined algorithms based on the ''induction time'' concept to describe selective bubble-particle attachment and separation of hydrophobic and hydrophilic particles.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Particle–bubble interaction and attachment in flotation","attachmentId":41754868,"attachmentType":"pdf","work_url":"https://www.academia.edu/21190091/Particle_bubble_interaction_and_attachment_in_flotation","alternativeTracking":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/21190091/Particle_bubble_interaction_and_attachment_in_flotation"><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="3" data-entity-id="21355080" 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/21355080/Particle_Bubble_Attachment_in_Mineral_Flotation">Particle–Bubble Attachment in Mineral Flotation</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="42445107" href="https://independent.academia.edu/DanielFornasiero">Daniel Fornasiero</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Colloid and Interface Science, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">Attachment efficiencies of rough, angular, methylated quartz particles with nitrogen bubbles are derived from experimental capture efficiency data in conjunction with a collision model termed the Generalized Sutherland Equation (GSE). The methylated quartz particles ranged in size from 7.5 to 70 m equivalent diameter and had advancing contact angles between 33°and 74°. They heterocoagulated with nitrogen bubbles between 0.77 and 1.52 mm in diameter in 0, 0.01, or 0.1 mol dm ؊3 KCl. The attachment efficiencies decreased with increasing particle size and bubble size, but increased with particle contact angle and KCl electrolyte concentration. These attachment efficiency data were then used to test the Dobby-Finch attachment model for potential flow conditions. The latter model was modified so that the conditions of approach of the particle toward the bubble surface are the same as those defined previously in the GSE collision model . Satisfactory agreement was obtained between the experimental attachment efficiencies obtained in this study and those calculated with the Dobby-Finch model. In the attachment efficiency calculations, the induction time (t ind ) varied with particle size (d p ) according to the well-known equation, t ind ‫؍‬ Ad p B . The parameter B, with a value of 0.6, was found to be independent of particle size, particle contact angle, bubble size, and KCl electrolyte concentration. Conversely, the value of the parameter A was dependent on the particle contact angle, especially for contact angles smaller than 50°, and on the bubble size but to a lesser extent on the electrolyte concentration. The value of A decreased with an increase in particle contact angle and an increase in bubble size. The values of the induction time obtained in this study are in a reasonable agreement with experimental and calculated induction times reported in the literature.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Particle–Bubble Attachment in Mineral Flotation","attachmentId":41830728,"attachmentType":"pdf","work_url":"https://www.academia.edu/21355080/Particle_Bubble_Attachment_in_Mineral_Flotation","alternativeTracking":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/21355080/Particle_Bubble_Attachment_in_Mineral_Flotation"><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="4" data-entity-id="753584" 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/753584/Bubble_particle_collision_and_attachment_probability_on_fine_particles_flotation">Bubble-particle collision and attachment probability on fine particles flotation</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="179043" href="https://modares.academia.edu/javadkoleini">javad koleini</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="53214123" href="https://modares.academia.edu/BehzadShahbazi">Behzad Shahbazi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chemical Engineering and …, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">Particle size is an important parameter in flotation and has been the focus of flotation research for decades. The difficulty in floating fine particles is attributed to the low probability of bubble-particle collision. In this research, the influence of hydrodynamic parameters on collision probability of fine particles was investigated. Collision probability was obtained using Stokes, intermediate I and intermediate II and potential equations. Maximum collision probability was 5.65% obtained with impeller speed of 1100 rpm, air flow rate of 30 l/h and particle size of 50 m. Also, attachment probability under Stokes flow, turbulent and potential flow conditions was calculated 100, 99.49 and 81.87% respectively. Maximum attachment probability was obtained with impeller speed of 700 rpm, contact angle of 90 • , particle size of 20 m and air flow rate of 15 l/h. Collision angles were obtained between 60.71 • and 60.18 • and attachment angles were obtained between 9.15 • and 59.83 • .</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Bubble-particle collision and attachment probability on fine particles flotation","attachmentId":51252291,"attachmentType":"pdf","work_url":"https://www.academia.edu/753584/Bubble_particle_collision_and_attachment_probability_on_fine_particles_flotation","alternativeTracking":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/753584/Bubble_particle_collision_and_attachment_probability_on_fine_particles_flotation"><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="5" data-entity-id="73649810" 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/73649810/Bubble_Detachment_from_a_Steel_Ball_in_Turbulent_Field_Application_to_Mineral_Flotation_Systems">Bubble Detachment from a Steel Ball in Turbulent Field: Application to Mineral Flotation Systems</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="51448878" href="https://independent.academia.edu/JyeshtharajJoshi">Jyeshtharaj Joshi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Procedia Engineering, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Coarse particle (typically more than 100 micrometers in diameter) flotation is adversely influenced by liquid motion resulting from energy input associated with mixing of the gas and solid phases. In particular, the collected particles can become detached from the bubble as the particle-bubble aggregate passes through regions of different turbulent levels. The dynamics of particlebubble-turbulence interaction is almost impossible to visualize within a real flotation environment as the phases are in constant motion which changes with time and position. To study the phenomenon of the particle bubble detachment process the problem was mimicked in such a way as to have a bubble detaching from a stationary 3 mm diameter steel particle in the turbulent field. A bubble of known volume was firstly introduced onto the submerged particle surface via a syringe needle. Image analysis was used to determine the bubble-particle contact angle and radial position of the three phase contact line under quiescent conditions. An oscillating grid device was then used to generate turbulent liquid motion around the particle-bubble aggregate. Particle image velocimetry (PIV) was used to quantify the instantaneous velocity field around the disturbed bubble. Laser induced-fluorescence (LIF) was applied to filter out the (green) internally reflected light from the bubble so that only the (orange) light from the fluorescing seeding particles was collected. The PIV-LIF images were then analysed by firstly utilising a masking technique to eliminate spurious velocity vectors inside the bubble. The velocity data in an envelope surrounding the bubble was extracted to calculate local, instantaneous values of liquid velocity, turbulent kinetic energy and energy dissipation rate. It was found that the flow structures generated by the oscillating grids resulted in a lateral inclination of the gas-liquid interface at the three phase contact line. The subsequent change in the dynamic contact angle resulted in a reduction in the capillary (attachment) force, and at a high enough turbulence level it became less than the buoyancy (lift-off) force and detachment of the bubble from the particle surface took place. The detachment events observed in this study is analogous to what actually takes place in mineral flotation cells where the bubble-particle aggregate is in motion.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Bubble Detachment from a Steel Ball in Turbulent Field: Application to Mineral Flotation Systems","attachmentId":82088485,"attachmentType":"pdf","work_url":"https://www.academia.edu/73649810/Bubble_Detachment_from_a_Steel_Ball_in_Turbulent_Field_Application_to_Mineral_Flotation_Systems","alternativeTracking":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/73649810/Bubble_Detachment_from_a_Steel_Ball_in_Turbulent_Field_Application_to_Mineral_Flotation_Systems"><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="20561433" 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/20561433/Investigations_of_bubble_particle_interactions">Investigations of bubble–particle interactions</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="282123" href="https://oxford.academia.edu/GeoffreyEvans">Geoffrey Evans</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Mineral Processing, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">Bubble -particle interaction during flotation comprises of collision, attachment and detachment. This paper presents a review of our investigations into these microprocesses. Analysis of collision phenomenon focuses on the physicochemical hydrodynamics of water flow passing the rising bubbles. The influence of the fore-and-aft asymmetry of water streamlines and of the mobility of the bubble surface on collision efficiency is quantified. In the case of attachment, the analysis considers contact and attachment times and reveals that the available models for contact times are far from satisfactory. It may be necessary to include short-range hydrodynamic interactions for the modeling of contact times. At present, the actual attachment time is difficult to predict from first principles. Finally, the examination of detachment focuses on models for predicting the tenacity of attached particles. The influence of the bubble size on tenacity is also analyzed. Simplified equations describing the maximum particle size for stable attachment to air bubbles are derived. D</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Investigations of bubble–particle interactions","attachmentId":41946383,"attachmentType":"pdf","work_url":"https://www.academia.edu/20561433/Investigations_of_bubble_particle_interactions","alternativeTracking":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/20561433/Investigations_of_bubble_particle_interactions"><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="7" data-entity-id="50383251" 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/50383251/Colloidal_Hydrodynamic_Theory_of_Flotation">Colloidal-Hydrodynamic Theory of Flotation</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="103758012" href="https://independent.academia.edu/NickolajRulyov">Nickolaj Rulyov</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Recent advances in the field of colloidal-hydrodynamic flotation theory are reviewed. Factors limiting the flotation of particles of all size classes are analyzed. The role of surface and hydrodynamic forces in the elementary act of flotation is investigated, as is the dependency of efficiency of particle capture by a bubble on the energy of their collision and the rate of its dissipation. Kinetic aspects of the flotation process are examined with consideration of the phenomenon of aggregation of particles and coalescence of bubbles. A brief list is presented on the main problems in flotation theory and certain promising paths of development of flotation technology are suggested.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Colloidal-Hydrodynamic Theory of Flotation","attachmentId":68394008,"attachmentType":"pdf","work_url":"https://www.academia.edu/50383251/Colloidal_Hydrodynamic_Theory_of_Flotation","alternativeTracking":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/50383251/Colloidal_Hydrodynamic_Theory_of_Flotation"><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="8" data-entity-id="17570729" 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/17570729/Determination_of_the_collision_frequency_between_bubbles_and_particles_in_flotation">Determination of the collision frequency between bubbles and particles in flotation</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="62134243" href="https://independent.academia.edu/DominiqueLegendre">Dominique Legendre</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37383779" href="https://independent.academia.edu/PascalGuiraud">Pascal Guiraud</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chemical Engineering Science, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d b ) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0 • to 180 • . The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d p /d b (d p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d p /d b (respectively (d p /d b ) 2 ) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d p /d b or (d p /d b ) 2 depending on both the level of contamination and the particle size.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Determination of the collision frequency between bubbles and particles in flotation","attachmentId":39587188,"attachmentType":"pdf","work_url":"https://www.academia.edu/17570729/Determination_of_the_collision_frequency_between_bubbles_and_particles_in_flotation","alternativeTracking":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/17570729/Determination_of_the_collision_frequency_between_bubbles_and_particles_in_flotation"><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="9" data-entity-id="41276212" 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/41276212/Modeling_the_bubble_loading_based_on_force_balance_on_the_particles_attached_to_the_bubble">Modeling the bubble loading based on force balance on the particles attached to the bubble</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="138962789" href="https://psu-us.academia.edu/AmirEskanlou">Amir Eskanlou</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="139699816" href="https://independent.academia.edu/QingqingHuang2">Qingqing Huang</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Loading of particles on a bubble is the result of a successful collision, attachment, and balancing of the forces between particles and the bubble. In this study, a mathematical model to estimate the bubble loading was developed based on the force balance on the lowest particle attached to the bubble. Gravity, buoyancy, hy-drostatic pressure, viscous drag, capillary, and capillary pressure induced forces were taken into account in the model. The resultant force of the tangential components of the normal force applied by particles on top of the lowest particle and the viscous drag exerted on the attached particles by the surrounding fluid is balanced with other forces to predict whether detachment of the lowest particle occurs or not. The model estimation results were further compared with the experimental measurements using monodisperse silica beads and two minerals with different densities in a steady state column flotation to validate the model. Comparison results indicate a close agreement with a very minor discrepancy that could be attributed to the shape and morphological features of solid particles used for the flotation experiments.</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Modeling the bubble loading based on force balance on the particles attached to the bubble","attachmentId":61495528,"attachmentType":"pdf","work_url":"https://www.academia.edu/41276212/Modeling_the_bubble_loading_based_on_force_balance_on_the_particles_attached_to_the_bubble","alternativeTracking":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/41276212/Modeling_the_bubble_loading_based_on_force_balance_on_the_particles_attached_to_the_bubble"><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></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":47577722,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":47577722,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_47577722" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="60380664" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/60380664/A_review_of_stochastic_description_of_the_turbulence_effect_on_bubble_particle_interactions_in_flotation">A review of stochastic description of the turbulence effect on bubble-particle interactions in flotation</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="28669400" href="https://usq.academia.edu/DucAnhAnVo">Duc-Anh An-Vo</a></div><p class="ds-related-work--metadata 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href="https://www.academia.edu/80789910/Investigation_of_bubble_particle_interactions_in_a_mechanical_flotation_cell_part_1_Collision_frequencies_and_efficiencies">Investigation of bubble-particle interactions in a mechanical flotation cell, part 1: Collision frequencies and efficiencies</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="55631554" href="https://amirkabir.academia.edu/BahramRezai">Bahram Rezai</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Minerals Engineering, 2019</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="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Investigation of bubble-particle interactions in a mechanical flotation cell, part 1: Collision frequencies and 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