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Continuity theory and settling model for spheres falling in non-Newtonian one- and two-phase media
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NSTL
Elsevier
<![CDATA[<ce:abstract xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns="http://www.elsevier.com/xml/ja/dtd" id="ab0005" xml:lang="en" view="all" class="author"><ce:section-title id="st0005">Abstract</ce:section-title><ce:abstract-sec id="as0005" view="all"><ce:simple-para id="sp0055" view="all">The particle settling is a basic phenomenon: however, it determines the design of many unit operations and machines of mineral processing. A new test device has been developed in order to measure the terminal settling velocity of large steel balls settling in fine particulate solids - water mixtures. The developed inductive sensor does not influence the motion of the ball and it can be applied for non-transparent and non-Newtonian fine suspensions. A new hypothesis, namely a continuity theory for coarse disperse systems is introduced here. According to this theory, if the particles of a fine suspension are so small that they fit into the laminar sub-layer around a settling coarse particle, the fine suspension can be treated as a continuum. If they do not fit, hindered settling dominates between the coarse and fine particles. It was also recognised that if a particle settles at a constant speed in any media that is in an equilibrium state, therefore, the “equilibrium mean surficial shear stress (τ<ce:inf loc="post">e</ce:inf>)” and the “equilibrium mean surficial shear rate” have been introduced. The equilibrium mean surficial shear stress can be calculated initially, because it is simply the force of gravity minus the buoyant force over three times the total surface of the particle. Once τ<ce:inf loc="post">e</ce:inf>is known, the equivalent Newtonian absolute viscosity can be determined and the terminal settling velocity of particles falling in non-Newtonian media can be calculated by the known procedures for Newtonian fluids.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:abstract xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns="http://www.elsevier.com/xml/ja/dtd" id="ab0010" class="author-highlights" xml:lang="en" view="all"><ce:section-title id="st0010">Highlights</ce:section-title><ce:abstract-sec id="as0010" view="all"><ce:simple-para id="sp0060" view="all"><ce:list id="l0005"><ce:list-item id="li0005"><ce:label>?</ce:label><ce:para id="p0005" view="all">A new settling test instrument was developed with inductive sensor.</ce:para></ce:list-item><ce:list-item id="li0010"><ce:label>?</ce:label><ce:para id="p0010" view="all">Settling velocity of balls in non-transparent, non-Newtonian real suspensions can be measured.</ce:para></ce:list-item><ce:list-item id="li0015"><ce:label>?</ce:label><ce:para id="p0015" view="all">If a particle is settling down with constant speed in any media that is an equilibrium state</ce:para></ce:list-item><ce:list-item id="li0020"><ce:label>?</ce:label><ce:para id="p0020" view="all">A universal terminal settling velocity calculation in non-Newtonian suspensions is presented.</ce:para></ce:list-item><ce:list-item id="li0025"><ce:label>?</ce:label><ce:para id="p0025" view="all">The introduced continuity theory helps understanding ball milling media behaviour.</ce:para></ce:list-item></ce:list></ce:simple-para></ce:abstract-sec></ce:abstract>]]>
Terminal settling velocityNon-Newtonian mediumFine suspensionWall effectContinuity theory
J. Faitli
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Institute of Raw Materials Processing and Environmental Process Engineering, University of Miskolc
NSTL
Elsevier
