Abstract
A hydrodynamic model describing the particle distribution over the cross-section of a finely dispersed flow is proposed. The model is constructed on the basis of notions concerning the diffusion of particles induced by their random displacements in the process of relative motion of neighboring layers at constant shear velocity. It is shown that the suspension capacity of the flow is large for small particles due to thermal fluctuations and for relatively large particles due to shear-induced particle pulsations. There are critical particle sizes for which the particles are suspended and transported by the flow less effectively than larger or smaller particles.
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References
R. F. Madsen,Hyperfiltration and Ultrafiltration in Plate-and-Frame Systems, Elsevier, Amsterdam (1977).
J. D. Henry, “Cross flow filtration,” in:Recent Develop. in Separation Sci. Vol. 2., CRC Press, Cleveland (1972), P. 205.
M. Martin and P. S. Williams, “Theoretical basis of field-flow fractionation”, in:Theor. Adv. in Chromatography and Related Separation Techniques, Kluwer, Dordrecht (1992), P.513.
Yu. A. Buyevich, “Hydrodynamics of dispersions including diffusional effects”,Arch. Mech.,42, No. 4–5, 429 (1990).
G. Green and G. Belfort, “Fouling of ultrafiltration membranes: lateral migration and particle trajectory model,”Desalination,35, 129 (1980).
W. F. Blatt, A. David, A. S. Michaels, and L. Nelsen, “Solute polarization and cake formation in membrane ultrafiltration: causes, consequences and control techniques,” in:Membrane Sci. and Technol., Plenum Press, New York (1970), P. 47.
M. C. Porter, “Concentration polarization with membrane ultrafiltration,”Ind. Engng. Chem. Prod. Res. Develop.,11, 234 (1972).
F. W. Altena and G. Belfort, “Lateral migration of spherical particles in porous flow channels. Application,”Chem. Engng. Sci.,39, 343 (1984).
K. Schneider and W. Klein, “The concentration of suspensions by means of crossflow-microfiltration,”Desalination,41, 263 (1982).
E. F. Leonard and C. S. Vassilieff, “The deposition of rejected matter in membrane separation processes,”Chem. Engng. Commun.,30, 209 (1984).
S. Birdsell,Mathematical Model of Cross Microfiltration, M. S. Thesis, Univ. Colorado, (1985).
D. Leighton and A. Acrivos, “Viscous resuspension,”Chem. Engng. Sci.,41, 1377 (1986).
R. H. Davis and D. T. Leighton, “Shear-induced transport of a particle layer along a porous wall,”Chem. Engng. Sci.,42, 275 (1987).
E. E. Eckstein, D. C. Bailey, and A. H. Shapiro, “Self-diffusion of particles in shear flow of a suspension,”J. Fluid Mech.,79, 191 (1977).
D. Leighton and A. Acrivos, “Measurement of shear-induced self-diffusion in concentrated suspensions of spheres,”J. Fluid Mech.,177, 109 (1987).
D. Leighton and A. Acrivos, “The shear-induced migration of particles in concentrated suspensions,”J. Fluid Mech.,181, 415 (1987).
G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,”J. Fluid Mech.,74, 1 (1976).
N. F. Carnahan and K. E. Starling, “Equation of state for non-attracting rigid spheres,”J. Chem. Phys.,51, 635 (1969).
Yu. A. Buyevich, “Statistical hydromechanics of disperse systems. Pt. 1,”J. Fluid Mech., No. 3, 489 (1971).
Yu. A. Buyevich, “Internal pulsations in flows of finely dispersed suspensions,”Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 91 (1993).
Yu. A. Buyevich, “Concentration fluctuations and self-diffusion of particles in monodisperse systems,”Inzh.-Fiz. Zh.,65, 39 (1993).
G. K. Batchelor, “A new theory of the instability of a uniform fluidized bed,”J. Fluid Mech.,193, 75 (1988).
I. G. Shaposhnikov, “The problem of the loss of diffusion effects in the equations of hydrodynamics,”Zh. Eksp. Teor. Fiz.,21, 1309 (1951).
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Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 112–121, January–February, 1995.
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Buevich, Y.A., Makarov, A.V. Particle suspension in a simple shear flow. Fluid Dyn 30, 93–100 (1995). https://doi.org/10.1007/BF02029932
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DOI: https://doi.org/10.1007/BF02029932