Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T08:25:59.823Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 October 2023

Pawel Kosinski
Pawel Kosinski
Affiliation:
Universitetet i Bergen, Norway
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Multiphase Flow with Solid Particles , pp. 262 - 275
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamson, J. 1975. Collision rates of small particles in a vigorously turbulent fluid. Chemical Engineering Science, 30, 1371–1379.Google Scholar
Aitken, J. 1884. On the formation of small clear spaces in dusty air. Earth and Environmental Science Transactions of The Royal Society of Edinburgh, 32, 239–272.Google Scholar
Allen, M. D., and Raabe, O. G. 1982. Re-evaluation of Millikan’s oil drop data for the motion of small particles in air. Journal of Aerosol Science, 13, 537–547.Google Scholar
Allen, M. D., and Raabe, O. G. 1985. Slip correction measurements of spherical solid aerosol particles in an improved Millikan apparatus. Aerosol Science and Technology, 4, 269–289.Google Scholar
Allen, M. P., and Tildesley, D. J. 1990. Computer Simulations of Liquids. Oxford Science Publications.Google Scholar
Anagnostopoulos, S. A. 1988. Pounding of buildings in series during earthquakes. Earth-quake Engineering and Structural Dynamics, 16, 443–456.Google Scholar
Anagnostopoulos, S. A. 2004. Equivalent viscous damping for modelling inelastic impacts in earthquake pounding problems. Earthquake Engineering and Structural Dynamics, 33, 897–902.CrossRefGoogle Scholar
Antypov, D., and Elliott, J. A. 2011. On an analytical solution for the damped Hertzian spring. EPL, 94, 50004.Google Scholar
Aryaei, A., Hashemnia, K., and Jafarpur, K. 2010. Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts. International Journal of Impact Engineering, 37, 1037–1044.Google Scholar
Asakura, K., Harada, S., Funayama, T., and Nakajima, I. 1997. Simulation of descending particles in water by the distinct element method. Powder Technology, 94, 195–200.Google Scholar
Awasthi, A., Hendy, S. C., Zoontjens, P., and Brown, S. A. 2006. Reentrant adhesion behavior in nanocluster deposition. Physical Review Letters, 97, 186103.Google Scholar
Awasthi, A., Hendy, S. C., Zoontjens, P., Brown, S. A., and Natali, F. 2007. Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition. Physical Review B, 76, 115437.CrossRefGoogle Scholar
Ayesh, A. I., Brown, S. A., Awasthi, A., Hendy, S. C., Convers, P. Y., and Nichol, K. 2010. Coefficient of restitution for bouncing nanoparticles. Physical Review B, 81, 195422.CrossRefGoogle Scholar
Balachandar, S., and Maxey, M. R. 1989. Methods for evaluating fluid velocities in spectral simulations of turbulence. Journal of Computational Physics, 83, 96–125.Google Scholar
Balakin, B. V., Kosinski, P., and Hoffmann, A. C. 2012. The collision efficiency in a shear flow. Chemical Engineering Science, 68, 305–312.Google Scholar
Barkla, H. M., and Auchterlonie, L. J. 1970. The Magnus or Robins effect on rotating spheres. Journal of Fluid Mechanics, 47, 437–44Google Scholar
Basset, A. B. 1888. On the motion of a sphere in a viscous liquid. Philosophical Transactions of the Royal Society of London A, 179, 43–63.Google Scholar
Batchelor, G. K. 1977. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. Journal of Fluid Mechanics, 83, 97–117.Google Scholar
Ben-Ammar, F., Kaviany, M., and Barber, J. R. 1992. Heat transfer during impact. International Journal of Heat and Mass Transfer, 35, 1495–1506.CrossRefGoogle Scholar
Bird, R. B., Stewart, W. E., and Lightfoot, E. N. 2002. Transport Phenomena. John Wiley & Sons, Inc.Google Scholar
Bordbar, M. H., and Hyppanen, T. 2007. Modeling of binary collision between multisize viscoelastic spheres. Journal of Numerical Analysis, Industrial and Applied Mathematics, 2, 115–128.Google Scholar
Boyer, F., Guazzelli, E., and Pouliquen, O. 2011. Unifying suspension and granular rheology. Physical Review Letters, 107, 188301.Google Scholar
Brach, R. M. 1984. Friction, restitution, and energy loss in planar collisions. Transactions of the ASME, 51, 164–170.CrossRefGoogle Scholar
Brach, R. M. 1989. Rigid body collisions. Journal of Applied Mechanics, 56, 133–138. Google Scholar
Brach, R. M. 1991. Mechanical Impact Dynamics: Rigid Body Collisions. John Wiley & Sons.Google Scholar
Brach, R. M., Dunn, P. L., and Li, X. 2000. Experiments and engineering models of microparticle impact and deposition. Journal of Adhesion, 74, 227–282.CrossRefGoogle Scholar
Bradley, R. S. 1932. The cohesive force between solid surface and the surface energy of solids. Philosophical Magazine Series 7, 13, 853–862.CrossRefGoogle Scholar
Brenner, H. 1964. The Stokes resistance of a slightly deformed sphere. Chemical Engineering Science, 19, 519–539.Google Scholar
Brilliantov, N. V., Spahn, F., Hertzsch, J. M., and Poschel, T. 1996a. The collision of particles in granular systems. Physica A, 231, 417–424.CrossRefGoogle Scholar
Brilliantov, N. V., Spahn, F., Hertzsch, J. M., and Poschel, T. 1996b. Model for collisions in granular gases. Physical Review E, 53, 5382.CrossRefGoogle ScholarPubMed
Brilliantov, N. V., Albers, N., Spahn, F., and Poschel, T. 2007. Collision dynamics of granular particles with adhesion. Physical Review E, 76, 051302.Google Scholar
Brilliantov, N. V., Pimenova, A. V., and Goldobin, D. S. 2015. A dissipative force between colliding viscoelastic bodies: Rigorous approach. EPL, 109, 14005.Google Scholar
Brock, J. R. 1962. On the theory of thermal forces acting on aerosol particles. Journal of Colloid Science, 17, 768–780.CrossRefGoogle Scholar
Brown, G. L., and Roshko, A. 1974. On density effects and large structure in turbulent mixing layers. Journal of Fluid Mechanics, 64, 775–816.Google Scholar
Bush, A. W., Gibson, R. D., and Thomas, T. R. 1975. The elastic contact of a rough surface. Wear, 35, 87–111.Google Scholar
Butt, H. J., and Kappl, M. 2010. Surface and Interfacial Forces. Wiley VCH.Google Scholar
Camp, T. R., and Stein, P. C. 1943. Velocity gradients and internal work in fluid motion. Journal of the Boston Society of Civil Engineers, 30, 219–1237.Google Scholar
Campbell, C. S., and Brennen, C. E. 1985. Computer simulation of granular shear flows. Journal of Fluid Mechanics, 151, 167–188.CrossRefGoogle Scholar
Chein, R., and Chung, J. N. 1987. Effects of vortex pairing on particle dispersion in turbulent shear flows. International Journal of Multiphase Flow, 13, 785–802.Google Scholar
Chein, R., and Chung, J. N. 1988. Simulation of particle dispersion in a two-dimensional mixing layer. AIChE Journal, 34, 946–954.CrossRefGoogle Scholar
Chen, M., Kontomaris, K., and McLaughlin, J. B. 1998. Direct numerical simulation of droplet collisions in a turbulent channel flow. Part II: Collision rates. International Journal of Multiphase Flow, 24, 1105–1138.Google Scholar
Cherukat, P., and Mclaughlin, J. B. 1994. The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. Journal of Fluid Mechanics, 263, 1–18.Google Scholar
Chung, J. N., and Troutt, T. R. 1988. Simulation of particle dispersion in an axisymmetric jet. Journal of Fluid Mechanics, 186, 192–222.Google Scholar
Clift, R., Grace, J. R., and Weber, M. E. 2005. Bubbles, Drops and Particles. Dover Publications, Inc.Google Scholar
Crowe, C., Sommerfeld, M., and Tsuji, Y. 1998. Multiphase Flow with Droplets and Particles. CRC Press.Google Scholar
Crowe, C. T. 2005. Multiphase Flow Handbook (Mechanical and Aerospace Engineering Series). CRC Press.Google Scholar
Crowe, C. T., Gore, R. A., and Troutt, T. R. 1985. Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology, 3, 149–158.CrossRefGoogle Scholar
Crowe, C. T., Chung, J. N., and Troutt, T. R. 1988. Particle mixing in free shear flows. Progress in Energy and Combustion Science, 14, 171–194.Google Scholar
Cummins, S. J., Thornton, C., and Cleary, P. W. 2012. Contact force models in elastic collisions. In: Ninth International Conference on CFD in the Minerals and Process Industries, Melbourne, Australia, 10–12 December 2012.Google Scholar
Cundall, P. A., and Strack, O. D. L. 1979. A discrete numerical model for granular assemblies. Geotechnique, 29, 47–65.Google Scholar
Dahl, S. R., Clelland, R., and Hrenya, C. M. 2002. The effects of continuous size distributions on the rapid flow of inelastic particles. Physics of Fluids, 14, 1972–1984.Google Scholar
Dahneke, B. E. 1972. The influence of flattening on the adhesion of particles. Journal of Colloid and Interface Science, 40, 1–13.CrossRefGoogle Scholar
Dahneke, B. E. 1973. Slip correction factors for nonspherical bodies-II free molecule flow. Journal of Aerosol Science, 4, 147–161.Google Scholar
Dandy, D. S., and Dwyer, H. A. 1990. A sphere in shear flow at finite Reynolds number: Effect of shear on particle lift, drag, and heat transfer. Journal of Fluid Mechanics, 216, 381–410.Google Scholar
Davies, C. N. 1945. Definitive equations for the fluid resistance of spheres. Proceedings of the Physical Society, 57, 259–270.Google Scholar
Davies, J. M. 1949. The aerodynamics of golf balls. Journal of Applied Physics, 20, 821–828.CrossRefGoogle Scholar
Deen, N. G., van Sint Annaland, M., van der Hoef, M. A., and Kuipers, J. A. M. 2007. Review of discrete particle modeling of fluidized beds. Chemical Engineering Science, 62, 28–44.Google Scholar
Delichatsios, M. A., and Probstein, R. F. 1975. Coagulation in turbulent flow: Theory and experiment. Journal of Colloid and Interface Science, 51, 394–405.Google Scholar
Delvosalle, C., and Vanderschuren, J. 1985. Gas-to-particle and particle-to-particle heat transfer in fluidized beds of large particles. Chemical Engineering Science, 40, 769–779.Google Scholar
Dennis, S. C. R., Singh, S. N., and Ingham, D. B. 1980. The steady flow due to a rotating sphere at low and moderate Reynolds-numbers. Journal of Fluid Mechanics, 101, 257–279.Google Scholar
Deresiewicz, H. 1968. A note on Hertz’s theory of impact. Acta Mechanica, 6, 110–112.Google Scholar
Derjaguin, B. V., Muller, V. M., and Toporov, Yu. P. 1975. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science, 53, 314–326.Google Scholar
Djerassi, S. 2009a. Collision with friction; Part A: Newton’s hypothesis. Multibody System Dynamics, 21, 37–54.Google Scholar
Djerassi, S. 2009b. Collision with friction; Part B: Poisson’s and Stornge’s hypotheses. Multibody System Dynamics, 21, 55–77.Google Scholar
Dong, H., and Moys, M. H. 2003. Measurement of impact behaviour between balls and walls in grinding mills. Minerals Engineering, 16, 543–550.Google Scholar
Dong, H., and Moys, M. H. 2006. Experimental study of oblique impacts with initial spin. Powder Technology, 161, 22–31.Google Scholar
Dyagel, R. V., and Lapshin, V. V. 2011. On a nonlinear viscoelastic model of Hunt- Crossley impact. Mechanics of Solids, 46, 798–806.Google Scholar
Eaton, J. K., and Fessler, J. R. 1994. Preferential concentration of particles by turbulence. International Journal of Multiphase Flow, 20, 169–209.Google Scholar
Einstein, A. 1905. Eine neue Bestimmung der MolekÃijldimensionen. Annalen der Physik, 19, 289–306.Google Scholar
Ellendt, N., Lumanglas, A. M., Moqadam, S. I., and Mädler, L. 2015. A model for the drag and heat transfer of spheres in the laminar regime at high temperature differences. International Journal of Thermal Sciences, 133, 98–105.CrossRefGoogle Scholar
Epstein, P. S. 1924. On the resistance experienced by spheres in their motion through gases. Physical Review, 23, 710–733.Google Scholar
Epstein, P. S. 1929. Zur Theorie des Radiometers. Zeitschrift für Physik, 54, 537–563.Google Scholar
Falcon, E. 1997. Comportements dynamiques associes au contact de Hertz: processus collectifs de collision et propagation d’ondes solitaires dans les milieux granulaires. PhD thesis, Universite Claude Bernard Lyon.Google Scholar
Falcon, E., Laroche, C., Fauve, S., and Coste, C. 1998. Behavior of one inelastic ball bouncing repeatedly off the ground. The European Physical Journal B, 3, 45–57.Google Scholar
Fan, L. S., and Zhu, C. 2005. Principles of Gas-Solid Flows. Cambridge University Press.Google Scholar
Farrell, M., Lun, C. K. K., and Savage, S. B. 1986. A simple kinetic theory for granular flow of binary mixtures of smooth, inelastic, spherical particles. Acta Mechanica, 63, 45–60.Google Scholar
Fessler, J. R., Kulick, J. D., and Eaton, K. K. 1994. Preferential concentration of heavy particles in a turbulent channel flow. Physics of Fluids, 9, 3742–3749.Google Scholar
Feuillebois, F., and Lasek, A. 1978. On the rotational historic term in non-stationary Stokes flow. Quarterly Journal of Mechanics and Applied Mathematics, 31, 435–443.Google Scholar
Fiszdon, J. K. 1978. Melting of powder grains in a plasma flame. International Journal of Heat and Mass Transfer, 22, 749–761.Google Scholar
Fleckhaus, D., Hishida, K., and Maeda, M. 1987. Effect of laden solid particles on the turbulent flow structure of a round free jet. Experiments in Fluids, 5, 323–333.Google Scholar
Flores, P., Machado, M., Silva, M. T., and Martins, J. M. 2011. On the continuous contact force models for soft materials in multibody dynamics. Multibody System Dynamics, 25, 357–375.Google Scholar
Foerster, S. F., Louge, M. Y., Chang, H., and Allia, K. 1994. Measurements of the collision properties of small spheres. Physics of Fluids, 6, 1108–1115.Google Scholar
Friedlander, S. K. 1957. Behavior of suspended particles in a turbulent fluid. AIChE Journal, 3, 381–385.Google Scholar
Friedlander, S. K. 2000. Smoke, Dust, and Haze. Fundamentals of Aerosol Dynamics. Oxford University Press.Google Scholar
Gallas, J. A. C., Herrmann, H. J., and Sokolowski, S. 1992. Convection cells in vibrating granular media. Physical Review Letters, 69, 1371–1374.Google Scholar
Gidaspow, D. 1995. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press.Google Scholar
Gnielinski, V. 1975. Berechnung mittlerer Wärme- und Stoffübergangskoeffizienten an laminar und turbulent überströmten Einzelkörpern mit Hilfe einer einheitlichen Gleichung. Forschung im Ingenieurwesen A, 41, 145–153.Google Scholar
Goldsmith, W. 1960. Impact: The Theory and Physical Behaviour of Colliding Solids. Dover Publications, Inc.Google Scholar
Gonthier, Y., McPhee, J., Lange, C., and Piedboeuf, J. C. 2004. A regularized con- tact model with asymmetric damping and dwell-time dependent friction. Multibody System Dynamics, 11, 209–233.Google Scholar
Greenwood, J.A, and Williamson, J. B. P. 1966. Contact of nominally flat surfaces. Pro- ceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 295, 300–319.Google Scholar
Gu, Q. F., Krauss, G., Steurer, W., Gramm, F., and Cervellino, A. 2008. Unexpected high stiffness of Ag and Au nanoparticles. Physical Review Letters, 100, 045502.Google Scholar
Haff, P. K., and Anderson, R. S. 1993. Grain scale simulations of loose sedimentary beds: The example of grain-bed impacts in aeolian saltation. Sedimentology, 40, 175–198.Google Scholar
Haff, P. K., and Werner, B. T. 1986. Computer simulation of the mechanical sorting of grains. Powder Technology, 53, 239–245.Google Scholar
Hamaker, H. C. 1937. The London-van der Waals attraction between spherical particles. Physica, 4, 1058–1072.Google Scholar
Han, L. B., An, Q., Luo, S. N., and III, W. A. Goddard. 2010. Ultra-elastic and inelastic impact of Cu nanoparticles. Materials Letters, 64, 2230–2232.Google Scholar
Herbert, R. G., and McWhannell, D. C. 1977. Shape and frequency composition of pulses from an impact pair. Journal of Engineering for Industry – Transactions of the ASME, 99, 513–518.Google Scholar
Hetsroni, G., and Sokolov, M. 1971. Distribution of mass, velocity, and intensity of tur- bulence in a two-phase turbulent jet. Transactions of the ASME. Series E, Journal of Applied Mechanics, 38, 315–327.CrossRefGoogle Scholar
Hoomans, B. P. B., Kuipers, J. A. M., Briels, W. J., and van Swaaij, W. P. M. 1996. Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach. Chemical Engineering Science, 51, 99–118.Google Scholar
Hunt, K. H., and Crossley, F. R. E. 1975. Coefficient of restitution interpreted as damping in vibroimpact. Journal of Applied Mechanics, 7, 440–445.Google Scholar
Hunter, S. C. 1957. Energy absorbed by elastic waves during impact. Journal of the Mechanics and Physics of Solids, 5, 162–171.Google Scholar
Hutchins, D. K., Harper, M. H., and Felder, R. L. 1995. Slip correction measurements for solid spherical particles by modulated dynamic light scattering. Aerosol Science and Technology, 22, 202–218.Google Scholar
Israelachvili, J. N. 2010. Intermolecular and Surface Forces. 3. edn. Academic Press.Google Scholar
Iveson, S. M., and Litster, J. D. 1998. Liquid-bound granule impact deformation and coefficient of restitution. Powder Technology, 99, 234–242.Google Scholar
Jankowski, R. 2005. Non-linear viscoelastic modelling of earthquake-induced structural pounding. Earthquake Engineering and Structural Dynamics, 34, 517–524.Google Scholar
Jin, G., He, G. W., and Wang, L. P. 2010. Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence. Physics of Fluids, 22, 055106.Google Scholar
Johnson, K. L. 1985. Contact Mechanics. Cambridge University Press.Google Scholar
Johnson, K. L., Kendall, K., and Roberts, A. D. 1971. Surface energy and contact of elastic solids. Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 324, 301–313.Google Scholar
Joseph, G. G., Zenit, R., Hunt, M. L., and Rosenwinkel, A. M. 2001. Particle-wall collisions in a viscous fluid. Journal of Fluid Mechanics, 443, 329–346.Google Scholar
Jung, S.C., Suh, D., and Yoon, W. S. 2010. Molecular dynamics simulation on the energy exchanges and adhesion probability of a nano-sized particle colliding with a weakly attractive static surface. Journal of Aerosol Science, 41, 745–759.Google Scholar
Kada, H., and Hanratty, T. J. 1960. Effects of solids on turbulence in a fluid. AIChE Journal, 6, 624–630.Google Scholar
Kaltweit, M., and Drikakis, D. 2006. Collision dynamics of nanoscale Lennard-Jones potential. Physical Review B, 74, 235415.Google Scholar
Keller, J. B. 1986. Impact with friction. Journal of Applied Mechanics, 53, 1–4.Google Scholar
Kendall, K. 1994. Adhesion: Molecules and mechanics. Science, 263, 1720–1725.Google Scholar
Kharaz, A. H., and Gorham, D. A. 2000. A study of the restitution coefficient in elastic- plastic impact. Philosophical Magazine Letters, 80, 549–559.Google Scholar
Kharaz, A. H., Gorham, D. A., and Salman, A. D. 1999. Accurate measurements of particle impact parameters. Measurement Science and Technology, 10, 31–35.Google Scholar
Kharaz, A. H., Gorham, D. A., and Salman, A. D. 2001. An experimental study of the elastic rebound of spheres. Powder Technology, 120, 281–291.Google Scholar
Kim, J. H., Mulholland, G. W., Kukuck, S. R., and Pui, D. Y. H. 2005. Slip correction measurements of certified PSL nanoparticles using a nanometer differential mobility analyzer (Nano-DMA) for Knudsen number from 0.5 to 83. Journal of Research of the National Institute of Standards and Technology, 110, 31–54.Google Scholar
Knudsen, M., and Weber, S. 1914. Luftwiderstand gegen die langsame Bewegung kleiner Kugeln. Annalen der Physik, 36, 981–994.Google Scholar
Kosinski, P., and Hoffmann, A. C. 2009. Extension of the hard-sphere particle-wall collision model to account for particle deposition. Physical Review E, 79, 061302–1–061302–11.Google Scholar
Kosinski, P., and Hoffmann, A. C. 2010. An extension of the hard-sphere particle-particle collision model to study agglomeration. Chemical Engineering Science, 65, 3231–3239.Google Scholar
Kosinski, P., and Hoffmann, A. C. 2011. Extended hard-sphere model and collisions of cohesive particles. Physical Review E, 84, 031303.Google Scholar
Kosinski, P., Balakin, B. V., Middha, P., and Hoffmann, A. C. 2013. Heat conduction during collisions of cohesive and viscoelastic particle. International Journal of Heat and Mass Transfer, 58, 107–116.Google Scholar
Kosinski, P., Balakin, B. V., Middha, P., and Hoffmann, A. C. 2014. Collisions between particles in multi-phase flows: Focus on contact mechanics and heat conduction. International Journal of Heat and Mass Transfer, 70, 674–687.Google Scholar
Kosinski, P., Balakin, B. V., and Kosinska, A. 2020. Extension of the hard-sphere model for particle-flow simulations. Physical Review E, 102, 022909.Google Scholar
Krieger, I. M., and Dougherty, T. J. 1959. A mechanism for non-Newtonian flow in suspensions of rigid spheres. Transactions of the Society of Rheology, 3, 137–152.Google Scholar
Kruggel-Emden, H., Wirtz, S., and Scherer, V. 2007. An analytical solution of different configurations of the linear viscoelastic and frictional-elastic tangential contact model. Chemical Engineering Science, 62, 6914–6926.Google Scholar
Kruggel-Emden, H., Wirtz, S., and Scherer, V. 2008. A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior. Chemical Engineering Science, 63, 1523–1541.Google Scholar
Kruis, F. E., and Kusters, K. A. 1997. The collision rate of particles in turbulent flow. Chemical Engineering Communications, 158, 201–230.Google Scholar
Krupp, H., and Sperling, G. 1966. Theory of adhesion of small particles. Journal of Applied Physics, 37, 4176–4180.Google Scholar
Kumaran, V. 1997. Velocity distribution function for a dilute granular material in shear flow. Journal of Fluid Mechanics, 340, 319–341.Google Scholar
Kuninaka, H., and Hayakawa, H. 2009a. Simulation of cohesive head-on collisions of thermally activated nanoclusters. Physical Review E, 79, 031309.Google Scholar
Kuninaka, H., and Hayakawa, H. 2009b. Super-elastic collisions in a thermally activated system. Progress of Theoretical Physics Supplement, 178, 157–162.Google Scholar
Kuwabara, G., and Kono, K. 1987. Restitution coefficient in a collision between two spheres. Japanese Journal of Applied Physics, 26, 1230–1233.Google Scholar
Labous, L., Rosato, A. D., and Dave, R. N. 1997. Measurements of collisional properties of spheres using high-speed video analysis. Physical Review E, 56, 5717–5725.Google Scholar
Landau, L. D., and Lifshitz, E. M. 1959. Theory of Elasticity. Pergamon Press.Google Scholar
Langston, P. A., Heyes, D. M., and Tuzun, U. 1994. Continuous potential discrete particle simulations of stress and velocity fields in hoppers: Transition from fluid to granular flow. Chemical Engineering Science, 49, 1259–1275.Google Scholar
Langston, P. A., Tuzun, U., and Heyes, D. M. 1995. Discrete element simulation of granular flow in 2D and 3D hoppers: Dependence of discharge rate and wall stress on particle interaction. Chemical Engineering Science, 50, 967–987.Google Scholar
Lankarani, H. M. 1994. Continuous contact force models for impact analysis in multibody systems. Nonlinear Dynamics, 5, 193–207.Google Scholar
Lazaro, B. J., and Lasheras, J. C. 1989. Particle dispersion in a turbulent, plane, free shear layer. Physics of Fluids A, 1, 1035–1044.Google Scholar
Lee, J., and Herrmann, H. J. 1993. Angle of repose and angle of marginal stability: Molecular dynamics of granular particles. Journal of Physics A: Mathematical and Theoretical, 26, 373–383.Google Scholar
Lee, T. W., and Wang, A. C. 1983. On the dynamics of intermittent-motion mechanisms, Part 1: Dynamic model and response. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 105, 534–540.Google Scholar
Leighton, D., and Acrivos, A. 1985. Zeitschrift für angewandte Mathematik und Physik ZAMP. Chemical Engineering Science, 36, 174–178.Google Scholar
Levins, J. M, and Vanderlick, T. K. 1994. Impact of roughness on the deformation and adhesion of a rough metal and smooth mica in contact. Journal of Physical Chemistry, 99, 5067–5076.Google Scholar
Levy, Y., and Lockwood, F. C. 1981. Velocity measurements in a particle laden turbulent free jet. Combustion and Flame, 40, 323–333.Google Scholar
Li, L. Y., Thornton, C., and Wu, C. 2000. Impact behaviour of elastoplastic spheres with a rigid wall. Proceedings of the Institution of Mechanical Engineers Part C, 214, 1107–1114.Google Scholar
Li, W., and Davis, E. J. 1995. Measurement of the thermophoretic force by electrodynamic levitation: Microspheres in air. Journal of Aerosol Science, 26, 1063–1083.Google Scholar
Li, Z. G., and Wang, H. 2004. Thermophoretic force and velocity of nanoparticles in the free molecule regime. Physical Review E, 70, 021205.Google Scholar
Liffman, K., Chan, D. Y. C., and Hughes, B. D. 1992. Force distribution in a two dimensional sandpile. Powder Technology, 72, 255–267.Google Scholar
Lifshitz, E. M. 1956. The theory of molecular attractive forces between solids. Soviet Physics, 2, 73–83.Google Scholar
Lifshitz, E. M., and Kolsky, H. 1966. Some experiments on anelastic rebound. Journal of the Mechanics and Physics of Solids, 12, 35–43.Google Scholar
Lilly, G. P. 1974. Effect of particle size on particle eddy diffusivity. Industrial & Engineering Chemistry Fundamentals, 12, 268–275.Google Scholar
Longmire, E. K., and Eaton, J. K. 1992. Structure of a particle-laden round jet. Journal of Fluid Mechanics, 236, 217–257.Google Scholar
Loyalka, S. K. 1991. Thermophoretic force on a single particle-I. Numerical solu- tion of the linearized Boltzmann equation. Journal of Aerosol Science, 23, 291–300.Google Scholar
Lu, L. Y., Gu, Z. L., Lei, K. B., and Kase, K. 2010. Numerical simulation of contact heat transfer. AIP Conference Proceedings, 1207, 968–973.Google Scholar
Luding, S., Clement, E., Blumen, A., Rajchenbach, J., and Duran, J. 1994. Anomalous energy dissipation in molecular-dynamics simulations of grains: The “detachment” effect. Physical Review E, 50, 4113–4124.Google Scholar
Ludwig, C. 1856. Diffusion zwischen ungleich erwärmten Orten gleich zusammengesetzter Lösung. Kaiserlichen Akademie der Wissenschaften.Google Scholar
Lun, C. K. K., and Savage, S. B. 1987. A simple kinetic theory for granular flows of rough, inelastic spherical particles. Journal of Applied Mechanics (Transactions of the American Society of Mechanical Engineers), 54, 47–53.Google Scholar
Maccoll, J. W. 1928. Aerodynamics of a spinning sphere. Aeronautical Journal, 32, 777–798.Google Scholar
Magnus, G. 1852. Über die Abweichung der Geschosse. Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin.Google Scholar
Maio, F. P. Di, and Renzo, A. Di. 2004. Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model. Chemical Engineering Science, 59, 3461–3475.Google Scholar
Mangwandi, C., Cheong, Y. S., Adams, M. J., Hounslow, M. J., and Salman, A. D. 2007. The coefficient of restitution of different representative types of granules. Chemical Engineering Science, 62, 437–450.Google Scholar
Mann, R. P., Carter, R. E., and Hazra, S. S. 2007. Experimental study of an impact oscillator with viscoelastic and Hertzian contact. Nonlinear Dynamics, 50, 587–596.Google Scholar
Marhefka, D. W., and Orin, D. E. 1999. A compliant contact model with nonlinear damp- ing for simulation of robotic systems. IEEE Transactions on Systems, Man and Cybernetics – Part A: Systems and Humans, 29, 566–572.Google Scholar
Marshall, J. S., and Li, S. 2014. Adhesive Particle Flow: A Discrete-Element Approach. Cambridge University Press.Google Scholar
Mason, E. A., and Chapman, S. 1962. Motion of small suspended particles in nonuniform gases. Journal of Chemical Physics, 36, 627–632.Google Scholar
Matsumoto, S., and Saito, S. 1970. Monte Carlo simulation of horizontal pneumatic con- veying based on the rough wall model. Journal of Chemical Engineering of Japan, 3, 223–230.Google Scholar
Maugis, D., and Barquins, M. 1978. Fracture mechanics and the adherence of viscoelastic bodies. Journal of Physics D: Applied Physics, 11, 1989–2023.Google Scholar
Maugis, D., and Pollock, H. M. 1984. Surface forces, deformation and adherence at metal microcontacts. Acta Metallurgica, 32, 1323–1334.Google Scholar
Maw, N., Barber, J. R., and Fawcett, J. N. 1976. Oblique impact of elastic spheres. Wear, 38, 101–114.Google Scholar
Maxey, M. R. 1987. The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. Journal of Fluid Mechanics, 174, 441–465.Google Scholar
McCabe, W. L., Smith, J. C., and Harriott, P. 2005. Unit Operations of Chemical Engineering. Vol. 7. McGraw-Hill.Google Scholar
McLaughlin, J. B. 1991. Inertial migration of a small sphere in linear shear flows. Journal of Fluid Mechanics, 224, 261–274.Google Scholar
Mei, R. 1992. An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. International Journal of Multiphase Flow, 18, 145–147.Google Scholar
Memmott, V. J., and Smoot, L. D. 1978. Cold flow mixing rate data for pulverized coal reactors. AIChE Journal, 24, 466–473.Google Scholar
Meyer, C. J., and Deglon, D. A. 2011. Particle collision modelling – A review. Minerals Engineering, 24, 719–730.Google Scholar
Millikan, R. A. 1924. The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Physical Review, 22, 1–23.Google Scholar
Mindlin, R. D. 1949. Compliance of elastic bodies in contact. Journal of Applied Mechanics (Transactions of the American Society of Mechanical Engineers), 16, 259–268.Google Scholar
Mindlin, R. D., and Deresiewicz, H. 1953. Elastic spheres in contact under varying oblique forces. Journal of Applied Mechanics, 20, 327–344.Google Scholar
Mishra, B. K., and Murty, C. V. R. 2001. On the determination of contact parameters for realistic DEM simulations of ball mills. Powder Technology, 115, 290–297.Google Scholar
Mohaupt, M., Minier, J. P., and Taniere, A. 2011. A new approach for the detection of particle interactions for large-inertia and colloidal particles in a turbulent flow. International Journal of Multiphase Flow, 37, 746–755.Google Scholar
Monchick, L., Yun, K. S., and Mason, E. A. 1963. Formal kinetic theory of transport phenomena in polyatomic gas mixtures. Journal of Chemical Physics, 39, 654–669.Google Scholar
Mooney, M. 1951. The viscosity of a concentrated suspension of spherical particles. Journal of Colloid Science, 16, 162–170.Google Scholar
Morgado, W. A. M., and Oppenheim, I. 1997. Energy dissipation for quasielastic granular particle collisions. Physical Review E, 55, 1940–1945.Google Scholar
Morrison, A. 2013. An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Mueller, P., Antonyuk, S., Stasiak, M., Tomas, J., and Heinrich, S. 2011. The normal and oblique impact of three types of wet granules. Granular Matter, 13, 455–463.Google Scholar
Oesterle, B., and Petitjean, A. 1993. Simulation of particle-to-particle interactions in gas-solid flow. International Journal of Multiphase Flow, 19, 199–211.Google Scholar
Oesterle, T., and Dinh, T. Bui. 1998. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Experiments in Fluids, 25, 16–22.Google Scholar
Ozturk, I., Kara, M., Uygan, F., and Kalkan, F. 2010. Restitution coefficient of chick pea and lentil seeds. International Agrophysics, 24, 209–211.Google Scholar
Pasha, M., Dogbe, S., Hare, C., Hassanpour, A., and Ghadiri, M. 2014. A linear model of elasto-plastic and adhesive contact deformation. Granular Matter, 116, 151–162.Google Scholar
Persson, B. N. J. 2001. Theory of rubber friction and contact mechanics. Journal of Chemical Physics, 115, 3840–3861.Google Scholar
Phillips, W. F. 1972. Thermal force on spherical particles in a rarefied gas. Physics of Fluids, 15, 999–1003.Google Scholar
Podczeck, F. 1998. Particle-particle Adhesion in Pharmaceutical Powder Handling. Imperial College Press.Google Scholar
Popov, V. L. 2010. Contact Mechanics and Friction. Springer.Google Scholar
Popper, J., Abuaf, N., and Hetsroni, G. 1974. Velocity measurements in a two-phase turbulent jet. International Journal of Multiphase Flow, 1, 715–726.Google Scholar
Poschel, T., and Schwager, T. 2005. Computational Granular Dynamics. Models and Algorithms. Springer-Verlag.Google Scholar
Potyondy, D. O., and Cundall, P. A. 2004. A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41, 1329–1364.Google Scholar
Prodi, F., Santachiara, G., and Prodi, V. 1979. Measurements of thermophoretic velocities of aerosol particles in the transition region. Journal of Aerosol Science, 10, 421–425.Google Scholar
Prodi, F., Santachiara, G., Travaini, S., Vedernikov, A., Dubois, F., Minetti, C., and Legros, J. C. 2006. Measurements of phoretic velocities of aerosol particles in microgravity conditions. Atmospheric Research, 82, 183–189.Google Scholar
Qin, Z., and Pletcher, R. H. 2011. Particle impact theory including surface asperity deformation and recovery. Journal of Aerosol Science, 42, 852–858.Google Scholar
Quemada, D. 1982. Unstable flows of concentrated suspensions. Pages 210–247 of Casas-Vasques, J. (ed), Stability of Thermodynamic Systems (Lecture Notes in Physics). Springer-Verlag.Google Scholar
Rabinovich, Y. I., Adler, J. J., Ata, A., Singh, R. K., and Moudgil, B. M. 2000. Adhesion between nanoscale rough surfaces – I. Role of asperity geometry. Journal of Colloid and Interface Science, 232, 10–16.Google Scholar
Ramirez, R., Poschel, T., Brilliantov, N. V., and Schwager, T. 1999. Coefficient of restitution of colliding viscoelastic spheres. Physical Review E, 60, 4465–4472.Google Scholar
Ramkrishna, D. 2000. Population Balances: Theory and Applications to Particulate Systems in Engineering. Academic Press.Google Scholar
Ranz, W. E., and Marshall, W. R. 1952. Evaporation from Drops. Chemical Engineering Progress, 48, 141–146.Google Scholar
Ray, S., Kempe, T., and Frohlich, J. 2015. Efficient modelling of particle collisions using a non-linear viscoelastic contact force. International Journal of Multiphase Flow, 76, 101–110.Google Scholar
Reed, J. 1985. Energy losses due to elastic wave propagation during an elastic impact. Journal of Physics D: Applied Physics, 18, 2329–2337.Google Scholar
Reeks, M. W. 1977. On the dispersion of small particles suspended in an isotropic turbulent field. Journal of Fluid Mechanics, 83, 529–546.Google Scholar
Renzo, A. Di, and Maio, F. P. Di. 2004. Comparison of contact-force models for the simula- tion of collisions in DEM-based granular flow codes. Chemical Engineering Science, 59, 525–541.Google Scholar
Renzo, A. Di, and Maio, F. P. Di. 2005. An improved integral non-linear model for the contact of particles in distinct element simulations. Chemical Engineering Science, 60, 1303–1312.Google Scholar
Rhodes, M. 2008. Introduction to Particle Technology. John Wiley & Sons Ltd.Google Scholar
Ristow, G. H. 1992. Simulating granular flow with molecular dynamics. Journal de Physique I France, 2, 649–662.Google Scholar
Roscoe, R. 1952. The viscosity of suspensions of rigid spheres. British Journal of Applied Physics, 3, 267–269.Google Scholar
Rosenblatt, P., and LaMer, V. K. 1946. Motion of a particle in a temperature gradient: Thermal repulsion as a radiometer phenomenon. Physical Review, 70, 385–395.Google Scholar
Rubinov, S. I., and Keller, J. B. 1961. The transverse force on a spinning sphere moving in a viscous fluid. Journal of Fluid Mechanics, 11, 447–459.Google Scholar
Rumpf, H. 1974. Science of agglomeration. Chemie Ingenieur Technik, 1, 1–11.Google Scholar
Rutgers, R. 1965. Relative viscosity and concentration. Rheologica Acta, 2, 305–348.Google Scholar
Saffman, P. G., and Turner, J. S. 1956. On the collision of drops in turbulent clouds. Journal of Fluid Mechanics, 1, 16–30.Google Scholar
Sagot, B., Antonini, G., and Buron, F. 2009. Annular flow configuration with high depo- sition efficiency for the experimental determination of thermophoretic diffusion coefficients. Journal of Aerosol Science, 40, 1030–1049.Google Scholar
Santachiara, G., Prodi, F., and Cornetti, C. 2002. Experimental measurements on ther- mophoresis in the transition region. Journal of Aerosol Science, 33, 769–780.Google Scholar
Savkoor, A. R., and Briggs, G. A. D. 1977. The effect of tangential force on the contact of elastic solids in adhesion. Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 356, 103–114.Google Scholar
Sawatzki, O. 1970. Das Strömungsfeld um eine rotierende Kugel. Acta Mechanica, 9, 159–214.Google Scholar
Schafer, J., Dippel, S., and Wolf, D. E. 1996. Force Schemes in simulations of granular materials. Journal de Physique I France, 6, 5–20.Google Scholar
Schlichting, H., and Gersten, K. 2017. Boundary-Layer Theory. Springer.Google Scholar
Schwager, T., and Poschel, T. 1998. Coefficient of restitution of viscous spheres and cooling rate of granular gases. Physical Review E, 57, 650–654.Google Scholar
Schwager, T., and Poschel, T. 2007. Coefficient of restitution and linear-dashpot model revisited. Granular Matter, 9, 465–469.Google Scholar
Scott, G. D., and Kilgour, D. M. 1969. The density of random close packing of spheres. Journal of Physics D: Applied Physics, 2, 863.Google Scholar
Sheen, H. J., Jou, B. H., and Lee, Y. T. 1994. Effect of particle size on a two-phase turbulent jet. Experimental Thermal and Fluid Science, 8, 315–327.Google Scholar
Singamsetti, S. R. 1966. Diffusion of sediment in a submerged jet. Journal of the Hydraulic Division, ASCE, 92, 153–168.Google Scholar
Smith, C. E., and Liu, P. 1992. Coefficients of restitution. Journal of Applied Mechanics, 59, 963–969.Google Scholar
Smoluchowski, M. 1917. Versuch einer mathematischen Theorie der Koagulationskinetic kolloider Losungen. Zeitschrift für Physikalische Chemie, 92, 129–168.Google Scholar
Sommerfeld, M. 2000. Theoretical and Experimental Modelling of Particulate Flows. Tech. rept. Lecture Series 2000–06, von Karman Institute for Fluid Dynamics.Google Scholar
Sondegaard, R., Chaney, K., and Brennen, C. E. 1990. Measurements of solid spheres bouncing off flat planes. Journal of Applied Mechanics, 112, 694–699.Google Scholar
Sone, Y., and Aoki, K. 1983. A similarity solution of the linearized Boltzmann equation with application to thermophoresis of a spherical particle. Journal de Mecanique Theorique et Appliquee, 2, 3–12.Google Scholar
Soo, S. L. 1965. Dynamics of multiphase flow systems. Industrial Engineering Chemistry Fundamentals, 4, 426–433.Google Scholar
Soret, C. 1879. Concentrations differentes d’une dissolution dont deux parties sont à des températures differéntes. Archives des Sciences Physiques et Naturelles, 2, 48–61.Google Scholar
Squires, K. D., and Eaton, J. K. 1990. Particle response and turbulence modification in isotropic turbulence. Physics of Fluids A, 2, 1191–1203.Google Scholar
Squires, K. D., and Eaton, J. K. 1991a. Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence. Journal of Fluid Mechanics, 226, 1–35.Google Scholar
Squires, K. D., and Eaton, J. K. 1991b. Preferential concentration of particles by turbulence. Physics of Fluids A, 3, 1169–1178.Google Scholar
Stevens, A. B., and Hrenya, C. M. 2005. Comparison of soft-sphere models to mea- surements of collision properties during normal impacts. Powder Technology, 154, 99–109.Google Scholar
Stronge, W. J. 2000. Impact Mechanics. Cambridge University Press.Google Scholar
Stronge, W. J. 2013. Smooth dynamics of oblique impact with friction. International Journal of Impact Engineering, 51, 36–49.Google Scholar
Sun, J., and Chen, M. M. 1988. A theoretical analysis of heat transfer due to particle impact. International Journal of Heat and Mass Transfer, 31, 969–975.Google Scholar
Sundaram, S., and Collins, L. R. 1996. Numerical considerations in simulating a turbu- lent suspension of finite-volume particles. Journal of Computational Physics, 124, 337–350.Google Scholar
Suri, M., and Dumitrica, T. 2008. Efficient sticking of surface-passivated Si nanospheres via phase-transition plasticity. Physical Review B, 78, 081405(R).Google Scholar
Tabor, D. 1948. A simple theory of static and dynamic hardness. Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 192, 247–274.Google Scholar
Tabor, D. 1977. Surface forces and surface interactions. Journal of Colloid and Interface Science, 11, 2–13.Google Scholar
Tabor, D. 2000. The Hardness of Metals (Oxford Classic Texts in the Physical Sciences). Oxford University Press.Google Scholar
Taguchi, Y. H. 1992. New origin of a convective motion – Elastically induced convection in granular-materials. Physical Review Letters, 68, 1367–1370.Google Scholar
Takato, Y., Sen, S., and Lechman, J. B. 2014. Strong plastic deformation and softening of fast colliding nanoparticles. Physical Review E, 89, 033308.Google Scholar
Talbot, L., Cheng, R. K., Schefer, R. W., and Willis, D. R. 1980. Thermophoresis of particles in a heated boundary layer. Journal of Fluid Mechanics, 101, 737–758.Google Scholar
Tang, L., Wen, F., Yang, Y., Crowe, C. T., Chung, J. N., and Troutt, T. R. 1993. Self-organizing particle dispersion mechanism in a plane wake. Physics of Fluids A 4, 10, 2244–2251.Google Scholar
Taylor, G. I. 1922. Diffusion by continuous movements. Proceedings of the London Mathematical Society, 20, 196–212.Google Scholar
Thompson, P. A., and Grest, G. S. 1991. Granular flow – Friction and the dilatancy transition. Physical Review Letters, 65, 1751–1754.Google Scholar
Thornton, C. 1997. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Journal of Applied Mathematics, 64, 383–386.Google Scholar
Thornton, C. 2015. Granular Dynamics, Contact Mechanics and Particle System Simula- tions: A DEM Study (Particle Technology Series). Springer.Google Scholar
Thornton, C., and Ning, Z. 1998. A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres. Powder Technology, 99, 154–162.Google Scholar
Thornton, C., and Randall, C. W. 1988. Applications of theoretical contact mechanics to solid particle system simulation. Pages 133–142 of Satake, M., and Jenkins, J. T. (eds), Micromechanics of Granular Materials. Elsevier.Google Scholar
Thornton, C., and Yin, K. K. 1991. Impact of elastic spheres with and without adhesion. Powder Technology, 65, 153–166.Google Scholar
Thornton, C., Cummins, S. J., and Cleary, P. W. 2011. An investigation of the compara- tive behaviour of alternative contact force models during elastic collisions. Powder Technology, 210, 189–197.Google Scholar
Thornton, C., Cummins, S. J., and Cleary, P. W. 2013. An investigation of the compara- tive behaviour of alternative contact force models during inelastic collision. Powder Technology, 233, 30–46.Google Scholar
Toda, A., Ohnishi, H., Dobashi, R., and Hirano, T. 1998. Experimental study on the relation between thermophoresis and size of aerosol particles. International Journal of Heat and Mass Transfer, 41, 2710–2713.Google Scholar
Tong, N. T. 1975. Experiments on photophoresis and thermophoresis. Journal of Colloid and Interface Science, 51, 143–151.Google Scholar
Tsuji, Y., Morikawa, Y., and Mizuno, O. 1985. Experimental measurement of the Magnus force on a rotating sphere at low Reynolds numbers. Journal of Fluids Engineering, 107, 484–488.Google Scholar
Tsuji, Y., Tanaka, T., and Ishida, T. 1992. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology, 71, 239–250.Google Scholar
Tsuji, Y., Kawaguchi, T., and Tanaka, T. 1993. Discrete particle simulation of 2- dimensional fluidized-bed. Powder Technology, 77, 79–87.Google Scholar
Tyndall, J. 1870. Scientific Addresses. C.C. Chatfield and Co.Google Scholar
Volkov, A. N., Tsirkunov, Y. M., and Oesterle, B. 2005. Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle colli- sions and two-way coupling effects. International Journal of Multiphase Flow, 31, 1244–1275.Google Scholar
Vu-Quoc, L., and Zhang, X. 1999. An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations. Mechanics of Mate- rials, 31, 235–269.Google Scholar
Waldmann, L. 1959. Über die Kraft eines inhomogenen Gases auf kleine suspendierte Kugeln. Zeitschrift für Naturforschung A, 14a, 589–599.Google Scholar
Walton, O. R. 1993. Numerical simulation of inelastic frictional particle-particle interac- tions. In: Rocco, M. C. (ed), Particulate Two-Phase Flow. Butterworth-Heinemann.Google Scholar
Walton, O. R., and Braun, R. L. 1986. Viscosity, granular-temperature, and stress calcula- tions for shearing assemblies of inelastic, frictional disks. Journal of Rheology, 30, 949–980.Google Scholar
Wang, L. P., and Maxey, M. R. 1993. Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics, 256, 27–68.Google Scholar
Wang, L. P., Wexler, A. S., and Zhou, Y. 2000. Statistical mechanical description and modelling of turbulent collision of inertial particles. Journal of Fluid Mechanics, 415, 117–153.Google Scholar
Weber, M. W., Hoffman, D. K., and Hrenya, C. M. 2004. Discrete-particle simula- tions of cohesive granular flow using a square-well potential. Granular Matter, 6, 239–254.Google Scholar
Wen, F., Kamalu, N., Chung, J. N., Crowe, C. T., and Troutt, T. R. 1992. Particle disper- sion by vortex structures in plane mixing layers. Journal of Fluids Engineering, 114, 657–666.Google Scholar
Whitaker, S. 1972. Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AICHE Journal, 18, 361–371.Google Scholar
Whittaker, E. T. 1904. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press.Google Scholar
Wu, C. Y., Li, L. Y., and Thornton, C. 2003. Rebound behaviour of spheres for plastic impacts. International Journal of Impact Engineering, 28, 929–946.Google Scholar
Xu, B. H., and Yu, A. B. 1997. Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chemical Engineering Science, 52, 2785–2809.Google Scholar
Yamamoto, K., and Ishihara, Y. 1988. Thermophoresis of a spherical particle in a rarefied gas of a transition regime. Physics of Fluids, 31, 3618–3624.Google Scholar
Yang, Y., Crowe, C. T., Chung, J. N., and Troutt, T. R. 2000. Experiments on par- ticle dispersion in a plane wake. International Journal of Multiphase Flow, 26, 1583–1607.Google Scholar
Yeung, P. K., and Pope, S. B. 1988. An algorithm for tracking fluid particles in numeri- cal simulations of homogeneous turbulence. Journal of Computational Physics, 79, 373–416.Google Scholar
Zhang, D., and Whiten, W. J. 1996. The calculation of contact forces between particles using spring and damping models. Powder Technology, 88, 59–64.Google Scholar
Zhang, Y., and Sharf, I. 2009. Validation of nonlinear viscoelastic contact force models for low speed impact. Journal of Applied Mechanics, 76, 051002–1–051002–12.Google Scholar
Zhang, Y., and Sharf, I. 2010. Force reconstruction for low velocity impacts using force and acceleration measurements. Journal of Vibration and Control, 17, 407–420.Google Scholar
Zheng, F. 2002. Thermophoresis of spherical and non-spherical particles: A review of theories and experiments. Advances in Colloid and Interface Science, 97, 255–278.Google Scholar
Zhou, J. H., Yu, A. B., and Horio, M. 2008. Finite element modelling of the transient heat conduction between colliding particles. Chemical Engineering Journal, 139, 510–516.Google Scholar
Zhou, Y., Wexler, A. S., and Wang, L. P. 1998. On the collision rate of small particles in isotropic turbulence. II. Finite inertia case. Physics of Fluids, 10, 1206–1216.Google Scholar
Zukas, J. A. 1990. High Velocity Impact Dynamics. John Wiley & Sons.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Pawel Kosinski, Universitetet i Bergen, Norway
  • Book: Multiphase Flow with Solid Particles
  • Online publication: 05 October 2023
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Pawel Kosinski, Universitetet i Bergen, Norway
  • Book: Multiphase Flow with Solid Particles
  • Online publication: 05 October 2023
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Pawel Kosinski, Universitetet i Bergen, Norway
  • Book: Multiphase Flow with Solid Particles
  • Online publication: 05 October 2023
Available formats
×