Abstract
A continuum theory for the distribution of incompressible particles in an incompressible fluid is employed to study the behaviour of plane shock waves in a particulate suspension. An expression is derived for the speed of displacement in terms of the jump in the volume fraction of one of the constituents across the shock. A differential equation is derived to govern the evolutionary behaviour of the shock wave propagating into a region which is in a uniform equilibrium state before the arrival of the shock wave. The implications of this equation are examined in detail.
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References
Jackson, R., The Mechanics of Fluidized Beds: Part 1: The Stability of the State of Uniform Fluidization. Trans. Inst. Chem. Eng. 41, 13–28 (1963).
Murray, J. D., On the Mathematics of Fluidization: Part 1: Fundamental Equations and Wave Propagation. J. Fluid Mech. 21, 465–493 (1965).
Soo, S. L., Fluid Dynamics of Multiphase Systems, Blaisdell, Waltham, Massachusetts (1967).
Anderson, T. B., & R. Jackson, A Fluid Mechanical Description of Fluidized Beds. Ind. and Eng. Chem. Fund. 6, 527–539 (1967).
Anderson, T. B., & R. Jackson, A Fluid Mechanical Description of Fluidized Beds: Stability of the State of Uniform Fluidization. Ind. and Eng. Chem. Fund. 7, 12–21 (1968).
Panton, R., Flow Properties for the Continuum Viewpoint of a Non-Equilibrium Gas-Particle Mixture. J. Fluid Mech. 31, 273–303 (1968).
Garg, S. K., & J. W. Pritchett, Dynamics of Gas Fluidized Beds. J. App. Physics 46, 4493–4500 (1975).
Drew, D. A., Two Phase Flows: Constitutive Equations for Lift and Brownian Motion and Some Basic Flows. Arch. Rational Mech. Anal. 62, 149–163 (1976).
Hill, C. D., A. Bedford & D. S. Drumheller, An Application of Mixture Theory to Particulate Sedimentation. J. Appl. Mech. 47, 261–265 (1980).
Bedford, A., & D. S. Drumheller, Theories of Immiscible and Structured Mixtures. Int. J. Engng. Sci. 21, 863–960 (1983).
Drumheller, D. S., & A. Bedford, A Thermomechanical Theory for Reacting Immiscible Mixtures. Arch. Rational Mech. Anal. 73, 257–284 (1980).
Tracker, W. C., & J. W. Lavelle, Stability of Settling of Suspended Sediments. Phys. Fluid 21, 291–292 (1978).
Hill, C. D., & A. Bedford, Stability of the Equations for Particulate Sedimentation. Phys. Fluids 22, 1252–1254 (1979).
Hill, C. D., Two Dimensional Analysis of the Stability of Particulate Sedimentation. Phys. Fluids 23, 667–668 (1980).
Batra, G., A. Bedford & M. F. McCarthy, Acceleration Waves in a Particulate Suspension. Int. J. Engng. Sci. 24, 1339–1349 (1986).
Bowen, R. M., & P. J. Chen, Shock Waves in Ideal Fluid Mixtures with Several Temperatures. Arch. Rational Mech. Anal. 53, 244–299 (1974).
Nunziato, J. W., One Dimensional Shock Waves in a Chemically Reacting Mixture of Elastic Materials. J. Chem. Phys. 58, 961–965 (1973).
Bowen, R. M., P. J. Chen & J. W. Nunziato, Growth and Decay of One Dimensional Shock Waves in Fluids with Internal State Variables (1975).
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Communicated by C. -C. Wang
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McCarthy, M.F. Shock waves in a particulate suspension. Arch. Rational Mech. Anal. 115, 167–178 (1991). https://doi.org/10.1007/BF00375225
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DOI: https://doi.org/10.1007/BF00375225