Identification of shock profile solutions for bidisperse suspensions

Shock-waves represent one of the most important mechanisms for creating and heating a plasma. In classical non-dissipative gas dynamics, the formation of a shock is indicated by the progressive steepening of a finite-amplitude compressive wave front to the point where it becomes multivalued and consequently without physical meaning. This difficulty is avoided by the inclusion of dissipative effects, usually in the form of heat flow and viscosity. The dissipative mechanisms become more effective as the wave front steepens, and the result is a steady wave profile for which the non-linear and dissipative effects are counterbalanced. The scale length for the dissipative transition zone or wave profile is the mean-free-path; the actual thickness may range from one to several mean-free-paths, or even more for very weak shocks. Given the strength of the shock, the state on one side of the shock may be computed from the state on the other side directly from the laws of conservation of mass, momentum and energy (Hugoniot relations). Accordingly, the nature of the particular dissipative mechanism affects only the shape of the shock profile but not the end states.

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Viscosity of concentrated noncolloidal bidisperse suspensions

Rheologica Acta ◽

10.1007/s003970100187 ◽

2001 ◽

Vol 40 (6) ◽

pp. 591-598 ◽

Cited By ~ 19

Author(s):

Da He ◽

Ndy N. Ekere

Keyword(s):

Bidisperse Suspensions

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Gravity separation of bidisperse suspensions: Light and heavy particle species

Chemical Engineering Science ◽

10.1016/0009-2509(87)80158-6 ◽

1987 ◽

Vol 42 (7) ◽

pp. 1527-1538 ◽

Cited By ~ 44

Author(s):

Hin-Sum Law ◽

Jacob H. Masliyah ◽

Robert S. MacTaggart ◽

K. Nandakumar

Keyword(s):

Heavy Particle ◽

Gravity Separation ◽

Particle Species ◽

Bidisperse Suspensions

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The velocity distribution function within a shock wave

Journal of Fluid Mechanics ◽

10.1017/s0022112067001557 ◽

1967 ◽

Vol 30 (3) ◽

pp. 479-487 ◽

Cited By ~ 51

Author(s):

G. A. Bird

Keyword(s):

Shock Wave ◽

Distribution Function ◽

Velocity Distribution ◽

Numerical Experiments ◽

Equilibrium Distribution ◽

Velocity Distribution Function ◽

Distribution Functions ◽

Rigid Sphere ◽

Lateral Velocity ◽

Shock Profile

The structure of normal shock waves in a gas composed of rigid sphere molecules is investigated by numerical experiments with a simulated gas on a digital computer. The non-equilibrium between the temperatures based on the longitudinal and lateral velocity components is studied and the results compared with the theory of Yen (1966). Details of the velocity distribution function are presented for a shock of Mach number 10. The distribution functions for both the longitudinal and lateral velocity components are plotted for a number of locations in the shock profile and are compared with the equilibrium distribution.

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