<i>Rational Thermodynamics</i>

Truesdell, C.; Baierlein, Ralph

doi:10.1119/1.13999

Cited by 88 publications

(167 citation statements)

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“…The additional ingredient with respect to the mechanics of simple bodies is, in fact, the need to account for the interactions between each constituent and the others and to represent them in some way. Truesdell suggested three methaphysical principles for mixtures (see [1]): (i) the properties of the whole mixture are consequences of the ones of the constituents, (ii) each of them can be isolated from the rest provided that the interactions with the others are accounted for, (iii) the whole mixture behaves as a single body.…”

Section: The Main Resultmentioning

confidence: 99%

“…To render (38) compatible with the pointwise balance of energy suggested by Truesdell (see [1] and [3]), we should assume for E α b the following expression:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The balance equations (20) and (21) of the whole mixture follow by summing over α equations (16) and (17); we make use of (18) and (19) and take into account that for any spatial field λ (x,t) = α c α λ α (x,t) we have (see [1]…”

Section: Proof Of Theoremmentioning

confidence: 99%

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invariance and covariance in mixtures of simple bodies

Mariano

2005

International Journal of Non-Linear Mechanics

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We adapt to mixtures the procedure of invariance of external power under the action of SO (3) to deduce balance equations. The two classical axioms about the growths of momentum and moment of momentum are derived with the help of a rule on the structure of the total power. We discuss also the covariance of the balance equations of each constituent and the nature of the constituent stress. Key words Mixtures, invariance1 Commentary to the theory of mixtures of simple bodies: the rôle of the invarance of the power. Preliminary remarks.Let B 0 be the regular (in the sense of "fit") region of the three-dimensional Euclidean point space E 3 occupied by the mixture in a reference place. We call part of B 0 any regular subset b of it and denote with X its generic point. The regular region B occupied by the mixture in the current place is obtained from B 0 through a sufficiently smooth orientation preserving mapping f such that f (B 0 ) = B; for any x ∈B we have then x =f (X). Motions are sufficiently smooth one-parameter mappings f t , with t ∈ [t 0 , t 1 ] the time. The velocity in the spatial description is denoted with v, while the acceleration with a = ∂ t v + (gradv) v.At the introduction of Lecture 5 of his "Rational Thermodynamics", Truesdell [1] describes the mixtures by assuming as a crucial point of view that all constituents occupy B simultaneously. Such an assumption is not

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Section: The Main Resultmentioning

confidence: 99%

“…To render (38) compatible with the pointwise balance of energy suggested by Truesdell (see [1] and [3]), we should assume for E α b the following expression:…”

Section: Proof Of Theoremmentioning

confidence: 99%

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invariance and covariance in mixtures of simple bodies

Mariano

2005

International Journal of Non-Linear Mechanics

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“…The fundamental mixture postulate (e.g. Truesdell 1984;Morland 1992) states that every point in the mixture is simultaneously occupied by all of the constituents, so that overlapping partial densities, ρ µ , partial velocities, u µ , and partial pressures, p µ , can be defined for each of the constituents µ = l, s per unit mixture volume. Each of the constituents satisfies individual mass and momentum conservation laws (e.g.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Each of the constituents satisfies individual mass and momentum conservation laws (e.g. Truesdell 1984;Morland 1992;Gray & Svendsen 1997) …”

Section: Governing Equationsmentioning

confidence: 99%

Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the sizedistribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particlesize segregation and diffusive remixing of large and small particles in shallow gravitydriven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation-remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation-remixing equation reduces to a logistic type equation and the 'S'-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation-remixing equation to Burgers equation and using the Cole-Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent twodimensional solutions are also constructed for plug-flow in a semi-infinite chute.

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Impulse waves generated by snow avalanches: Momentum and energy transfer to a water body

et al. 2016

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When a snow avalanche enters a body of water, it creates an impulse wave whose effects may be catastrophic. Assessing the risk posed by such events requires estimates of the wave's features. Empirical equations have been developed for this purpose in the context of landslides and rock avalanches. Despite the density difference between snow and rock, these equations are also used in avalanche protection engineering. We developed a theoretical model which describes the momentum transfers between the particle and water phases of such events. Scaling analysis showed that these momentum transfers were controlled by a number of dimensionless parameters. Approximate solutions could be worked out by aggregating the dimensionless numbers into a single dimensionless group, which then made it possible to reduce the system's degree of freedom. We carried out experiments that mimicked a snow avalanche striking a reservoir. A lightweight granular material was used as a substitute for snow. The setup was devised so as to satisfy the Froude similarity criterion between the real‐world and laboratory scenarios. Our experiments in a water channel showed that the numerical solutions underestimated wave amplitude by a factor of 2 on average. We also compared our experimental data with those obtained by Heller and Hager (2010), who used the same relative particle density as in our runs, but at higher slide Froude numbers.

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Rational Thermodynamics

Cited by 88 publications

References 0 publications

invariance and covariance in mixtures of simple bodies

invariance and covariance in mixtures of simple bodies

Particle-size segregation and diffusive remixing in shallow granular avalanches

Impulse waves generated by snow avalanches: Momentum and energy transfer to a water body

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