A Theory of Multiphase Mixtures

Passman, Stephen L.; Nunziato, Jace W.; Walsh, E. K.

doi:10.1007/978-1-4612-5206-1_15

Cited by 116 publications

(100 citation statements)

References 54 publications

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“…(7) causes it to predict motion of the sand and water for this example while Eq. (8) does not. In a 1978 paper [4], Bedford and the author first showed how this point of contention could be resolved by application of the volume fraction constraint Eq.(3).…”

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 93%

“…(7) but not in Eq. (8). The reason for the choice of this name is not totally clear, but the following specific example may shed light on this terminology as well as illustrate an important contradiction caused by this term.…”

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 96%

“…Two possibilities existed for the I-th constituent. When terms that represented the momentum interaction between the constituents were ignored, these two possibilities gave either or Ptat = -Y€ P d P t (8) where at is the acceleration of the I-th constituent. EquationA7-),-.…”

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 99%

“…In addition, we shall also refer to a summary article by Passman, Nunziato, and Walsh [8]. For simplicity we shall refer to [6], [7], and [8] as the primary references. There are subtle differences in the two theories, which $e shall point out.…”

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 99%

“…We shall show that they reduce to the equations of balance of momentum given in [8] but first we will discuss the equations of conservation of energy.…”

Section: Pementioning

confidence: 99%

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On theories for reacting immiscible mixtures

Drumheller¹

2000

International Journal of Engineering Science

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On some small scale each constituent of an immiscible mixture occupies a separate region of space. Given sufficient time and computing power, we could solve the continuum field equations and boundary conditions for this heterogeneous system. This usually represents an enormously difficult task that is well beyond today's computational capabilities. Mixture theories approximate this complex heterogeneous formulation with a set of field equations for an equivalent homogeneous material. In this work, we compare the theory for immiscible mixtures by Drumheller and Bedford with the theory of Passman, Nunziato, and Walsh. We describe the conditions under which these theories reduce to an equivalent formulation, and we also investigate the differences in their microinertial descriptions.Two variables play special roles in both theories. They are the true material density and the volume fraction. Here we use a kinematical approach based on two new variables-t he true deformation gradient and the distention gradient. We show how the true deformation gradient is connected to the true material density and, in the absence of chemical reactions, the volume fraction is the inverse of the determinant of the distention gradient. However, when chemical reactions occur, the distention gradient and the volume fraction are not directly connected.We also present a mixture model for a granuIar expIosive. This model is based upon the work of Baer and Nunziato, but our theory differs from their work in that we present a three-dimensioml model, -we cast the constitutive postulates in terms of the distention gradient rather than the volume fraction, and we incorporate elastic-plastic effects into the constitutive description of the solid granules.

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Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 93%

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 96%

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 99%

Section: The Definition Of Volume Fraction Eq (1) Then Leads To the mentioning

confidence: 99%

“…We shall show that they reduce to the equations of balance of momentum given in [8] but first we will discuss the equations of conservation of energy.…”

Section: Pementioning

confidence: 99%

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On theories for reacting immiscible mixtures

Drumheller¹

2000

International Journal of Engineering Science

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Hydration Swelling of Water-Absorbing Rocks: A Constitutive Model

Heidug

Wong

1996

Int. J. Numer. Anal. Methods Geomech.

186

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SUMMARYWater-absorbing rocks are formed from minerals that can hold water in their crystal structure or between grain boundaries. Such water absorption is often accompanied by a change in the crystar dimension that manifests itself as a swelling of the rock. Swelling is particularly pronounced in rocks containing phyllosilicates because of the ease with which these minerals hydrate; it is thus of geological and geotechnical relevance in shales, clay-rich soils and zeolitized tuffs. The model of hydration swelling that we present here is based on extended versions of the equations of poroelasticity and Darcy's transport law, which we derive using a non-equilibrium thermodynamics approach. Our equations account for the hydration reaction under the assumption that the reaction rate is fast in comparison with the rate at which hydraulic state changes are communicated through the rock, i.e. that local physico-chemical equilibrium persists. Using a finite-element scheme for solving numerically the governing equations of our model, we simulate the creep of shales during a routine swelling test and calculate the stress and strain distributions around wellbores drilled in shale formations that undergo swelling. We show that swelling effects promote tensile failure of the wellbore wall.

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Effects of the Interphase on the Mechanical Behavior of Thin Adhesive Films – a Modeling Approach

2005

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In the present conribution, we develop a continuum-based model to describe experimentally observable interphases in thin adhesive films. The model is based on an extended contiuum theory, i.e. the mechanical behaviour in these interphases is captured by an additional field equation. The introduced scalar order parameter models the microscopical mechanical properties of the film phenomenologically.As the film properties at the boundary to the substrate are thought to be extrinsic quantities, they are prescribed as Dirichlet-type boundary conditions in the present model.

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A Theory of Multiphase Mixtures

Cited by 116 publications

References 54 publications

On theories for reacting immiscible mixtures

On theories for reacting immiscible mixtures

Hydration Swelling of Water-Absorbing Rocks: A Constitutive Model

Effects of the Interphase on the Mechanical Behavior of Thin Adhesive Films – a Modeling Approach

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