Continual mechanics of monodisperse suspensions. rheological equations of state for suspensions of moderate concentration: PMM vol. 37, n≗6, 1973, pp. 1059–1077

• Published in: Journal of applied mathematics and mechanics Vol. 37; no. 6; pp. 1005 - 1022
• Main Authors: Buevich, Iu.A., Markov, V.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1973
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/0021-8928(73)90066-X

Rheological relationships linking mean and moment stresses and, also, the force and moment of interphase reaction in a macroscopic flow of small solid sphere suspension with the kinematic characteristics of the flow are derived. This makes it possible to close the system of equations of suspension hydrodynamics. Coefficients of viscosity and of moment viscosity of a suspension are obtained and calculated. The equations of conservation of mass, momentum and moment of momentum of suspension and of its phases, considered (from the macroscopic point of view) to be coexistent continuous media, were formulated in a general form in [1]. These equations contain unknown vectors and tensors which define the interaction between the considered continuous media and, also, stresses and moment stresses appearing when these are in motion. To close the equations of conservation it is necessary to express all these quantities in terms of unknown variables of these equations (mean concentration of suspension, pressure in the fluid phases, and phase velocities). This problem is the second of the fundamental problems of hydromechanics of suspensions indicated in [1]. Here this problem is solved with the use of a kind of self-consistent field theory, which is essentially an extension and generalization of methods developed in [2 – 7]. Expressions for all of the quantities mentioned above are derived. They can be considered to be rheological equations of state for suspensions. Expressions for the various coefficients of these equations and their dependence on parameters of phases and on the flow frequency spectrum are also considered.