Suspension rheology in the presence of rotary Brownian motion and external couples: elongational flow of dilute suspensions

Abstract A general dynamical theory is presented of the rheological properties of dilute suspensions of rigid particles of arbitrary shape dispersed in a Newtonian fluid, including rotary Brownian motion and external couples acting upon the suspended particles. Utilization of the theory for particles of specified shape requires knowledge of eight fundamental tensors that are intrinsic geometric properties of the external (i.e. wetted) surface of the particles. It is pointed out that the forms of these basic tensors can be deduced via group-theoretical arguments for particles of specified geometrical shape. These eight tensors are given explicitly for general triaxial ellipsoidal particles and for spherical dumbbells. The rheological behavior of suspensions of spheroidal and dumbbell particles in uniaxial elongational and compressive flows is worked out. Exact solutions of these problems are presented, and fundamental errors in the earlier work of a number of prior investigators are pointed out.

[1]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[2]  Andreas Acrivos,et al.  The constitutive equation for a dilute emulsion , 1970, Journal of Fluid Mechanics.

[3]  L. Scriven,et al.  Angular Momentum of Continua , 1961, Nature.

[4]  T. Kotaka.  Note on the Normal Stress Effect in the Solution of Rodlike Macromolecules , 1959 .

[5]  D. W. Condiff,et al.  Transport Mechanics in Systems of Orientable Particles. II. Kinetic Theory of Orientation Specific Transport for Hard‐Core Models , 1970 .

[6]  R. Roscoe,et al.  On the rheology of a suspension of viscoelastic spheres in a viscous liquid , 1967, Journal of Fluid Mechanics.

[7]  D. W. Condiff,et al.  Transport Mechanics in Systems of Orientable Particles , 1969 .

[8]  M. Fixman,et al.  Viscosity of Polymer Solutions , 1963 .

[9]  F. Bretherton.  The motion of rigid particles in a shear flow at low Reynolds number , 1962, Journal of Fluid Mechanics.

[10]  H. Brenner.  Rheology of a dilute suspension of dipolar spherical particles in an external field , 1970 .

[11]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[12]  M. Sugita,et al.  Energy Dissipation and Entropy Production in Irreversible Processes of Dilute Systems , 1952 .

[13]  H. Giesekus.  Strömungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von darin suspendierten Teilchen , 1962 .

[14]  H. Giesekus.  Elasto-viskose Flüssigkeiten, für die in stationären Schichtströmungen sämtliche Normalspannungskomponenten verschieden groß sind , 1962 .

[15]  Howard Brenner,et al.  The Stokes resistance of an arbitrary particle—III: Shear fields , 1964 .

[16]  J. Goddard,et al.  Nonlinear effects in the rheology of dilute suspensions , 1967, Journal of Fluid Mechanics.

[17]  S. G. Mason,et al.  PARTICLE MOTIONS IN SHEARED SUSPENSIONS: XVI. ORIENTATIONS OF RODS AND DISKS IN HYPERBOLIC AND OTHER FLOWS , 1965 .

[18]  Howard Brenner,et al.  The Stokes resistance of an arbitrary particleIV Arbitrary fields of flow , 1964 .

[19]  H. S. Lew.  Formulation of statistical equation of motion of blood. , 1969, Biophysical journal.

[20]  Nobuhiko Saitô,et al.  The Effect of the Brownian Motion on the Viscosity of Solutions of Macromolecules, I. Ellipsoid of Revolution. , 1951 .

[21]  H. Brenner.  Rheology of Two-Phase Systems , 1970 .

[22]  G. Batchelor,et al.  The stress system in a suspension of force-free particles , 1970, Journal of Fluid Mechanics.

[23]  H. Scheraga.  Non‐Newtonian Viscosity of Solutions of Ellipsoidal Particles , 1955 .

[24]  Howard Brenner,et al.  The Stokes resistance of a slightly deformed sphere , 1964 .

[25]  R. G. Cox,et al.  The rheology of a suspension of particles in a Newtonian fluid , 1971 .

[26]  G. Batchelor,et al.  The stress generated in a non-dilute suspension of elongated particles by pure straining motion , 1971, Journal of Fluid Mechanics.

[27]  L. G. Leal,et al.  On the effect of particle couples on the motion of a dilute suspension of spheroids , 1971, Journal of Fluid Mechanics.

[28]  H. Brenner,et al.  Rheological behavior of a dilute emulsion. , 1968, Journal of colloid and interface science.

[29]  Howard Brenner,et al.  Coupling between the translational and rotational brownian motions of rigid particles of arbitrary shape: II. General theory , 1967 .

[30]  H. Brenner.  The Stokes resistance of an arbitrary particle—II: An extension , 1964 .