scholarly journals The rheology of a suspension of nearly spherical particles subject to Brownian rotations

1972 ◽  
Vol 55 (4) ◽  
pp. 745-765 ◽  
Author(s):  
L. G. Leal ◽  
E. J. Hinch
Keyword(s):  
Constitutive Equations ◽  
Bulk Flow ◽  
Time Dependent ◽  
Spherical Particles ◽  
Experimental Investigations ◽  
Complex Materials ◽  
Rigid Particles ◽  
Dilute Suspension ◽  
Polymeric Solutions ◽  
Stress Patterns

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials.

Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

1976 ◽  
Vol 76 (1) ◽  
pp. 187-208 ◽  
Author(s):  
E. J. Hinch ◽  
L. G. Leal
Keyword(s):  
Constitutive Equations ◽  
Fluid Model ◽  
Second Order ◽  
Order Tensor ◽  
Rigid Particles ◽  
Dilute Suspension ◽  
Suspension Mechanics ◽  
Made In

Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

scholarly journals The extensional viscosity of a dilute suspension of spherical particles at intermediate microscale Reynolds numbers

1980 ◽  
Vol 99 (3) ◽  
pp. 513-529 ◽  
Author(s):  
G. Ryskin ◽  
G. Ryskin ◽  
J. M. Rallison
Keyword(s):  
Uniaxial Extension ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Extensional Viscosity ◽  
Spherical Particles ◽  
Rigid Sphere ◽  
Rigid Spheres ◽  
Viscous Drops ◽  
Rigid Particles ◽  
Dilute Suspension

The extensional viscosity of a dilute suspension of spherical particles (rigid spheres, viscous drops or gas bubbles) is computed for the case when the Reynolds number of the microscale disturbance motionRis not restricted to be small, as in the classical analysis of Einstein and Taylor. However, the present theory is restricted to steady axisymmetric pure straining flow (uniaxial extension). The rate of energy dissipation is expressed using the Bobyleff-Forsythe formula and then conditionally convergent integrals are removed explicitly. The problem is thereby reduced to a determination of the flow around a particle, subject to pure straining at infinity, followed (for rigid particles) by an evaluation of the volume integral of the vorticity squared. In the case of fluid particles, further integrals over the volume and surface of the particle are required. In the present paper, results are obtained numerically for 1 [les ]R[les ] 1000 for a rigid sphere, for a drop whose viscosity is equal to the viscosity of the ambient fluid, and for an inviscid drop (gas bubble). For the last case, limiting results are also obtained forR→ ∞ using Levich's approach.All of these results show a strain-thickening behaviour which increases with the viscosity of the particle. The possibility of experimental verification of the results, which is complicated by the inapplicability of the approximation of material frame-indifference in this case, is discussed.

The stress generated in a non-dilute suspension of elongated particles by pure straining motion

1971 ◽  
Vol 46 (4) ◽  
pp. 813-829 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Theoretical Formula ◽  
Rigid Sphere ◽  
Cross Sectional ◽  
Outer Flow ◽  
Rigid Particles ◽  
Bulk Stress ◽  
Order Of Magnitude ◽  
Sectional Plane ◽  
Dilute Suspension ◽  
A Minor

In a pure straining motion, elongated rigid particles in suspension are aligned parallel to the direction of the greatest principal rate of extension, provided the effect of Brownian motion is weak. If the suspension is dilute, in the sense that the particles are hydrodynamically independent, each particle of length 2l makes a contribution to the bulk deviatoric stress which is of roughly the same order of magnitude as that due to a rigid sphere of radius l. The fractional increase in the bulk stress due to the presence of the particles is thus equal to the concentration by volume multiplied by a factor of order l2/b2, where 2b is a measure of the linear dimensions of the particle cross-section. This suggests that the stress due to the particles might be relatively large, for volume fractions which are still small, with interesting implications for the behaviour of polymer solutions. However, dilute-suspension theory is not applicable in these circumstances, and so an investigation is made of the effect of interactions between particles. It is assumed that, when the average lateral spacing of particles (h) satisfies the conditions b [Lt ] h [Lt ] l, the disturbance velocity vector is parallel to the particles and varies only in the cross-sectional plane. The velocity near a particle is found to have the same functional form as for an isolated particle, and the modification to the outer flow field for one particle is determined by replacing the randomly placed neighbouring particles by an equivalent cylindrical boundary. The resulting expression for the contribution to the bulk stress due to the particles differs from that for a dilute suspension only in a minor way, viz. by the replacement of log 2l/b by log h/b, and the above suggestion is confirmed. The relative error in the expression for the stress is expected to be of order (log h/b)−1. Some recent observations by Weinberger of the stress in a suspension of glass-fibre particles for which 2l/h = 7·4 and h/2b = 7·8 do show a particle stress which is much larger than the ambient-fluid stress, although the theoretical formula is not accurate under these conditions.

Experimental Study on Compressive Strength of Recycled Aggregate Concrete

2008 ◽  
Vol 385-387 ◽  
pp. 381-384 ◽  
Author(s):  
Wei Wang ◽  
Hua Ling ◽  
Xiao Ni Wang ◽  
Tian Xia ◽  
Da Zhi Wang ◽  
...  
Keyword(s):  
Experimental Study ◽  
Compressive Strength ◽  
Coarse Aggregate ◽  
Recycled Aggregate Concrete ◽  
Time Dependent ◽  
Recycled Aggregate ◽  
Experimental Investigations ◽  
Aggregate Concrete ◽  
Cement Ratio ◽  
Practical Engineering

With the increase in the use of recycled aggregate concrete (RAC), it is necessary to clearly understand its behavior and characteristics. In this paper, experimental study on compressive strength of RAC with same water/cement ratio is conducted. Firstly, influence of recycled coarse aggregate contents on cube compressive strength of RAC is studied. Secondly, experiment on time-dependent strength developing process of RAC is conducted with different solidification ages. Finally, based on above experimental investigations, empirical formula for compress strengths of RAC with different ages is presented. The result of this paper is helpful to theoretical analysis and practical engineering design of RAC structures.

Thermoelastic Constitutive Equations for Chemically Hardening Materials

1974 ◽  
Vol 41 (3) ◽  
pp. 652-657 ◽  
Author(s):  
Bernard W. Shaffer ◽  
Myron Levitsky
Keyword(s):  
Bulk Modulus ◽  
Strain Rate ◽  
Chemical Reaction ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Elastic Solid ◽  
Time Dependent ◽  
Component Model ◽  
Two Component ◽  
Potential Applications

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

Sign in / Sign up

Export Citation Format

Share Document