摘要:

The statistical mechanical development of a theory of polymeric systems, developed previously, is reconsidered. The “Stokes law” type of empiricism of the previous development is replaced by the introduction of the concept of “time‐smoothing” the kinetic equations. The introduction of this time‐smoothing affects, in an essential manner, only those expressions of the previous development which involve the distribution function in the configuration space of pairs of molecules. These are the expressions for the “hydrodynamic force” and the term in the expression for the stress tensor which was previously neglected by the “short‐range force” approximation. The present development leads to molecular expressions for the matrix of effective friction tensors, which in the previous development, were obtained through the introduction of the Stokes law type of expression for the hydrodynamic force and the concept of hydrodynamic interaction. In addition, an indication of the effect of the short‐range force approximation is obtained.

ISSN:0148-6055    

DOI:10.1122/1.549977

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

The intrinsic rheology of a fluid‐fluid interface has been found significant to multiphase flows for which surfactant material is present and the surface‐to‐volume ratio is large, such as in emulsification and demulsification, foam and emulsion stability, foam rheology, the dynamics of small bubbles or droplets, and interfacial mass transfer. An understanding of surface rheology therefore has practical relevance to engineering technologies wherein such phenomena occur: examples include the enhanced recovery of oil and the processing of food materials. Herein, a rheological theory is developed for a planar fluid surface which supercedes previous dynamic theories by explicitly acknowledging the nonlocal nature of the three‐dimensional interfacial transition zone. Beyond providing insight into the nature of the surface excess pressure tensor without the complicating features accompanying surface curvature, the treatment will provide a foundation for subsequent articles which will examine the rheology of curved surfaces possessing curvature as large as occurs in microemulsion systems. In the equilibrium state, the surface excess pressure tensor is shown to result from the highly inhomogeneous nature of the phase interface, whereas in the dynamic state a linear constitutive assumption results in the classical surface properties of surface viscosity and surface tension.

ISSN:0148-6055    

DOI:10.1122/1.549974

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

The surface rheological theory presented in the first part of this series for the planar fluid surface is extended to curved fluid surfaces with curvature approaching that which is observed in microemulsion systems. Both the surface excess linear momentum equation and the moment of linear momentum equation are developed. The balances are for the first time generalized to include large surface curvature stresses, introducing new first and second moments of surface excess shear and dilatational viscosity. The classical “zeroth order” surface excess shear and dilatational viscosities are shown to be curvature dependent. The curvature dependency of each zeroth moment surface viscosity coefficient is shown completely defined by the respective first and second moment viscosity coefficients.

ISSN:0148-6055    

DOI:10.1122/1.549978

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

The surface stress boundary condition developed in an invarient form in the preceding contribution to this series for a highly curved fluid interface is expressed in component form for a spherical fluid surface. The stress condition is used to examine bounded and unbounded viscous flow over a microemulsion droplet. Surface viscous effects are shown to be increasingly significant with increasing surface curvature, with higher order surface viscosity coefficients gaining a hydrodynamic relevance in the large surface curvature limit.

ISSN:0148-6055    

DOI:10.1122/1.549979

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

Steady axisymmetric thin film flows on a rotating cone of Newtonian and non‐Newtonian liquids are analyzed by means of the axisymmetric boundary layer with swirl equations, Galerkin finite‐element discretization with free surface parameterization, and Newton iteration, which permits the simultaneous evaluation of the boundary layer thickness with the primary unknowns which are the three velocity components. The significance of the inlet boundary conditions on the accuracy of the finite‐element predictions is discussed in detail. It is shown that natural inlet boundary conditions compatible with the local dynamics are superior to essential boundary conditions which may give rise to artificial finite‐element solutions. The analysis accounts for inertia, viscous, and surface tension effects. Both centrifugal and Coriolis accelerations are included. Results are presented and compared for Newtonian, shear‐thinning and shear‐thickening, Bingham plastic, and second‐order viscoelastic liquids at different operating conditions. In the limiting case of a rotating disk, in spin coating, the effects of the Coriolis acceleration, which have been omitted in earlier analyses are investigated. Closed form asymptotic solutions agree with the finite‐element predictions at high rotation. At low rotation, the asymptotic solution breaks down and so the finite‐element solution becomes essential.

ISSN:0148-6055    

DOI:10.1122/1.549980

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

A model of rigid macromolecules dissolved at low concentration in a dielectric Newtonian fluid and subjected to shear and electric fields is developed. Macromolecules are taken to be rigid spheroids of arbitrary aspect ratio and with both permanent and induced dipole moments. Specific calculations are reported for the steady‐state birefringence, extinction angle, and rheological material functions. The procedure developed here is general, so that it may be applied both to transient properties and to strong field problems since terms of higher order in the shear and electric fields may be calculated readily.

ISSN:0148-6055    

DOI:10.1122/1.549999

出版商:The Society of Rheology    

年代:1988

数据来源: AIP

摘要:

A method of studying dynamic longitudinal volume viscosity(ηL*)at high pressure using a modified Instron capillary rheometer is described. Two model polymers were chosen as examples: an amorphous polysulfone and a semicrystalline high‐density polyethylene. Dynamic longitudinal volume viscosity was measured at a fixed pressure using a continuous temperature sweep. The pressure ranged up to 2000 bar, while temperatures were swept through the liquid to solid transition for each of the materials. The effects of frequency (from 0.0125 to 0.125 Hz) and strain (0.06 to 0.24%) onηL*were also investigated. In both polymer systems,|ηL*|andηL′increased as the pressure was increased or the frequency was decreased. In spite of the small strains employed, the viscosity was found to decrease as the strain was increased. The temperature‐dependentηL*varied with the nature of the transitions. In polysulfone,|ηL*|decreased sharply with temperature above theTg.However, in polyethylene, a positive dependence of|ηL*|on temperature, limited to only a small temperature range aboveTm,was observed. Under all conditions,|ηL*|varied only one decade, a much smaller change than that found for shear viscosity.

ISSN:0148-6055    

DOI:10.1122/1.550000

出版商:The Society of Rheology    

年代:1988

数据来源: AIP