摘要:

This paper is concerned with some aspects of the dynamic response of a three‐dimensional linear viscoelastic medium to prescribed boundary conditions. The constitutive equations, expressed in operator form, are applied to a three‐dimensional continuum and are combined with the equations of motion to yield a system of linear partial differential equations. This system may be expressed in terms of a scalar and vector potential and parameters called “generalized velocitiesc1*andc2*” (operators describing the properties of the medium). The free radial vibrations of a viscoelastic sphere and spherical shell are worked out for the prescribed boundary conditions. In particular the phase velocity is obtained as a function of the wave number and a complex frequency. The wave number is obtained from the roots of a transcendental equation. The free longitudinal vibrations of a viscoelastic cylinder are determined by solving the equations for the scalar and vector potentials with the appropriate boundary conditions. The phase velocity is obtained for the Voigt and Maxwell models. In addition, asymptotic results are obtained which reduce to either the thin rod or the Pochhammer approximation.

ISSN:0148-6055    

DOI:10.1122/1.549032

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Measurements of the recoverable shear,susing three different methods, recoil, Weissenberg rheogoniometer, and flow birefringence, have been made on solutions of polyisobutylene in oil and polystyrene in Aroclor. All three methods, within their applicability limits, gave consistent results, calculating the recoil values from the rheogoniometer without the factor of12required by the theories using constitutive equations for viscoelastic liquids. Especially, these experiments with “matching solvents” gave a very good agreement onsmeasured in the rheogoniometer and flow birefringence.

ISSN:0148-6055    

DOI:10.1122/1.549060

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Normal stress measurements were made on dilute solutions of polyisobutylene in three low‐viscosity solvents at high shear rates with a jet thrust apparatus in which the thrust tube was mounted on the frame of an analytical balance. Thrust measurements could be easily read to 0.01 g and replicate measurements agreed closely with the original ones. Mechanical degradation of polyisobutylene in cyclohexane and toluene caused significant reductions in(P11−P22)wvalues at high shear rates and in the amount of drag reduction in turbulent flow. Molecular weight distribution curves and estimates of viscosity‐average molecular weights of the fresh and degraded solutions in toluene indicate that these effects noted in this solvent are caused by the breakdown of small amounts of high molecular weight polymer, with only a small change in the viscosity‐average molecular weight.

ISSN:0148-6055    

DOI:10.1122/1.549033

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Reduced variables of time‐temperature and molecular weight are used to describe the stress relaxation failure of 0.95 density polyethylene in a stress cracking agent, Igepal CO‐630. This method was previously shown to work for 0.96 density linear polyethylene. The 0.95 density polyethylene has an apparent activation energy of 38 kcal for stress cracking. This is appreciably higher than the 22 kcal found for 0.96 density linear polyethylene. A much higher dependence on molecular weight was also found. The 0.95 density polyethylene has a lifetime that is proportional toMv5.8while the 0.96 density polyethylene has a lifetime proportional toMv3.4.Some data are also shown which indicate a difference in the sensitivity to strain for the two materials. This can lead to appreciably longer lifetimes for the 0.95 density polyethylene at low strain.

ISSN:0148-6055    

DOI:10.1122/1.549063

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Current literature indicates that considerable effort is being made to relate rheological behavior of various materials to molecular mechanisms of flow. Implicit in viscoelastic spectra are the molecular motions and configurations that give shape to the stress relaxation or creep compliance curves. In dilute solutions or concentrated melts at higher temperatures, flow curves give indications of molecular arrangements present which cause deviation from some previously defined standard. Both qualitative and quantitative descriptions of solution and flow mechanisms recognize the importance of intermolecular forces. While these treatments can be used with confidence in systems of low polarity, highly polar solvent‐solute mixtures are not adequately described by these relations. Our primary considerations here are directed at understanding the nature of the interaction of 2‐ethylhexyl carboxylates with poly(vinyl chloride) and its model 1,3‐dichloropropane. The method employed represents a departure from conventional thought in that rheological behavior, from tensile creep compliance, dilute solution, and melt viscosity, has been successfully correlated to both Hammett and Taft substituent constants as implied in Eyring's concept of absolute reaction rates. While changes in interaction free energies between solvent and ester evolve simply and naturally from this technique, the significant conclusion obtained from these data is that the generally accepted “hydrogen‐bonding” interaction hypothesis of poly(vinyl chloride) with esters is clearly absent.

ISSN:0148-6055    

DOI:10.1122/1.549064

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

As part of a continuing study of the mechanical behavior of materials which have temperature‐dependent properties, electric analog experiments on a nonlinear Maxwell Model Material are described. The circuit that is used contains thermistor elements which simulate the temperature‐dependent viscosity of the mechanical model. The inertial and elastic elements are simulated by electronic integrators instead of inductors and capacitors which assures the ideality of the elements and increases the versatility of the analog. The work leads to the identification of a natural “property” of the material which has advantages over the use of the viscosity coefficients and elastic moduli alone. The results show how, because of heating, the responses of the model change from elastic to viscous as the severity or duration of the excitation increases. The heating also leads to stress reduction in the trailing part of the disturbance. Since elements of the analog may be identified with elements of atomic scale models of material, the work relates to material development programs as well as to mechanical design studies.

ISSN:0148-6055    

DOI:10.1122/1.549034

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

The flow behavior of some low molecular weight polymers was studied as a function of shear rate, shear stress, and temperature. The polymers included polybutadienes, random carboxyl and carboxyl‐terminated polybutadienes, carboxyl‐terminated butadiene‐acrylonitrile, and acrylonitrile‐butadiene copolymers. Measurements were made in the temperature range 3.8–73°C. A cone and plate viscometer and pressure capillary viscometer were used to cover the shear rate range1−105 sec−1.Measurements were carried out with various capillary radius to length ratios.M̄wandM̄nvalues were calculated from molecular weight distribution data obtained by gel permeation chromatography. Limiting viscosity numbers were also determined. In the range of shear rates studied, all polymers showed a limiting viscosity at low rates of shear and a region of shear rate thinning. The log viscosity‐log shear rate flow curves for each sample at the various temperatures were superimposable by linear shifts. Energies of activation calculated according to the method of Fox and Loshaek were found to have values characteristic of the molecular structure. Normal stresses developed in capillary flow as measured by entrance effects showed some dependence on structure. Flow results were compared with the Bueche‐Harding experimental standard curve and the Bueche theoretical curve. The presence of polar groups in the polymer chain increased the energy of activation and the relative magnitude of the viscosity. The log viscosity‐log shear rate flow curves for all the samples at any constant temperature were superimposable by linear shifts in two distinct classes according to differences in molecular weight distribution.

ISSN:0148-6055    

DOI:10.1122/1.549065

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

The behavior of rigid and deformable particles suspended in viscoelastic fluids undergoing slow Couette and Poiseuille flows was studied experimentally. In tube flow, the particles migrated from the wall to a limiting radial position at which the velocity gradient was effectively zero; in Couette flow between concentric rotating cylinders, migration occurred towards the outer cylinder wall. The rotations of rigid rods and disks were similar to those in Newtonian liquids, except for a steady drift in orbit constant to asymptotic values which in Newtonian liquids correspond to minimum energy dissipation. Two‐body collisions of rigid uniform spheres were unsymmetrical and irreversible. The deformation and burst of Newtonian liquid drops were as in Newtonian suspending liquids of comparable suspending phase viscosity, except for the alignment angle of the drop at zero deformation.

ISSN:0148-6055    

DOI:10.1122/1.549066

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

In a recent series of articles Gruntfest has obtained numerical solutions of the equations relating the effects of a dissipative process like viscous flow on the observable flow patterns of a heat‐sensitive material. Gruntfest has implied that non‐Newtonian flow is at least partially due to this thermal feedback, and he has demonstrated its significance in the flow of polymer‐modified oils reported on by Philippoff. This raises the question of how important these effects are in general, i.e., is non‐Newtonian flow an experimental artifact. In this paper the qualitative and quantitative predictions of Grantfest's analysis are examined. These predictions are then compared to some experimental data obtained with simple fluids, polymer solutions, polymer melts, and colloidal dispersions. It is shown that non‐Newtonian flow usually appears well before the rates of shear at which thermal effects would be noticed. Hence, non‐Newtonian flow is not an experimental artifact brought about by the inability to transfer thermal energy away from heat‐sensitive materials.

ISSN:0148-6055    

DOI:10.1122/1.549035

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

A parallel capillary porous flow model is constructed from capillaries with “wall forces.” The model exhibits critical pressure gradients and nonlinear discharge velocity at low pressure gradients, while for high gradients the discharge velocity is linear.

ISSN:0148-6055    

DOI:10.1122/1.549036

出版商:The Society of Rheology    

年代:1966

数据来源: AIP