A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation
TL;DR: In this article, a non-linear constitutive equation for polymer melts and concentrated solutions is presented, which is based on known results of network theories, and the model contains a distinctive feature: that of letting the relaxation times depend upon the existing structure.
Abstract: A non-linear constitutive equation for polymer melts and concentrated solutions is presented. Based on known results of network theories, the model contains a distinctive feature: that of letting the relaxation times depend upon the existing structure. The model extends the constitutive equation of linear viscoelasticity to the non-linear region in a well-defined way, with the uncertainty of just a single adjustable parameter. Predictions of the model for common cases of non-linear response are derived and discussed.
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TL;DR: A history of thixotropy is given in this article, together with a description of how it is understood today in various parts of the scientific community, and a mechanistic description of the thixotropic system is presented.
Abstract: The ensuing mechanical response to stressing or straining a structured liquid results in various viscoelastic phenomena, either in the linear region where the microstructure responds linearly with respect to the stress and strain but does not itself change, or in the nonlinear region where the microstructure does change in response to the imposed stresses and strains, but does so reversibly. The complication of thixotropy arises because this reversible, microstructural change itself takes time to come about due to local spatial rearrangement of the components. This frequently found time-response of a microstructure that is itself changing with time makes thixotropic, viscoelastic behaviour one of the greatest challenges facing rheologists today, in terms of its accurate experimental characterisation and its adequate theoretical description. Here a history of thixotropy is given, together with a description of how it is understood today in various parts of the scientific community. Then a mechanistic description of thixotropy is presented, together with a series of applications where thixotropy is important. A list of different examples of thixotropic systems is then given. Finally the various kinds of theories that have been put forward to describe the phenomenon mathematically are listed.
1,367 citations
TL;DR: In this paper, a constitutive equation is derived from a Lodge-Yamamoto type of network theory for polymeric fluids, where the network junctions are not assumed to move strictly as points of the continuum but allowed a certain "effective slip".
Abstract: A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.
1,066 citations
TL;DR: In this paper, the evolution of the concept is traced back and a generalized definition is accepted, and various experimental methods are considered with which meaningful measurements of thixotropy can be performed.
Abstract: The time-dependent behaviour associated with thixotropy rather than with viscoelasticity is discussed. The evolution of the concept is traced back and a generalized definition is accepted. Subsequently, the various experimental methods are considered with which meaningful measurements of thixotropy can be performed. The specific experimental difficulties encountered with the systems under consideration are treated separately. It is impossible to enumerate all materials that show thixotropy or anti-thixotropy. Instead, they are classified in groups according to their origin or application. The resulting table is used to deduce the characteristics which accompany thixotropic phenomena. This leads to a discussion of the time effects in terms of the molecular or microscopic structure. An attempt is made to provide a systematic outline of the published models and possible constitutive equations for thixotropic materials. Both inelastic and viscoelastic descriptions are included.
481 citations
TL;DR: In this paper, the authors measured the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids and compared it with the swimming speed in a Newtonian fluid, calculated using slender body theories and a boundary element method.
Abstract: We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids The fluids are highly viscous to replicate the low Reynolds number environment of microorganisms The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis By adjusting the translation speed to make the net hydrodynamic force vanish, we measure the force-free swimming speed as a function of helix rotation rate, helix geometry, and fluid properties We compare our measurements of the force-free swimming speed of a helix in a high-molecular weight silicone oil with predictions for the swimming speed in a Newtonian fluid, calculated using slender-body theories and a boundary-element method The excellent agreement between theory and experiment in the Newtonian case verifies the high accuracy of our experiments For the viscoelastic fluid, we use a polymer solution of polyisobutylene dissolved in polybutene This solution is a Boger fluid, a viscoselastic fluid with a shear-rate-independent viscosity The elasticity is dominated by a single relaxation time When the relaxation time is short compared to the rotation period, the viscoelastic swimming speed is close to the viscous swimming speed As the relaxation time increases, the viscoelastic swimming speed increases relative to the viscous speed, reaching a peak when the relaxation time is comparable to the rotation period As the relaxation time is further increased, the viscoelastic swimming speed decreases and eventually falls below the viscous swimming speed
164 citations
TL;DR: In this article, a novel approach for modeling the mechanical behavior of thixotropic viscoplastic fluids is presented, which involves two evolution equations, one for the stress and the other for the structure parameter.
Abstract: A novel approach for modeling the mechanical behavior of thixotropic viscoplastic fluids is presented. Non-monotonic flow curves, stress overshoot during microstructure breakdown flows at constant shear rate, and viscosity bifurcation are some of the common aspects of structured fluids that are predicted by the new model. It involves two evolution equations, one for the stress and the other for the structure parameter. Simple ideas are employed to describe the microstructure, and, as a result, a model with a clear physical basis is obtained. In addition to the flow curve, which by construction is exactly predicted, it is shown that the model is able to predict correctly the behavior observed in the usual rheometric transient flows, among which abrupt changes in shear rate (microstructure buildup or breakdown experiments) and abrupt changes in shear stress (viscosity bifurcation experiments). The model is frame-indifferent and applicable to complex flows.
152 citations
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TL;DR: The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed in this article, where the right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material.
Abstract: The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed. The right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material, but it is necessary to transform to a fixed frame of reference in order to solve the equations of state simultaneously with the equations of continuity and of motion. An illustration is given of the process of formulating equations of state suitable for universal application, based on non-invariant equations obtained from a simple experiment or structural theory. Anisotropic materials, and materials whose properties depend on previous rheological history, are included within the scope of the paper.
1,714 citations
01 Mar 1972
TL;DR: In this paper, two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network and experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations.
Abstract: Lodge's molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate‐of‐strain dependence of various material functions By allowing the junction‐creation rate and the probability of loss of junctions to depend on the second invariant of the rate‐of‐strain tensor, more realistic constitutive equations were obtained Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations For steady simple shearing and small‐amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η, −(τ11−τ22), η′, and G′ rather well over many decades of shear rate or frequency For suddenly changing flow experiments model A is inadequate Model B however appears to be the
1,270 citations
TL;DR: In this article, the second law of thermodynamics is used to define dissipation of energy at constant temperature and explicit expressions for dissipation energy for any strain history are obtained, inasmuch as relaxation during straining causes an essential reorganization of structure which is in fact the cause of dissipation.
Abstract: A molecular theory of relaxing media is presented which gives an expression for the stress in terms of the strain history. At any given time the strain history produces a distribution in internal strains which for mechanical properties can be characterized by a limited number of internal strain parameters. The second law of thermodynamics is used to define dissipation of energy at constant temperature and explicit expressions for dissipation of energy for any strain history are obtained. Inasmuch as relaxation during straining causes an essential reorganization of structure which is in fact the cause of dissipation, the kinetic theory of elasticity is extended to non‐isotropic polymeric networks. A tensor expression for the stress‐strain‐time relations is thereby developed.
766 citations
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