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.

Thixotropy—a review

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.

A new constitutive equation derived from network theory

In a controlled release system a drug, pesticide, or other bio-active agent is incorporated into a carrier, generally a polymeric material. The rate of release of the substance is determined by the properties of the polymer itself and is only weakly dependent on environmental factors (such as the pH of bodily fluids). Controlled release systems are capable of delivering substances slowly and continuously for up to several years.

Chemical and Physical Structure of Polymers as Carriers for Controlled Release of Bioactive Agents: A Review

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.

Thixotropy - a general review

Several aspects of the growth and departure of bubbles from a submerged needle are considered. A simple model shows the existence of two different growth regimes according to whether the gas flow rate into the bubble is smaller or greater than a critical value. These conclusions are refined by means of a boundary-integral potential-flow calculation that gives results in remarkable agreement with experiment. It is shown that bubbles growing in a liquid flowing parallel to the needle may detach with a considerably smaller radius than in a quiescent liquid. The study also demonstrates the critical role played by the gas flow resistance in the needle. A considerable control on the rate and size of bubble production can be achieved by a careful consideration of this parameter. The effect is particularly noticeable in the case of small bubbles, which are the most difficult ones to produce in practice.

Dynamics of bubble growth and detachment from a needle

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.

A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation

A model of non-linear viscoelasticity with relaxation times which depend on the structure is compared with experimental results reported in the literature for a L.D. polyethylene. The single parameter of the model is determined by comparison with steadystate shear results. The model is then used to interpret various transient data. These are: tangential and normal stress growth in shear, stress growth in elongation, normal stresses in shear creep. The comparison shows a good general agreement, thus supporting the suggestion of relating the change in time of the relaxation spectrum to structural variables.

A non-linear viscoelastic model with structure-dependent relaxation times: II. Comparison with l.d. polyethylene transient stress results

Melt strength (MS) and breaking stretching ratio (BSR) data relative to polyethylenes with different molecular structure (high density (HDPE), low density (LDPE), and linear low density (LLDPE)) are shown. HDPE and LLDPE samples show high breaking stretching ratio and low melt strength values. The LDPE samples exhibit very large melt strength values but low breaking stretching ratio values. For the last mentioned samples, differences are shown in the non-isothermal elongational behavior between samples polymerized with tubular and vessel technology. For all the samples, MS decreases with increasing melt index while BSR increases with melt index.

Influence of the molecular structure on the melt strength and extensibility of polyethylenes

The rheological behavior of dilute solutions of flexible macromolecules is studied by means of a freely jointed multiple bead–rod model. The solution of the equations describing the mechanics of the system is obtained by means of a numerical procedure, which applies to arbitrary flow conditions. The case of the transient stress in uniaxial elongational flow is developed in some detail. A comparison with bead–spring models shows both quantitative and qualitative differences which are briefly discussed.

D. Acierno

Papers

A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation

A non-linear viscoelastic model with structure-dependent relaxation times: II. Comparison with l.d. polyethylene transient stress results

Influence of the molecular structure on the melt strength and extensibility of polyethylenes

Dilute solution rheology of flexible macromolecules (bead–rod model)

Increasing the elastic modulus of polyamides