Viscous flow time-dependent behavior

Thixotropy is the tendency of certain substances to flow under external stimuli (e.g., mild vibrations). A more general property is viscoelasticity, a time-dependent transition from elastic to viscous behavior, characterized by a relaxation time. When the transition is confined to small regions within the bulk of a solid, the substance is said to creep. A substance which creeps is one that stretches at a time-dependent rate when subjected to constant stress and temperature. The approximately constant stretching rates at intermediate times are used to characterize the creeping characteristics of the material. 

To fully understand the behavior of biological materials we need to address the issue of viscoelasticity. When a weight is placed on viscoelastic material, there is an instantaneous elastic response and a time-dependent viscous response (see Figure 7.1). For polymers the elastic response reflects the change in macromoleular conformation, which is usually time independent if no bonds are broken. The viscous response is the flow of macromolecules by each other similar to what happens during the flow of fluids in a tube. Fluid flow is a time-dependent process. Polymers exhibit viscoelastic behavior because they have both a time-independent response and a time-dependent response. 

If we have a model for linear elastic behavior, we must surely have one for Newtonian viscous flow and we do, the dashpot shown also in Figure 13-87. This is simply a piston in a cylinder that can be filled with various Newtonian fluids, each with a different value of the viscosity. Pulling (or pushing) on the piston causes it to move, as the fluid flows past the small gap between the piston and the cylinder walls, but the rate of deformation will depend on the viscosity of the fluid. (Some students who are a bit slow on the uptake or, more probably, trying to give us a hard time, ask what happens when the piston clunks to a stop at the bottom of the cylinder or pops out of the end don t be too literal minded here, this is just a picture representing a type of behavior )... 

Polymeric (and other) solids and liquids are intermediate in behavior between Hookean, elastic solids, and Newtonian, purely viscous fluids. They often exhibit elements of both types of response, depending on the time scale of the experiment. Application of stresses for relatively long times may cause some flow and permanent deformation in solid polymers while rapid shearing will induce elastic behavior in some macromolecular liquids. It is also frequently observed that the value of a measured modulus or viscosity is time dependent and reflects the manner in which the measuring experiment was performed. Tliese phenomena are examples of viscoelastic behavior. 

Figure 4-22 The Flow Curves of Cross-Linked Waxy Maize Samples Heated at 120°C for 5, 15, and 30 min were More Viscous After Shearing, that is. They Exhibited Time-Dependent Shear-Thickening (antithixotropie) Behavior.

In Figure 5.8d an intermediate behavior, called viscoelastic, is depicted such a relation is often called a creep curve, and the time-dependent value of the strain over the stress applied is called creep compliance. On application of the stress, the material at first deforms elastically, i.e., instantaneously, but then it starts to deform with time. After some time the material thus exhibits flow for some materials, the strain can even linearly increase with time (as depicted). When the stress is released, the material instantaneously loses some of it deformation (which is called elastic recovery), and then the deformation decreases ever slower (delayed elasticity), until a constant value is obtained. Part of the deformation is thus permanent and viscous. The material has some memory of its original shape but tends to forget more of it as time passes. 

Viscoelasticity - A property of a material that exhibits both elastic and viscous behavior. Viscoelastic materials have both solid-like characteristics—elasticity, strength, and stability of form— and liquid-like characteristics, such as flow that depends on time, temperature, and stress. All plastics exhibit some degree of viscoelasticity. 

By stressing a viscoelastic plastic material there are three deformation behaviors to be observed. They are an initial elastic response, followed by a time-dependent delayed elasticity that may also be fully recoverable, and the last observation is a viscous, non-recoverable, flow component. Most... 

Unlike elastic deformation in which the atoms maintain their nearest neighbors, flow involves changes in nearest neighbors and is a process of shear. This process is also dependent on time, so that one is concerned with the change of strain with time. The ease of flow in a liquid is characterized by its viscosity. Viscous flow is usually associated with liquids but it can occur in amorphous solids. For such materials, elastic and viscous processes can coexist. This is termed viscoelasticity and one can view elastic and viscous deformation as the limiting conditions of such behavior. Flow processes, such as creep, can also occur in crystalline materials. In this situation, the deformation processes involve different mechanisms but they can mimic viscoelastic behavior. 

In many materials, the mechanical response can show both elastic and viscous types of behavior the combination is known as viscoelasticity. In elastic solids, the strain and stress are considered to occur simultaneously, whereas viscosity leads to time-dependent strain effects. Viscoelastic effects are exhibited in many different forms and for a variety of structural reasons. For example, the thermoelastic effect was shown earlier to give rise to a delayed strain, though recovery of the strain was complete on unloading. This delayed elasticity is termed anelastic-ity and can result from various time-dependent mechanisms (internal friction). Figure 5.9 shows an example of the behavior that occurs for a material that has a combination of elastic and anelastic behavior. The material is subjected to a constant stress for a time, t. The elastic strain occurs instantaneously but, then, an additional time-dependent strain appears. On unloading, the elastic strain is recovered immediately but the anelastic strain takes some time before it disappears. Viscoelasticity is also important in creep but, in this case, the time-dependent strain becomes permanent (Fig. 5.10). In other cases, a strain can be applied to a material and a viscous flow process allows stress relaxation (Fig. 5.11). 

Creep. Creep is a time-dependent strain increase under a constant stress. As already mentioned, the constant stress can be quite simply provided by a gravitational field of the earth. The creep behavior is most often analyzed in terms of the Kelvin-Voigt model in which a spring and a dashpot are parallel. The model is characterized by a constant representing the elastic (modulus) and viscous flow (viscosity) deformations. From the geometry of model, individual strain in each element is equal to total strain and applied stress is supported jointly by the spring and dashpot. 

Amorphous solid dispersions are prepared primarily with amorphous and/or semicrystalline materials, and therefore, the mechanical behavior of the extrudate is generally viscoelastic in nature. The materials viscoelasticity implies a strain-rate dependence of the mechanical response and time-dependent mechanical behavior such as creep and stress relaxation. For example, in cases of high strain rates, these materials tend to be more brittle than under slower strain rates where viscous flow and other molecular relaxations can dissipate the energy without fracture. Thus, high strain rates are beneficial for particle size reduction operations. 

Dispersions can behave either as pure viscous substances or viscoelastic materials. In the case of viscous substances, the deformation does not recover after the stress has been removed. Part of the deformation can be recovered after the removal of shear stress for viscoelastic materials. Thick-film pastes may exhibit both time-dependent and viscoelastic flow behavior. The classification of flow behavior is shown in Table 8.21. Various types of flow behavior are shown in Fig. 8.79. This figure shows the plots of shear stress versus shear rate and corresponding plots of viscosity versus shear rate. 

Nonlinear rheology vastly extends all the phenomena (elastic, viscous, and linear time dependent) discussed in Chapters 1-3. Elastic, viscous, and linear viscoelastic behaviors are but coastal zones on a continent of nonlinear rheology see Figure 4.1.2. The abscissa on Figure 4.1.2 is the Deborah number, which is generally defined as the ratio of the material s characteristic relaxation time k to the characteristic flow time t. 

If no stress threshold is required to initiate viscous flow, the behavior is called viscoelastic, if a certain stress threshold (yield strength) needs to be overcome before the beginning of time-dependent viscous flow, the behavior is addressed as viscoplastic. 

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