Flow models viscoelastic behavior

The Maxwell model is also called Maxwell fluid model. Briefly it is a mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus (E) in series with a dashpot of coefficient of viscosity (ji). It is an isostress model (with stress 5), the strain (f) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as d /dt = (l/E)d5/dt + (5/Jl)-This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis. 

Real polymers are more complex than these simple mechanical models. Qualitatively, when a real polymer is forced to flow through a contraction or expansion in an extrusion screw, it will exhibit viscoelastic behaviour. The polymer molecules will be elongated if forced through a contraction, or they will retract when they flow into an expansion. The effect of viscoelastic behavior in a capillary rheometer is observed in the form of recirculation flow just before the polymer enters the... 

Accordingly, given the necessity from equilibrium coil dimensions that bt> 1, the shear rate and frequency departures predicted by FENE dumbbells are displaced from each other. Moreover, the displacement increases with chain length. This is a clearly inconsistent with experimental behavior at all levels of concentration, including infinite dilution. Thus, finite extensibility must fail as a general model for the onset of nonlinear viscoelastic behavior in flexible polymer systems. It could, of course, become important in some situations, such as in elongational and shear flows at very high rates of deformation. 

Differential Viscoelastic Models. Differential models have traditionally been the choice for describing the viscoelastic behavior of polymers when simulating complex flow systems. Many differential viscoelastic models can be described by the general form... 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

The arterial circulation is a multiply branched network of compliant tubes. The geometry of the network is complex, and the vessels exhibit nonlinear viscoelastic behavior. Flow is pulsatile, and the blood flowing through the network is a suspension of red blood cells and other particles in plasma which exhibits complex non-Newtonian properties. Whereas the development of an exact biomechanical description of arterial hemodynamics is a formidable task, surprisingly useful results can be obtained with greatly simplified models. 

While the Choi and Schowalter [113] theory is fundamental in understanding the rheological behavior of Newtonian emulsions under steady-state flow, the Palierne equation [126], Eq. (2.23), and its numerous modifleations is the preferred model for the dynamic behavior of viscoelastic liquids under small oscillatory deformation. Thus, the linear viscoelastic behavior of such blends as PS with PMMA, PDMS with PEG, and PS with PEMA (poly(ethyl methacrylate))at <0.15 followed Palierne s equation [129]. From the single model parameter, R = R/vu, the extracted interfacial tension coefficient was in good agreement with the value measured directly. However, the theory (developed for dilute emulsions) fails at concentrations above the percolation limit, 0 > (p rc 0.19 0.09. 

As mentioned above, interfacial films exhibit non-Newtonian flow, which can be treated in the same manner as for dispersions and polymer solutions. The steady-state flow can be described using Bingham plastic models. The viscoelastic behavior can be treated using stress relaxation or strain relaxation (creep) models as well as dynamic (oscillatory) models. The Bingham-fluid model of interfacial rheological behavior (27) assumes the presence of a surface yield stress, cy, i.e.. 

Both creep and stress relaxation is modeled using computer simulation software based on simple spring (elastic deformation) and dashpot (viscous flow) models. Many polymers, when they approach the Tg, will exhibit viscoelastic behavior in which the physical characteristics are best described by considering the material as having both solid- and liquid-like properties. Viscoelasticity is an important property to be found in polymeric materials (see Viscoelasticity). 

The behavior shown here represents the most general type behavior possible for a viscoelastic material, instantaneous elasticity, delayed elasticity and flow. Some texts do not include the flow term as a viscoelastic component, preferring instead to define viscoelastic behavior only for models with no free damper or flow term. 

In the case of polymers, viscosity is considered an important property to explain the viscoelastic behavior of polymers under stress and strain [154]. At this point, two theories are considered which deal with the flow behavior of polymer mixtures the first, which was proposed by Rouse [155] and is based on the studies of Kargin and Slonimsky, is KSR model the second, as proposed by Zimm [156] and based on the studies of Kirkwood and Risemann, is the KRZ model. 

Pressing the molten or softened surfaces is used to deform surface asperities and expel entrapped gases from the joint area to produce intimate contact at the interface. The process can be described and modeled as squeezing flow of viscoelastic fluids [2]. It entails flow at the microscale to deform asperities, and at the macroscale where melt squeezes out of the joint area forming weld flash. However, a complete description of the process is quite complicated due to the complex melt behavior, irregularity of the joint surfaces, nonuniform temperature field, and air entrapment. It is also important to note that additives or reinforcements can increase the effective viscosity of the melt, making the flow slower. 

Most adhesives are polymer-based materials and exhibit viscoelastic behavior. Some adhesives are elastomer materials and also exhibit full or partial rubberlike properties. The word elastic refers to the ability of a material to return to its original dimensions when unloaded, and the term mer refers to the polymeric molecular makeup in the word elastomer. In cases where brittle material behavior prevails, and especially, when inherent material flaws such as cracks, voids, and disbonds exist in such materials, the use of the methods of fracture mechanics are called for. For continuum behavior, however, the use of damage models is considered appropriate in order to be able to model the progression of distributed and non-catastrophic failures and/or irreversible changes in material s microstructure, which are sometimes described as elastic Hmit, yield, plastic flow, stress whitening, and strain hardening. Many adhesive materials are composite materials due to the presence of secondary phases such as fillers and carriers. Consequently, accurate analysis and modeling of such composite adhesives require the use of the methods of composite materials. 

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