Elastic flow

Deformation is the relative displacement of points of a body. It can be divided into two types flow and elasticity. Flow is irreversible deformation when the stress is removed, the material does not revert to its original form. This means that work is converted to heat. Elasticity is reversible deformation the deformed body recovers its original shape, and the appHed work is largely recoverable. Viscoelastic materials show both flow and elasticity. A good example is SiEy Putty, which bounces like a mbber ball when dropped, but slowly flows when allowed to stand. Viscoelastic materials provide special challenges in terms of modeling behavior and devising measurement techniques. 

In Fig. 24(a) the purely elastic deformation and the plastic elastic flow processes are plotted and hatched in a different manner. Figure 24(b) shows the dependence of stress on time. It can also be seen, that with discharge at time t0 the purely elastic residual deformation disappears at once, whereas the plastic-elastic portion does so gradually (diffusion processes). 

It is known that a viscoelastic fluid, e.g., a solution with a trace amount of highly deformable polymers, can lead to elastic flow instability at Reynolds number well below the transition number (Re 2,000) for turbulence flow. Such chaotic flow behavior has been referred to as elastic turbulence by Tordella [2]. Indeed, the proper characterization of viscoelastic flows requires an additional nondimensional parameter, namely, the Deborah number, De, which is the ratio of elastic to viscous forces. Viscoelastic fluids, which are non-Newtonian fluids, have a complex internal microstructure which can lead to counterintuitive flow and stress responses. The properties of these complex fluids can be varied through the length scales and timescales of the associated flows [3]. Typically the elastic stress, by shear and/or elongational strains, experienced by these fluids will not immediately become zero with the cessation of fluid motion and driving forces, but will decay with a characteristic time due to its elasticity. 

Non-Newtonian liquids are used in numerous microfluidics applications, including microscale viscosity and rheology measurements, amplification and sequencing of DNA, fundamental investigations of elastic flows, and development of fluidic memory and control devices. Although these applications span a wide range of flow conditions and non-Newtonian fluid properties, similar experimental methods are used. In this section we summarize some of the experimental... 

The resistance to motion that a solid experiences while moving across a surface is called friction. Frictional forces between solids affect the sliding between two solid materials and are strongly related to the type and nature of the interfaces and thin films existing at the surface of these solids. Deformation phenomena like elasticity, flow and creep, adhesion, friction, and lubrication arise during sliding of two solids over each other. 

The study of polymer viscoelasticity treats the interrelationships among elasticity, flow, and molecular motion. In reality, no liquid exhibits pure Newtonian viscosity, and no solid exhibits pure elastic behavior, although it is convenient to assume so for some simple problems. Rather, all deformation of real bodies includes some elements of both flow and elasticity. Because of the long-chain nature of polymeric materials, their visco-elastic characteristics come to the forefront. This is especially true when the times for molecular relaxation are of the same order of magnitude as an imposed mechanical stress. 

Roy, J.S., Nayak, P, Dash, J., 1981. Heat transfer in pulsatile visco-elastic flow in a porous channel. Acta Mech. 40, 33 8. 

The first region (viscous sublayer) extends to about y " = 5. The drag-reducing flows intersect the maiximum drag reduction line instead of = y ". The region between the viscous sublayer and Newtonian plug is known as the elastic sublayer since the solution in this zone exhibits an elastic flow behavior. 

Total deformation of the polymer is composed of an elastic, rubbery (high elastic) flow and deformation. When considering the polymer in the rubberlike (high elasticity) state accepts that the macroscopic viscosity of the material is great and flows absent. 

In the elastic state, even thongh the bulk behaviour involves flow (that is, a significant part of the bulk deformation is permanent), the behavionr of the flow unit itself is elastic. Under the imposed large deformation, the elastic flow nnit deforms to its ultimate strain, breaks np, and recovers its strain [26]. This process is schematically depicted in Figure 11.8. 

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