Question

The theory of viscoelasticity is used to describe the behaviour of materials in liquid phase.
a. Describe an industrial application where viscoelasticity occurs.
b. Describe any two models of viscoelasticity
c. For each of the models, identify a real life engineering problem where it is applied and describe this.
d. How can the knowledge be used in design applications for the problem you identified
above.
e. What are the challenges in the use of the knowledge for solving practical problems.

Answer 1

SOLUTIONS:

a) Applications of viscoelastic fluids involving hydrodynamic stability and heat transfer.

Viscoelastic fluids are very common in very important applications. Paints are very good example since almost all buildings are painted with combination of polymer and solbvent for different reasons. More complex applications involving polymeric solutions and some kind of process may exist. Some of these may have biologial nature or even may be intended for some optical applications.

Viscoelastic fluids may be so different to each other that a reasonable number of constitutive equations have been developed to model thier behaviour. In the case of deoxyribonucleic acid replications and fabrication corruated surfaceses, for eg. viscoelasticity is then at the same level of importanace that natural convection.

The present constribution is devoted to expose the link between iscoelasticity and rayleigh and maramgoni convection and how these fit in industrial application and for polymer rheology appliations.

Corrugated surfaces: The fabrication process of these corrugated surfeses briefly includes,

Preparation of polymeric suspension

Applicaton of the suspesion in a plate surface

• Heating from below of the plate
• Thermal control of the convection process in order to achieve and maintain the critical conditions
• Formation of desired pattern in the polymeric suspension
• Evporation of the solvant and depostion of polymeric pattern

Fig. shows brief schematic for the fabricaion of corrugated surfaces based on thermal convection. Notice that the begining rayleigh convection dominates the process but a the certain fluid level surface layer thickeness the maramgoni convection rules the process until the solvent evaporates completely.

As the viscoelastic fluid is heated form below the critical condition for the one set of convection may be achieved. All depend upon the control of heating source, on the plate thermal and geometrical properties, on the fluid properties and the desired pattern. This technique has been made so that good quality can be achieved.

DNA replication: DNA suspension are considered as viscoelastic fluid because these are combination of an aqueous solvent and the kind of polymer in the form of DNA chains. Hydrodynamics of biological fluids has become a subject of growing interest in recent decades because of its link to biochemical reaction. DNA replication needs a temperature gradient and an enzyme to be done so that possibly convective motions are involved. The thermo cyclyer is small specilized equipment that has become an indispensable tool for research for industry. This work is based on physical mechanism of thermal covection.

• The complicated DNA replication process can now be very briefly outlined. Thus the process is as follows:
• An aqueous dilute suspension of DNA fragment and polymeried enzyme is prepared.
• The suspenson is placed in nearly cylindrical containers called VIALS.

• The thermal gradient is set in the Vial.
• The temperature of 95 degree celsicus is maintained in order that the polymerized chain reaction is takes place.
• DNA replication also used in molecular biology

B) Models of viscoelasticity:

1) Maxwell model:

A spring and a dashpot is connected in series in the model suggests that there is unifrm distribution of stress in the model predicts that stress decays exponetially with time can be also descibed stress relaxation.

Representation by pure viscous damper and a purely elastic spring connected in series. The model can be represneted by :

Predicts that stress decays exponetially with time.

Model doesnt accurately predicts creep. Predicts that stain will increase linerally with time actually strain rate descareses with time.

2) Kelvin Viogt model:

• Suggets that there is unifrm distribution of strain, the spring and dashpot will be in parallel in the model gives a retarded response but does not allow for ideal stress relaxation since the model cannot be instataneously deformed for a given strain. Creep is constant.

• Represented by newtonian damper and hooke an elastic sprig in parallel.

• The model can be expresses as linear first order diffrential equations  
• Represents a solid undergoing reversible viscoelastic strain
• At constant stress predicts strain to tend to as time continues to infinity. The model is less accurate with relaxation in material.
• Relaxation,