The Dashpot (Maxwell Model)

Location:

Concepts Shown:

The Maxwell Model

Equipment:

The dashpot model provided and a supply of viscous slime that will serve as the viscous fluid in the pot.

Procedure:

All polymers are strained both elastically as well as viscously under the influence of an applied stress. Such behavior consisting of recoverable elastic strain and irrecoverable viscous strain, is termed viscoelasticity. Most students have probably heard of the Maxwell dashpot model. However, few of them may have actually seen a working model. The model that has been provided, will allow students to see this 'mysterious' dashpot, that everyone seems to talk about. The actual setup is given in the figure on the last page. The dashpot itself is filled with slime made from polyvinyl alcohol and borax solution (1:5 ratio). Immersed in the slime, is a movable piston connected at the other end to a spring. As the spring is pulled from one end, it begins to stretch. At first, the piston will remain unmoved in the slime. However at some point it will begin to translate through the slime. When all the stress has been removed the spring goes back to its unstretched state. However, the piston does not go back to its original position. The slime in the pot will have to be prepared ahead of time. Since the top of the jar is not sealed, there is a chance that the slime will lose water and increase its viscosity. Before this happens, to the point of dryness, the slime can be made less viscous by adding a little more of the borax solution and stirring. This is only a temporary solution. Eventually, new slime will have to be made.

Science:

The model shows the phenomenon of stress relaxation. Ideally, it should be possible to predict the stress relaxation behavior from the knowledge of the creep curve. IN practice however, with real polymers, this is somewhat difficult to do. But the situation is often simplified by assuming that the polymer behaves as a linear viscoelastic material. It can be assumed that the deformation of the polymer is divided into an elastic component and a viscous component, and that the deformation of the polymer can be described by a combination of Hooke's law and Newton's law. The linear elastic behavior is given by Hooke's law as:

s = Ee

or ds/dt = E de/dt

where E is the elastic modulus and Newton's law describes the linear viscous behavior through the equation s = n de/dt where n is the viscosity and de/dt the strain rate. It should be noted that these equations only apply at small strains. The various models on the next page involve different combinations of these two basic elements. The Maxwell model was proposed to explain the time-dependent mechanical behavior of viscous materials. Under the action of an overall stress there will be an overall strain e in the system which is given by e = e1 + e2 where e1 is the strain in the spring and e2 the strain in the dashpot. Once the external stress has been removed the elastic strain is recovered while the viscous strain is permanent. Thus, the viscous pot demonstrates lost energy. Since the spring and dashpot are in series, both of them should experience the same stress. At this stage it is useful to consider how closely the Maxwell model predicts the mechanical behavior of a polymer. The model predicts that strain is expected to increase linearly with time, which is clearly not the case for a viscoelastic polymer where de/dt decreases with time. However, the model is perhaps of more use in predicting the response of a polymer during stress relaxation. Remarks: The Maxwell model is not the only model used to estimate viscoelastic behavior. In the diagrams below are the diagrams of mechanical models used to represent the viscoelastic behavior of polymers. [eq].Rahul Pinto

References:

Author:
Rahul Pinto
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