# Shear

To **shear** something is to cause a shear strain, by application of a shear stress. Recall that the shear stress *σ* is given by the applied force *F* over the area *A*, namely

<math>\sigma = \frac{F}{A}</math> ,

and the shear strain <math>\gamma</math> is given by

<math>\gamma = \frac{\Delta x}{y}</math> .

See Figure 1 for clarification.

## Shear melting

When shear is applied to a colloidal suspension, it causes the particles to flow relative to each other. This phenomenon, unique to colloidal systems, is called **shear melting** and is a topic of recent research.

In 2009, Eisenmann *et al* investigated the phase transition between diffusive and non-diffusive behavior near a specific shear strain that is necessary to produce shear melting of a colloidal glass. They found that diffusive behavior and homogeneous particle motion can be observed for shear strains beyond <math>\gamma \approx 0.08</math> . For larger strains, they summarized, "the applied shear drives diffusive behavior."

It can also be demonstrated that an effective diffusion coefficient can be found if the thermal energy in the Stokes-Einstein equation is replaced with "shear energy". The result is that in a shear melted colloid glass, the diffusion coefficient is proportional to the shear-rate <math>\dot{\gamma}</math>. This diffusion coefficient also depends on the average size of the clusters of particles which move together under shear. Evidence of the existence of these clusters came from the data shown in Figure 2.

## References

[1] R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).

[2] C. Eisenmann *et al*. "Shear melting of a colloidal glass," Harvard University, Cambridge, MA (preprint, 2009). [1]