Shear Effects

The effect of shear rate is normally not a consideration for blending applications. However, it can be useful when blending non-Newtonian fluids high into a low-viscosity fluid or vice versa. A static mixer can readily handle non-Newtonian fluids, but the shear rate characteristics need to be known to calculate the apparent viscosity, and hence the Reynolds number and the number of mixing elements.

Water treatment applications often request a certain velocity gradient, or 'G' factor. This is actually the average microscale shear rate in the mixer, which can also be calculated. It should be noted that although all these applications are dependent on shear, they are in fact all different shear rates.

Non-Newtonian fluids are dependent on the apparent shear rate, High viscosity ratio fluids on the wall shear rate, and water treatment applications on the average microscale shear rate. These all have different values, so care should be taken to ensure that the correct figures are used.

Mixing of non-Newtonian fluids is relatively easy in a Static Mixer. As all the fluid travels through the mixing zones, Static Mixers get none of the problems associated with cavern formation in agitated tanks. The only difficulty is calculating the pressure drop, as the viscosity varies with the shear rate in the mixer. If a graph of shear rate vs. viscosity is obtained from standard tests on a Brookfield viscometer, the apparent shear rate can be used to calculate the apparent viscosity. It should be noted that shear vs. viscosity tests should be done at considerably higher pressure shear rates for a Static Mixer than for an agitator system. The various shear rates associated with Static Mixers are detailed below: -Wall Shear Rate; This is essentially the same as the wall shear rate in a pipe and is a function of the fluid velocity.

Where v is the pipe velocity, D is the pipe diameter, and Q is the volumetric flowrate. The wall shear rate can be used to ensure that the additive is drawn off the pipe wall when adding low into high viscosity fluids.

Apparent Shear Rate

The apparent shear rate in the pipe is used to calculate the apparent viscosity and hence the pressure drop in non-Newtonian systems. It is basically a function of the wall shear rate, with a suitable factor added to take into account the increase in velocity due to the elements causing the fluid to rotate and the reduced free area in the pipe. This method of calculating the apparent shear rate for the mixer is analogous to the Metzner and Otto shear rates used for calculating apparent viscosities in agitated tank systems.

Where γ _app is the apparent shear rate, γ _wall is the wall shear rate, v is the velocity and D is the pipe diameter.

Average Shear Rate

The average shear rate has fairly recently been given more consideration in mixer sizing. Essentially, it is the same as the velocity gradient used in water treatment applications, so it is a function of the energy usage in terms of pressure drop through the mixer. The following includes a derivation of the formula: -The average shear rate is defined as;

Where G is the average shear rate, P is the power, m is the viscosity, V, D, and l are the Mixer volume, diameter, and length, respectively, Q is the volumetric flowrate, v is the velocity, and ∆ P is the mixer pressure loss.

Note that the average shear values obtained will be substantially higher than those usually associated with an agitated tank. Static mixers create uniform shear distributions, whereas an agitated tank does not. The shear rate is relatively high, but the maximum shear rate is still likely to be substantially lower than that of an agitated tank.