Spinning a spoon in a cup of tea to mix it can show you how pertinent it is to understand the dynamics of fluids in everyday life. Using physics to describe the flow and behavior of liquids can show you the intricate and complicated forces that go into such a simple task as stirring a cup of tea. The shear rate is one example that can explain the behavior of fluids.

## Shear Rate Formula

A fluid is "sheared" when different layers of the fluid move past one another. Shear rate describes this velocity. A more technical definition is that the shear rate is the flow velocity gradient perpendicular, or at a right angle, to the flow direction. It poses a strain on the liquid that may break bonds between particles in its material, which is why it's described as a "shear."

When you observe the parallel motion of a plate or a layer of a material that's above another plate or layer that's still, you can determine the shear rate from the velocity of this layer with respect to the distance between the two layers. Scientists and engineers use the formula *γ = V/x* for shear rate *γ* ("gamma") in units of s^{-1}, velocity of the moving layer *V* and distance between the layers *m* in meters.

This lets you calculate shear rate as a function of the motion of the layers itself if you assume the top plate or layer moves parallel to the bottom. The shear rate units are generally s^{-1} for different purposes.

## Shear Stress

Pressing a fluid such as lotion onto your skin makes the fluid's motion parallel to your skin and opposes the motion that presses the fluid directly onto the skin. The shape of the liquid with respect to your skin affects how the particles of the lotion break up as they're being applied.

You can also relate shear rate *γ* to the shear stress *τ* ("tau") to viscosity, a fluid's resistance to flow, *η* ("eta") through

*i*n which *τ* is the same units as pressure (N/m^{2} or pascals Pa) and *η* in units of *(*N/m^{2} s). The **viscosity** gives you another way of describing the motion of the fluid and calculating a shear stress that's unique to the substance of the fluid itself.

This shear rate formula lets scientists and engineers determine the intrinsic nature of sheer stress to the materials they use in studying the biophysics of mechanisms such as the electron transport chain and chemical mechanisms such as polymer flooding.

## Other Shear Rate Formulas

More complicated examples of the shear rate formula relate shear rate to other properties of liquids such as flow velocity, porosity, permeability and adsorption. This lets you use shear rate in complicated **biological mechanisms**, such as the production of biopolymers and other polysaccharides.

These equations are produced through theoretical calculations of the properties of the physical phenomena themselves, as well as through testing which types of equations for shape, motion and similar properties that best match the observations of fluid dynamics. Use them to describe fluid motion.

## C-factor in Shear Rate

One example, the **Blake-Kozeny/Cannella** correlation, showed that you can compute shear rate from the average of a pore-scale flow simulation while adjusting the "C-factor," a factor that accounts for how the fluid's properties of porosity, permeability, fluid rheology and other values vary. This finding came about through adjusting the C-factor within a range of acceptable amounts that experimental results had shown.

The general form of the equations for calculating shear rate remains relatively the same. Scientists and engineers use the velocity of the layer in motion divided by the distance between the layers when coming up with equations of shear rate.

## Shear Rate vs. Viscosity

More advanced and nuanced formulas exist for testing the shear rate and viscosity of various fluids for different, specific scenarios. Comparing shear rate vs. viscosity for these cases can show you when one is more useful than the other. Designing screws themselves that use channels of space between metallic spiral-like sections can let them fit easily into designs that they're meant for.

The process of **extrusion**, a method of making a product by forcing a material through openings in steel disks to form a shape, can let you make specific designs of metals, plastics and even foods like pasta or cereal. This has applications in creating pharmaceutical products like suspensions and specific drugs. The process of extrusion also demonstrates the difference between shear rate and viscosity.

With the equation

for screw diameter *D* in mm, screw speed *N* in revolutions per minute (rpm) and channel depth *h* in mm, you can calculate the shear rate for extrusion of a screw channel. This equation is starkly similar to the original shear rate formula (*γ = V/x)* in dividing the velocity of the moving layer by the distance between the two layers. This also gives you an rpm to shear rate calculator that accounts for revolutions per minute of different processes.

## Shear Rate When Making Screws

Engineers use the shear rate between the screw and the barrel wall during this process. In contrast, the shear rate as the screw penetrates the steel disk is

with the volumetric flow *Q* and hole radius *R*, which still bears resemblance to the original shear rate formula.

You calculate *Q* by dividing the pressure drop across the channel *ΔP* by the polymer viscosity *η*, similar to the original equation for shear stress *τ.* This specific examples gives you another method of comparing shear rate vs. viscosity, and, through these methods of quantifying the differences in the motion of fluids, you can understand the dynamics of these phenomena better.

## Shear Rate and Viscosity Applications

Other than studying the physical and chemical phenomena of fluids themselves, shear rate and viscosity have uses in a variety of applications across physics and engineering. Newtonian liquids that have a constant viscosity when temperature and pressure are constant because there are no chemical reactions of changes in phase occurring in those scenarios.

Most real-world examples of fluids aren't so simple, though. You can calculate viscosities of non-Newtonian fluids as they depend on shear rate. Scientists and engineers typically use rheometers in measuring shear rate and related factors as well as performing the shearing itself.

As you change the shape of different fluids and how they're arranged with respect to the other layers of fluids, the viscosity can vary significantly. Sometimes scientists and engineers refer to the "**apparent viscosity**" using the variable *ηA* as this type of viscosity. Research in biophysics has shown that apparent viscosity of blood increases swiftly when shear rate falls below 200 s^{-1}.

For systems that pump, mix and transport fluids, the apparent viscosity alongside the shear rates gives engineers a way of manufacturing products in the pharmaceutical industry and the production of ointments and creams.

These products take advantage of the non-Newtonian behavior of these fluids so that the viscosity decreases when you rub ointment or cream on your skin. When you stop rubbing, the shearing of the liquid also stops so that the product's viscosity increases and the material settles.

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About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.