# Relationship between shear stress and rate viscometer

### How revolution per minute (rpm) is converted into shear rate in case of viscometers.?

According to Newton's Law, shear stress is viscosity times shear rate. Therefore by shear rate. Only Newtonian liquids can be described by this simple relation. After that we have a set of values shear stress and shear rate. Then, we plot this data and calculate plastic viscosity, yield stress etc. The question is how a I have attached the exact equation for what you are looking for. If you want to know . Depending on their viscosity behavior as a function of shear rate, stress, of fluids with a simple linear relation between shear stress [mPa] and shear rate [1/s ].

From ideally viscous liquids to elastic solids.

### Basics of viscometry :: Anton Paar Wiki

Viscoelastic materials in everyday life. The two plates model Figure 3: The virtual viscous sandwich: Laminar flow consisting of infinitesimally thin layers.

The two-plates model provides a mathematical description for viscosity.

Think of a kind of sandwich [1]: There are two plates with fluid placed in-between. The correct calculation of parameters related to viscosity depends on two criteria: The fluid does not glide along the plates but is in good contact with them.

Scientifically speaking, an adhesive force operates between fluid and plates. The flow is laminar. It forms infinitesimally thin layers and no turbulence i. You can picture laminar flow as a stack of paper sheets or beer mats.

## The relationship between viscosity and shear stress rate.

The lower plate does not move. The upper plate drifts aside very slowly and subjects the fluid to a stress, which is parallel to its surface: Shear stress Figure 4: Using the two-plates model to calculate the shear stress.

Using the two-plates model to calculate the shear rate. Shear rate is the velocity of the moving plate divided by the distance between the plates. The two-plates model allows for calculating another parameter: The shear rate is the velocity of the upper plate in meters per second divided by the distance between the two plates in meters. Therefore, the viscosity eta is shear stress divided by shear rate.

Only Newtonian liquids can be described by this simple relation.

Dynamic viscosity is shear stress divided by shear rate. What are Newtonian liquids? Viscosity functions show dynamic viscosity vs. Different types of flow behavior: A viscosity function shows the viscosity over the shear rate. For a Newtonian liquid, this function is a straight line curve 1 ; see figure 6.

Typical Newtonian liquids are water or salad oil. If its viscosity changes with the shear rate, a liquid is non-Newtonian and — for exact definition — one has to specify the apparent viscosity. Different shear-dependent fluids behave differently: For some, their viscosity decreases when the shear rate increases curve 2 e.

The flow behavior of non-Newtonian liquids can be far more complex than these basic examples. Some gels and pastes behave like a fluid when worked or agitated and then settle into a nearly solid state when at rest.

Such materials are examples of shear-thinning fluids. House paint is a shear-thinning fluid and it's a good thing, too. Brushing, rolling, or spraying are means of temporarily applying shear stress.

This reduces the paint's viscosity to the point where it can now flow out of the applicator and onto the wall or ceiling.

### Rheology measurements

Once this shear stress is removed the paint returns to its resting viscosity, which is so large that an appropriately thin layer behaves more like a solid than a liquid and the paint does not run or drip. Think about what it would be like to paint with water or honey for comparison. The former is always too runny and the latter is always too sticky.

Toothpaste is another example of a material whose viscosity decreases under stress.

Toothpaste behaves like a solid while it sits at rest inside the tube. It will not flow out spontaneously when the cap is removed, but it will flow out when you put the squeeze on it.

## How revolution per minute (rpm) is converted into shear rate in case of viscometers.?

Now it ceases to behave like a solid and starts to act like a thick liquid. You don't have to worry about it flowing off the brush as you raise it to your mouth.

This particular geometry requires only 0. All experiments were run at conditions ensuring on-scale readings. Figure 4 presents data for the above samples. The cream data are in red, while the ointment data are in blue. The apparent viscosity of each sample decreases greatly with increasing shear rate. Viscosity increases as the shear rate decreases again, but to values less than those measured in the initial, increasing-rate ramp.

This response is thixotropy. Structure in the material breaks down over time and needs time to recover. The non-Newtonian behavior, in these cases, is useful—the viscosity decreases as the materials are rubbed on the skin, for example, easing application.

Stopping the rubbing, and ceasing the shearing, allows the viscosity to increase, helping the ointment or cream to stay on the area. One example is the use of cone-plate geometry to test a sample at one speed, waiting a few minutes before taking the data point. Shearing the material for some time helps to break down the structure; the viscosity readings decrease and then plateau after some time.

Therefore, more consistent readings may be taken from sample to sample, after a suitable shearing time. Representative data are shown for the ointment in Figure 5.

The data show that the viscosity plateaus within about 2 minutes for this material. Therefore, an appropriate, single-point QC test may be to shear each ointment sample at 1 rpm for 2 minutes before recording a reading.