# Evaluating the Elasticity Recovery Following Extrusion From a Tube

Many consumer products are packaged in tubes or bottles where product application involves pumping the product through a nozzle.

Such consumer products tend to be shear thinning products where the viscosity is reduced during extrusion due to the increase in shear rate, and then recovers as it exits the orifice as the shear rate is reduced. The radius of the orifice (r) and the volumetric flow rate influence the shear rate during extrusion, as per the equation below:

In the above equation, n is the power law index, which is equal to 1 for Newtonian liquids and ranges between 0 and 1 for non-Newtonian fluids. By applying the shear rate during extrusion can be calculated by measuring the internal radius of the orifice and the volumetric flow rate, which is nothing but the volume dispensed at a given time.

The delicate microstructures of consumer products like coatings, cosmetics, toiletries and food stuff is easily broken during extrusion and the recovery to the original structure happens only after a finite amount of time. Those materials whose structure recovery or rebuilding is time dependent are called thixotropic materials.

The structural breakdown that occurs during extrusion can be simulated by using the shear rate calculated during extrusion in the intermediate stage of step strain-shear rate test. The structural recovery of the material and the structural integrity of the product at the time of use can be determined by tracking structural recovery through the elastic modulus G’ as a function of time. Product characteristics like slump resistance or physical appearance, or the product functionality or in use texture, for instance its clinging ability on a vertical surface, can be examined based on the structural recovery studies.

## Experimental

In the experiment, the structural recovery of hair gel and toothpaste were evaluated based on shear rate conditions that prevailed when the product was extruded during use. A Kinexus rotational rheometer along with a Peltier plate cartridge and a roughened parallel plate measuring system were used for making rotational rheometer measurements.

A standard pre-configured sequence provided by the rSpace software was also used in order to ensure that a consistent and controllable loading protocol was followed for both samples. The temperature for all rheology measurements was 25°C. Based on the input values of extrusion time, extruded volume and aperture radius, the corresponding extrusion shear rates were automatically determined during the test sequence. The test sequence was programmed such that the calculated value was used as the intermediate shear rate in the step shear rate test in which steps 1 and 2 of the experiment used a constant strain value within samples LVER at a frequency of 1Hz.

After the test was completed, the time taken to recover 90% of the original elasticity (G’) of the product was determined automatically.

## Results and Discussion

The shear rate in the extrusion process was automatically calculated as 86s-1 for the toothpaste and as 240s-1 for the hair gel. The calculated values were used in the intermediate shear rate stage of the test. The test results of the toothpaste sample are shown in Figure 1.

Figure 1. Step strain/shear rate curves for a toothpaste. (Elastic Modulus G’ in red; Viscous Modulus G’’ in blue; phase angle δ in green)

The recovery curve of the toothpaste does not show complete recovery in the timescale of the test, which proves the highly thixotropic nature of the toothpaste sample. The toothpaste sample recovers only 50% of its original G’ value after a period of 500 seconds.

In case of the hair gel an almost instant recovery of the structure was observed, with 90% of the recovery within the first 5 seconds and complete recovery within 20 seconds (Figure 2). This recovery rate is vital for the hair gel since it needs to provide instant hold to hair before an elastic film is formed by the resin for a longer-term hold. However, both the samples exhibit yield stress behavior at the measured frequency because G’ is more than G”, which is illustrates a solid dominant or interconnected microstructure.

Figure 2. Step strain/shear rate curves for a hair gel. (Elastic Modulus G’ in red; Viscous Modulus G’’ in blue; phase angle δ in green)

## Conclusion

The toothpaste and hair gel samples were subjected to a three step strain-shear test for determining the rate and the extent of elastic recovery after extrusion from a tube. It was seen that the toothpaste showed high thixotropic behavior, taking 500 seconds for 50% recovery, while the hair gel recovered almost instantly.

This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.

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