Rheological measurements for prediction of pumping and squeezing pressures of toothpaste

Abstract

Methods of non-Newtonian fluid mechanics are applied to predict processability and use of toothpaste, specifically its pumpability through long pipes and squeezability from tubes. The goal is to define procedures which would allow estimating pumping pressure and squeezing force from the data obtained on conventional rotational rheometers which are critical for product development and quality control. 11 commercially available and 28 lab-made model toothpastes are examined. The latter are engineered so as to cover wide range of toothpaste properties ranging from high yield stress products to weakly shear thinning ones by varying the concentration of polymers (xanthan gum and carboxymethyl cellulose) and particulate thickener (silica). Rotational rheometry is represented by narrow-gap Couette concentric cylinders and wide-gap vane-cup geometries. Equilibrium flow curves measured with both geometries are shown to agree, provided proper data processing is used.To assess pumping pressure in long pipes, a capillary rheometer equipped with pipes of different lengths is used. Thus measured pressure drop is compared to the pressures calculated from the equilibrium flow curves. It turns out that while the measurements agree quite well for pastes with higher concentration of silica, there is a systematic overestimation of pressure for pastes with lower concentration of silica and at lower flow rate. A possible explanation for this observation is the presence of wall slippage presumably caused by migration of silica from the pipe wall. This is found to be consistent for the calculations with slip boundary conditions.Vane-cup geometry is used to measure start-up curves from the state of rest which are more representative of tube squeezing during usage. A tube extrusion apparatus is used to quantify squeezability in terms of the force required to pull the tube through two rollers while squeezing toothpaste out of their tubes. Thus measured force correlates with the squeezing pressure calculated using the flow curves measured from the rest.