(94g) Mixing of Non-Newtonian Fluids for Non-Aqueous Oral Health Products: Experimental Investigations and CFD Simulations

Introduction

Mechanically stirred vessels are widely used in a broad
range of chemical process industries, and their purpose varies from mixing
different materials, generating solids suspensions or enhancing heat and mass
transfer. The geometric configuration of both impeller and tank together with
the fluid physical properties, in particular viscosity, dramatically affect the
fluid dynamics of the system. For Newtonian fluids general guidelines for the
most appropriate geometric configuration in different applications are
available in the literature. Conversely, even if non-Newtonian fluids are
employed in many industrial processes, less information is available. These
fluids are complicated to mix, and often sophisticated impeller designs are
required. This is the case in the oral health industry, where highly viscous
non-Newtonian fluids are used in the production of non-aqueous specialized oral
care products, such us non-aqueous toothpastes.

Computational fluid dynamics (CFD) is a powerful tool that
yields relevant process information and permits assessing the performance of
stirred vessels. The software relies on basic balance equations of fluid
mechanics, such as mass, linear momentum and energy balance equations, solved
on discretized fluid domains defined by the user. CFD can be used, among
others, to evaluate the mixing performance of stirred tanks, which is
particularly useful when dealing with non-Newtonian fluids. The objective of this
research is twofold: we first aim to characterise the rheology of the two-fluid
mixture of interest (glycerol and a polymer made of polyethylene glycol and
Carbomer) and to derive a constitutive equation to model it. The second
objective is to use this rheological information to numerically simulate the
fluid dynamic behaviour of the mixture in a stirred vessel and to validate the
model predictions against accurate experimental results of power consumption.

Experimental setup and methodology

The fluids of interest in this research are glycerol and a
polymer made of polyethylene glycol and Carbomer at a specific ratio. The
rheology of the polymer has not been studied before. For the development of the
CFD model for the mixing of these fluids we need to determine the constitutive
equation that describes the viscosity of mixtures of this particular polymer
with glycerol at different polymer mass fractions and shear rates at different
temperatures.

We studied the polymer mass fraction in intervals of 10%,
from 0 to 100%. Each mixture was studied at thirteen equally-spaced temperatures,
between 25 ºC and 85 ºC, according to the operating conditions of the
industrial mixing process. For each polymer concentration and temperature
considered, the viscosity of the mixture was evaluated at fifteen equidistant
points in a logarithmic scale of shear rate in the range of 1 s^-1 to
250 s^-1, where the experimental results were repeatable. Indicative
results are shown in Figure 1, which correspond to low and high values of
polymer mass fraction (40% and 100%) and to low and high values of temperature
(40ºC and 60ºC).  We used the rheological
data to determine the coefficients of a power law model for each experimental case
(Eq. 1).

(Eq. 1)

Figure
1. Shear stress profiles of samples with different polymer mass
fractions and temperatures

This same approach was followed for all conditions studied,
and a total of 143 values for each coefficient, K and n,
were determined, which correspond to the 11 polymer mass fractions and 13
temperatures evaluated. The coefficients can be calculated at any value of
polymer mass fraction from 0 to 1 and temperatures from 25 to 85 ºC through
linear interpolation. Experimental measurements of power consumption

Power requirements for the mixing of the polymer/glycerol
solutions were measured experimentally at certain concentrations and
temperatures in order to validate the CFD model of the stirred tank with the
viscosity function developed from the rheological measurements. The
measurements were carried out in a stirred tank fitted with a standard Rushton
impeller. The height of the fluid H was set equal to the tank diameter. The
impeller has a diameter D=1/3H; it was located at the centre of the tank, and was
driven by a variable-speed motor that could operate in the range of 50 – 2000
rpm. To measure power consumption we used a combination of an air bearing and a
load cell (Figure 2).

Figure
2. Schematics of the experimental setup

CFD modelling strategy

The two main approaches for modelling stirred tanks are the
Reference Frame (RF) and the Sliding Mesh (SM). The main advantage of RF is the
speed of convergence, but it can only be used for steady-state flows. In
contrast, SM provides a time dependent solution, but the computational effort
and time required to perform SM simulations are quite significant. RF is
therefore the preferred approach when its predictions are the same as those
given by the SM approach. To decide what approach to use, we tested both of
them by modelling the mixing of glycerol at 25 ºC at 100 rpm impeller speed in
the set up described above. It was found that the RF approach is applicable. The
computations were carried out using a 3.50 GHz Intel® Xeon ® CPU E5-1650 v2
with 16.0 GB RAM. The fluid dynamics were modelled using ANSYS Fluent 16.1. Results and Discussion

The torque and power consumption were measured for the
mixing of five non-Newtonian glycerol/polymer mixtures at six impeller speeds
and two different temperatures. In Figures 3 and 4, the power curves (plot of
Power number against Reynolds number) are plotted for two different cases, 100%
polymer mass fraction at 40 ºC and 40% polymer mass fraction at 60 ºC. In the
same Figures, the CFD predictions are also included.

Figure
3. Power curve for 100% gel mass fraction and 40 ºC

Figure
4. Power curve for 40% gel mass fraction and 60 ºC

The agreement between the computational and experimental
data is very good, which indicates that the CFD model can be used to predict
the torque applied by a Rushton turbine using the experimental rheology model.
Similar results are found for the remaining cases.

We currently study the mixing time of the two fluids both
experimentally and computationally. For these studies the tank is filled with
glycerol and the polymer is added at a particular location. Experimentally the
concentration profiles in the tank are monitored with planar laser induced
fluorescence (PLIF).

Acknowledgements

The authors would like to express their gratitude to GSK and
the EPSRC for the funding to carry out this research.