# Optimised Twin Fluid Atomiser Design for High-Viscosity, Shear-Thinning Fluids
## 2 Materials and Methods
### Setup  
The experimental setup, illustrated in Figure 1, comprised an air supply line for the atomising agent and a liquid supply line for the surrogate liquid. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Fluid** & \(T\) & \(\sigma\times 10^{3}\) & \(\eta_{L}^{50,000}\) & \(\rho_{L}\) & \(We_{L}/Re_{L}\) & \(Oh\times 10^{3}\) \\  & **K** & \(\mathbf{N}\mathbf{m}^{-1}\) & **Pa s** & \(\mathbf{kg}\mathbf{m}^{-3}\) & - & - \\ \hline Water & 298 & 72 & 0.00089 & 997 & 4 & 5 \\ Sewage Sludge & 298 & 40 & 2.2 & 1100 & 16,500 & 14,832 \\ Silicone oil & 298 & 21.4 & 2 & 970 & 28,037 & 19,631 \\ \hline \end{tabular}
\end{table} 
Table 1: Fluid properties of water, surrogate liquid, and target sludge. \begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{T}_{L}\) & \(\eta_{L}^{0}\) & \(\rho_{L}\) & \(\sigma\times 10^{3}\) \\
**K** & **Pa s** & \(\mathbf{kg}\mathbf{m}^{-3}\) & \(\mathbf{N}\mathbf{m}^{-1}\) \\ \hline
273 & 17.3 & 992 & - \\
278 & 15.5 & 988 & - \\
283 & 13.7 & 984 & - \\
288 & 12.3 & 9 The liquid was stored inside a 20 L capacity pressurised tank. The total pressure exceeded the geostatic pressure inside the tank at least by one order of magnitude throughout all experiments. The change in liquid level during each experiment was negligible, ensuring a constant volume flow rate \(\dot{V}_{L}\). The determination of \(\dot{m}_{L}\) was established through means of a weighting scale (Bosche MWI-A) with a measurement accuracy of \(\pm 0.01\) kg. The weight of the silicone oil tank was measured before and after each experiment to determine the change in mass \(\Delta m\). A flow time \(\Delta t\) of 30 s was selected for the liquid and consequently, \(\dot{V}_{L}\) is obtained through Equation (4), where \(\rho_{L}\) represents the temperature-dependent density of the liquid silicone oil. \[\dot{m}_{L}=\rho_{L}\cdot\dot{V}_{L}=\frac{\Delta m}{\Delta t} \tag{4}\]  
Figure 1: Experimental setup, consisting of the following: atomiser; air supply line (1); liquid supply line (2); acrylic glass containment; photography equipment (Sony RX10 M3, Sony, Tokyo, Japan) or Photron Fastcam SA 1.1, (Photron, West Wycombe, UK); weighting scale (Bosche MWI-A, Bosche, Damme, Germany). Each experiment to determine \(\dot{V}_{L}\) was repeated three times and the average \(\dot{V}_{L}\) was calculated. The standard deviation for \(\dot{V}_{L}\) was \(3\times 10^{-7}\) m\({}^{3}\)s\({}^{-1}\), ensuring reproducibility and the adjustment of a constant liquid flow rate. Due to the test rig being positioned outdoors, the density and the viscosity of the surrogate was subject to fluctuations as a result of ambient temperature (\(T_{A}\)) changes. The temperature of the surrogate inside the tank (\(T_{L}\)) was therefore measured to determine the viscosity via the manufacturer's data sheet [28]. The air supply line to the nozzle incorporates a pressure regulator, enabling the adjustment of the air volume flow rate \(\dot{V}_{G}\), that can be setup to \(1.11\times 10^{-1}\) std m\({}^{3}\)/s. The air supply line was allowed to stabilise until \(\dot{V}_{G}\) reached a steady state. \(\dot{V}_{G}\) was measured using the SD 9000 flowmeter (IFM, Essen, Germany). This study examined volumetric air-to-liquid ratios between 3849 and 20,477. A pressure measurement point was installed upstream of the nozzle air inlet, where the static pressure was recorded using a PMR Type PIT-C pressure sensor (PMR HandelsgmbH, Lassnitzhohe, Austria). The accuracy of the pressure sensor is \(\pm 0.15\%\) of the measured value and \(\pm 0.15\%\) of the final reading (\(9\times 10^{5}\) Pa). Figure 2 illustrates a configuration of a complete nozzle assembly, indexed by the number (3). A complete nozzle assembly comprises a welded nozzle cage and nozzle blank, with a nozzle insert positioned internally. The apex angle of the atomising agent is indicated in (2).