Optimised Twin Fluid Atomiser Design for High-Viscosity, Shear-Thinning Fluids

Abstract

This study explores the optimisation of nozzle design for external twin fluid, single-stage atomisation in handling high-viscosity, shear-thinning polydimethylsiloxane (PDMS). A single PDMS grade was employed and atomised using unheated sonic air and the viscosity was varied by the fluid temperature. A systematic experimental approach was used, varying nozzle geometry—specifically apex angle, gas nozzle diameter, and number of gas nozzles—to identify the optimal nozzle configuration (ONC). The spray qualities of the nozzle configurations were evaluated via high-speed imaging at 75,000 FPS. Shadowgraphy was employed for the optical characterisation of the spray, determining the optimal volumetric air-to-liquid ratio (ALR), a key parameter influencing energy efficiency and operational cost, and for assessing droplet size distributions under varying ALR and viscosity of PDMS. The ONC yielded a Sauter mean diameter $d_{32}$ of 570 × 10⁻⁶ $\mathrm{m}$, at an ALR of 8532 and a zero-shear viscosity of 15.9 $\mathrm{Pa}$ $\mathrm{s}$. The results are relevant for researchers and engineers developing twin fluid atomisation systems for challenging industrial fluids with similar physical properties, such as those in wastewater treatment and coal–water slurry atomisation (CWS). This study provides design guidelines for external twin fluid atomisers to enhance atomisation efficiency under such conditions.

1. Introduction

Sewage sludge incineration is being increasingly adopted in many countries due to its advantages in volume reduction, pathogen elimination, and potential for energy and material recovery. Alternative treatments, such as landfill disposal, are limited or prohibited by concerns related to heavy metals, microplastics, and pharmaceuticals. To support circular economy objectives and address phosphorus scarcity, Germany will begin phosphorus recovery from sewage sludge starting in 2029 [1]. One potential technological approach for phosphorus recovery could involve the following two-stage process: In the first stage, sewage sludge is atomised and dried in a spray drying tower, i.e., fluidised bed reactor. In the second stage, the dried sludge particles are combusted in a rotary kiln. The resulting ash contains concentrated phosphorus recoverable through chemical or thermo-chemical processes [2,3].

A previous study successfully realised the above mentioned cost-effective two-stage process, in which an atomiser, with no specific information available on the atomiser design, was utilised inside a fluidised bed reactor for sewage sludge incineration [4]. According to the reference [4], the nozzle must be wear-resistant and generate droplet sizes between 30 and 500 microns. It is clear that robust atomisation is essential for the effective implementation of this approach, highlighting the critical role of atomiser design. This study is therefore motivated by the need to design a suitable atomiser for the high-viscosity sewage sludge employed in a specific resource recovery application. The use of polydimethylsiloxane (silicone oil) in our study as a surrogate fluid allows for the simulation of atomisation behaviour under controlled conditions, as its density, surface tension, and shear-dependent viscosity are comparable to those of the target sludge. The odourless, homogeneous, and non-separating nature of silicone oil facilitates laboratory handling and optical analysis.

The literature on coal–water slurry (CWS) atomisation was consulted, as CWS generally constitutes a shear-thinning fluid containing suspended solid particles [5,6]—a characteristic shared with sewage sludge. Internal-mixing twin fluid atomisers offer enhanced atomisation efficiency in comparison to external designs [7]; however, their inherent tendency to suffer from erosion and clogging when handling particulate-laden fluids remains a major drawback [8]. Several studies on high-viscosity twin fluid atomisation employ nozzle throat diameters below 8 mm, despite the associated increase in clogging risk [5,9,10,11,12]. In our proposed external-mixing atomiser design, a nozzle diameter of 8$\mathrm{m}$$\mathrm{m}$ was selected to minimise the risk of clogging encountered with viscous, particle-laden fluids. By keeping gas and liquid streams separate prior to atomisation, the external geometry reduces abrasion and facilitates easier maintenance. External atomiser designs, however, result in higher gas consumption and larger droplet sizes compared to internal-mixing variants [13], a trade-off that was deliberately accepted in favour of operational robustness.

Research on shear-thinning high-viscosity fluids, i.e., bio slurry, water-based solutions, and suspensions, typically examine a single nozzle geometry and lack systematic evaluation of critical nozzle design parameters, such as apex angle of the atomising agent and orifice arrangement [5,9,10,11,14,15,16]. Multiple nozzle designs, in fact, originate from atomising low-viscosity fluids [9], raising concerns regarding their atomisation efficiency, when applied to high-viscosity media.

One area that remains unexplored in the available literature is the atomisation of PDMS at a zero-shear viscosity of 10$\mathrm{Pa}$$\mathrm{s}$. This study addresses this shortcoming by systematically analysing how variations in atomiser geometry and process parameters affect the atomisation quality of the high-viscosity PDMS. The findings presented here may serve as a basis for the atomisation of other non-Newtonian fluids of similar rheological and physical material properties [11,17,18,19,20,21]. The importance of the efficient atomisation of such liquids is increasing [11,20,22,23,24,25]. Given the lack of systematic, parametric design studies for atomising high-viscosity, shear-thinning media, this work presents a detailed investigation to identify an efficient geometry for an external, single-stage, twin fluid atomiser.

While this work is motivated by the challenge of atomising high-viscosity sewage sludge, the identified optimal nozzle configuration and its optimal operating parameters may also be applicable to other sprayable media of interest with comparable rheological and physical properties, thereby supporting a range of resource recovery processes. Given the complex interplay between fluid properties, however, caution must be exercised when generalising the findings to other fluids or the determined optimal operational settings. Although rheological similarity provides a useful initial indication of transferability, differences in chemical composition, heterogeneity, temperature sensitivity or shear-rate sensitivity may lead to deviations in spray behaviour.

The paper is structured as follows: Section 2 describes the methodology and materials used, Section 3 presents the results and discusses implications, and Section 4 concludes.

2. Materials and Methods

2.1. Model Fluid and Atomising Agent Properties

The physical and rheological properties of sewage sludge are subject to considerable variation as a result of numerous influencing factors, including temperature, solids concentration, wastewater composition, chemical additives, and preprocessing steps related to digestion and fermentation [18,19,22]. Consequently, it remains challenging to define universally applicable physical and rheological properties for sewage sludge.

Sewage sludge exhibits non-Newtonian, shear-thinning behaviour in general [26]. At low shear rates, the viscosity remains constant, reflecting Newtonian fluid behaviour. This constant viscosity is referred to as the zero-shear viscosity. Beyond a certain critical shear rate, a progressive decline in viscosity is observed as the shear rate increases. This phenomenon, described by the apparent viscosity, results from the disruption of flocculated particle networks [27]. At sufficiently high shear rates, a limiting viscosity value is approached, beyond which the fluid again behaves in a Newtonian manner. This asymptotic viscosity value is termed the infinite-shear viscosity.

When selecting a non-Newtonian shear-thinning surrogate liquid, it is essential to determine the characteristic shear rate first, encountered in the atomisation process. Ensuring comparable atomisation behaviour necessitates that the apparent viscosity of both the sludge and the surrogate liquid coincide at the characteristic shear rate. The application of unheated air at sonic speed as the atomising agent resulted in an estimated shear rate of 50,000 s⁻¹.

Various suppliers provide polydimethylsiloxane (PDMS) [28,29,30]. According to manufacturers’ data [28,29], PDMS with a kinematic viscosity of 10,000 mm² s⁻¹ at 25 °C exhibits an apparent viscosity of 2 Pa s under the relevant shear rate, thereby closely matching the apparent viscosity of the target sludge under equivalent conditions. For this investigation, Wacker silicone oil type AK 10,000 was therefore selected as the surrogate liquid [28]. The chemical structure of the surrogate liquid is provided in Formula (1).

$${\left({\mathrm{H}}_3\mathrm{C}\right)}_3\mathrm{S}\mathrm{i}-\mathrm{O}-{[\mathrm{S}\mathrm{i}{\left(\mathrm{C}{\mathrm{H}}_3\right)}_2-\mathrm{O}]}_{\mathrm{n}=500}-\mathrm{S}\mathrm{i}{\left(\mathrm{C}{\mathrm{H}}_3\right)}_3$$

(1)

In addition to viscosity, both the density and surface tension of the atomised medium constitute critical parameters in atomisation. Density and surface tension substantially influence spray formation and droplet breakup, necessitating minimal deviation between model fluid and target medium [31]. The Ohnesorge number, shown in Equation (2), serves as a dimensionless quantity that captures the interplay of viscosity, density, and surface tension in atomisation processes. Here, ${\rho }_L$ denotes the density of the spray medium, D a characteristic length scale, ${\eta }_L$ the apparent viscosity of the spray medium, and $\sigma$ the surface tension of the spray medium.

$$Oh={\displaystyle \frac{{\eta }_L}{\sqrt{D·{\rho }_L·\sigma }}}={\displaystyle \frac{W{e}_L^{0.5}}{R{e}_L}}$$

(2)

Equation (3) defines a dimensionless quantity that expresses the balance between viscous and surface tension forces opposing atomisation, where $\mathrm{\Delta }U$ denotes the relative velocity between the atomising agent and the spray medium. A higher value of $W{e}_L/R{e}_L$ implies an increased influence of viscous forces opposing the atomisation process [31].

$${\displaystyle \frac{E_{\eta }}{E_{\sigma }}}={\displaystyle \frac{{\eta }_L·\mathrm{\Delta }U·D^2}{\sigma ·D^2}}={\displaystyle \frac{{\eta }_L·\mathrm{\Delta }U}{\sigma }}={\displaystyle \frac{W{e}_L}{R{e}_L}}$$

(3)

In the CWS atomisation literature, it is common practice to report the apparent viscosity of CWS at a shear rate of 100 s⁻¹ [17]. According to the manufacturer’s data of the model fluid [28], the apparent viscosity ${\eta }_L^{100}$ at a shear rate of 100 s⁻¹ corresponds to the zero-shear viscosity ${\eta }_L^0$. For consistency, the apparent viscosity at a shear rate of 100 s⁻¹ is therefore employed throughout the Results Section for the surrogate liquid.

Table 1. Fluid properties of water, surrogate liquid, and target sludge.

Fluid	T K	$\mathit{\sigma }\times {10}^3$ Nm−1	${\mathit{\eta }}_{\mathit{L}}^{50,000}$ Pa s	${\mathit{\rho }}_{\mathit{L}}$ kgm−3	WeL/ReL -	$\mathit{O}\mathit{h}\times {10}^3$ -
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

presents the relevant material properties and dimensionless numbers for both sewage sludge and the selected surrogate fluid, based on an assumed relative velocity of 300 m s⁻¹ and a characteristic length scale of $500\times {10}^{-6}$ $\mathrm{m}$. The apparent viscosity was evaluated at a representative shear rate of 50,000 s⁻¹, reflecting the conditions encountered during atomisation.

The atomisation of silicone oil was performed using unheated, over-pressurised air accelerated to sonic velocity. The Mach number and excess pressure of the atomising agent were summarised in the Results Section, due to the dependency of the gas nozzle geometry. A gas volumetric flow rate of 105.56 × 10⁻³ std m³s⁻¹ was selected and maintained constant throughout the experiments.

The nozzles were designed to ensure the atomising agent exits at sonic velocity rather than subsonic, owing to the atomisation resistance induced by viscosity, as outlined in Table 1. An over-pressurised atomising agent promotes finer droplet formation, as demonstrated in the atomisation of molten metals [32,33,34] and in the dispersion of highly viscous shear-thinning media under elevated system pressures [35].

For the purpose of this study, manufacturer-provided data for the surrogate fluid were used, indicating a viscosity tolerance of ±5%. Using temperature-dependent correlations for density and kinematic viscosity obtained from manufacturer-provided data [28], dynamic viscosity values for varying temperature were calculated and shown in

Table 2. Physical properties of the surrogate liquid AK 10,000.

${\mathit{T}}_{\mathit{L}}$ K	${\mathit{\eta }}_{\mathit{L}}^0$ Pa s	${\mathit{\rho }}_{\mathit{L}}$ kgm−3	$\mathit{\sigma }\times {10}^3$ Nm−1
273	17.3	992	-
278	15.5	988	-
283	13.7	984	-
288	12.3	980	-
293	11.1	975	-
298	9.7	970	21.5

.

2.2. 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.

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 $\pm 0.01\mathrm{kg}$.

The weight of the silicone oil tank was measured before and after each experiment to determine the change in mass $\mathrm{\Delta }m$. A flow time $\mathrm{\Delta }t$ 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.

$${\dot{m}}_L={\rho }_L·{\dot{V}}_L={\displaystyle \frac{\mathrm{\Delta }m}{\mathrm{\Delta }t}}$$

(4)

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 × 10⁻⁷ m³s⁻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 × 10⁻¹ std m³/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, Laßnitzhöhe, Austria). The accuracy of the pressure sensor is $\pm 0.15\%$ of the measured value and $\pm 0.15\%$ of the final reading (9 × 10⁵ 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).

Ten nozzle blanks and ten nozzle cages were available for this study, resulting in ten different nozzle assemblies, each varying in the number and diameter of gas holes $d_G$ as well as in apex angle $\theta$. Gas nozzle holes were drilled in a discrete and equidistant arrangement with respect to each nozzle configuration (NC). Figure 2 shows a nozzle assembly consisting of six gas nozzle holes, each with a diameter of 6 mm ($d_G$), and $\theta$ = 90°. With regards to Figure 2, a nozzle insert was placed inside the nozzle assembly to enable atomisation. An O-ring in the nozzle insert ensured that the liquid flowed through the liquid hole with diameter $d_L$ of the nozzle insert, while it also secured the nozzle insert in its position.

The investigated nozzle configurations were operated in either confined or free-fall mode, depending on the presence and geometry of the nozzle insert. In setups with a nozzle insert, atomisation was initiated directly at the insert tip, consistent with confined atomisers. In the absence of the nozzle insert, the liquid flowed in a free-fall manner before being impinged by the atomising agent, resembling a free-fall atomiser [36]. The geometric impingement distance (IDG) was defined as the axial distance between the exit of the gas nozzle and the first point of contact with the liquid at the liquid nozzle tip, considering the unwidened gas jet, as shown in Figure 3. Regarding the investigated atomiser design, IDG increases as the apex angle of the atomising agent decreases.

A preliminary sizing of six 6 × 10⁻³ m diameter holes was selected, based on the assumption of air flowing at standard conditions with a normal volume flow rate of 5.56 × 10⁻² std m³s⁻¹. This specific design flow rate was selected to ensure that the air exits the nozzle at sonic speed, under over-pressure conditions, for a maximum flow rate of 1.11 × 10⁻¹ std m³s⁻¹. Standard thermodynamic law for isentropic gas flow was applied, confirming sonic outflow under over-pressure conditions at the gas nozzle exits.

Building upon the baseline design shown in Figure 2, additional nozzle configurations, listed in

Table 3. Tested nozzle configurations (NC).

NC	n -	${\mathit{d}}_{\mathit{G}}\times {10}^3$ m	θ °	${\mathit{A}}_{\mathit{G}}/{\mathit{A}}_{\mathit{L}}$ -	$\mathit{s}/{\mathit{d}}_{\mathit{G}}$ -
No. 1	3	8	90	3	4.65
No. 2	4	7	90	3.06	3.98
No. 3	6	6	60	3.38	3.1
No. 4	6	6	90	3.38	3.1
No. 5	6	6	120	3.38	3.1
No. 6	8	5	90	3.13	2.79
No. 7	10	4.5	90	3.16	2.48
No. 8	12	4	90	3	2.32
No. 9	24	3	30	3.38	1.55
No. 10	24	3	90	3.38	1.55

, were manufactured with the objective of maintaining a nearly constant area ratio $A_G/A_L$, constrained by the available drill bit increments of $5\times {10}^{-4}$ $\mathrm{m}$. The ratio $A_G/A_L$ represents the relationship between the cross-sectional area of all gas nozzle holes and the liquid pouring hole with its corresponding diameter $d_L$. The nozzle inserts had an inner diameter $d_L$ of 8 × 10⁻³ m. The ratio $s/d_G$ represents the circumferential distance s relative to the diameter of the gas nozzle holes $d_G$, as described in Figure 2.

2.3. Video Analysis

The nozzle configurations listed in Table 3 were validated using high-speed imaging based on the shadowgraph method. The high-speed CMOS camera, Photron Fastcam SA 1.1, is capable of recording images at up to 128 × 32 pixels at a frame rate of 150,000 frames per second (FPS). For this study, a frame rate of 75,000 FPS was chosen to increase the image resolution to 256 × 128 pixels, providing an optimal balance between temporal and spatial resolution for analysing atomisation behaviour. The validation was conducted to evaluate the atomisation quality 100 × 10⁻³ m below the nozzle exit for the tested nozzle configurations as well as for the validation of the optimal volumetric ALR for the ONC.

The focus of the Photron Fastcam was adjusted so that the downward pouring liquid jet was captured at its centre axis. Four video recordings were made at distinct measurement points (MP) downstream of the nozzle (e.g., 100 × 10⁻³ m, 500 × 10⁻³ m, 700 × 10⁻³ m and 1050 × 10⁻³ m) for the determination of droplet velocity and atomisation quality.

The camera’s focus distance was set to 50 × 10⁻³ m throughout all experiments. The camera lens had a focal length of 30 × 10⁻³ m. The pixel size of the camera sensor was 20 × 10⁻⁶ m, ensuring good light capture, though this also resulted in a minimum resolvable droplet size of 250 × 10⁻⁶ m. This resolution made the camera suitable for recording the high-speed liquid droplets that have not fully disintegrated near the nozzle, but it limited the ability to capture smaller droplets below 250 × 10⁻⁶ m in diameter. The Sony RX10M3 was therefore utilised for determining droplet size distributions.

The open-source image processing software Image J (Version 1.54f)was utilised to obtain an averaged droplet velocity across 100 tracked droplets. The “TrackMate” plugin was employed for this purpose. A thresholding detector was selected, and a filter was applied to track only droplets with a pixel area size smaller than 200. This filter was introduced to exclude false positives arising from overexposed or brightly illuminated regions in the video of the high speed camera. These overexposed regions were mistakenly detected as droplets, even though they were not part of the actual spray. A Kalman tracker was used with the following settings: an initial search radius of 15 pixels, a search radius of 20 pixels, and a maximum frame gap of 5 frames.

2.4. Image Analysis

The Sony RX10M3 was employed to determine droplet size distributions at smaller length scales. The shadowgraph method was applied. The zoom lens was set to a focal length of 600 × 10⁻³ m with a focusing distance of 950 × 10⁻³ m. The pixel size of the Sony CMOS sensor is 3.4 × 10⁻⁶ m, resulting in a resolvable minimum length of 21 × 10⁻⁶ m in diameter for the given conditions. The aperture was set to F4.0, while the ISO value was set to 200 to minimise image noise and therefore false positives. The exposure time was set to 1/32,500 s.

Droplet size distributions were derived from a sample of 1000 droplets. For the determination of droplet size distributions, the camera was positioned 1050 × 10⁻³ m downstream of the nozzle exit, the lowest feasible point, ensuring that the atomisation process had reached a sufficient level of development. Each trial was repeated up to three times to ensure sufficient image acquisition and to verify reproducibility. The repetition of trials was also necessary due to the fact that the acrylic glass containment was sprayed with silicone oil droplets, reducing visibility in seconds. The affected section of the containment was therefore cleaned after each trial. The images were taken at the centre of the spray, corresponding to a radial displacement of zero from the spray axis. The accuracy and reliability of the camera system was ensured by calibration. The calibration of the image scale was performed using a reference object of known size placed in the field of view at the measurement distance.

Each image underwent post-processing through conversion to binary format. The images were further refined and analysed in “Fiji” (v. 2.9.0) to identify and correct any missing or falsely detected droplets, as depicted in Figure 4. The droplet diameters $d_i$ were determined using a MATLAB (Version R2023B) routine that read in the area of each droplet and used the information to compute the diameter of an equivalent circle. A histogram with 20 bins was generated using the histogram function to visualise the frequency distribution of droplet diameters. To obtain a smoothed cumulative distribution, the ksdensity function was used with the ‘function’, ‘cdf’ option, applying kernel smoothing to estimate the cumulative probability distribution of droplet sizes. The bin edges were defined using logarithmic spacing to account for the wide range of droplet sizes. The Sauter mean diameter $d_{32}$ was calculated from the equivalent diameters to quantify the droplet volume to surface area ratio and is expressed by Equation (5).

$$d_{32}={\displaystyle \frac{{\sum }_i{d}_i^3}{{\sum }_i{d}_i^2}}$$

(5)

3. Results

3.1. Nozzle Inserts

First, atomisation investigations were performed with the nozzle configuration (NC) No. 4, consisting of six holes with a diameter of 6 × 10⁻³ m each. The apex angle was chosen as 90°. Compared to the literature, an apex angle of 90° is unusual, as most studies have experimented with external atomisers using apex angles up to 65° [10,14,33,35,37,38].

Figure 5 shows four different nozzle assemblies, each distinguishable by different nozzle inserts that are illustrated in black or by the absence of a nozzle insert. The first configuration tested, indexed by the number 1 in Figure 5, resulted in the production of fibre-like structures. In order to exclude doubts on the nozzle insert’s length to diameter ratio of the second configuration, a third configuration with a ratio of 2.5 was investigated (3). The second and third configuration did not result in any improvements towards achieving atomisation.

The formation of recirculation zones and vortices in twin fluid atomisation nozzles were researched at length [33,39]. The formation of recirculation zones as well as vortices interacted with the free-falling liquid and deflected the downward-pouring liquid stream. It was notable that inhibiting recirculation zones and vortices must be taken into even greater consideration, as highly viscous liquids seemed to be more prone to insufficient atomisation when deflected. Those deflected structures were then not disintegrated further, as they appeared too far away from the geometrical impingement point of the gas jets and thus, the relative velocities between the gas jets and the disintegrated liquid columns were too low to achieve further breakup. Consequently, single-staged, free-fall atomisers were deemed unsuitable for the atomisation of the investigated high-viscosity surrogate liquid.

It is known that highly viscous liquids require maximised relative velocities to achieve fine sprays [35]. The impingement distance between the liquid cluster agglomerating along the liquid nozzle tip and the gas jets (IDL) must be therefore minimised to ensure sufficient disintegration. This was achieved by the use of a nozzle insert shown in Figure 5, marked by the number 4. The variation in length of the nozzle insert is indicated in yellow.

Preliminary investigations showed that both overly long and overly short nozzle inserts resulted in insufficient atomisation performance. As the radial distance from the core of the gas jet increases, the axial velocity of the jet diminishes. This reduction in velocity results from the momentum transfer between the jet and the surrounding air due to shear forces, leading to the dissipation of kinetic energy [40]. Consequently, it can be inferred that IDL should be minimised to maximise the shear rate. Following this reasoning, one might consider directing the gas jet to impact the nozzle insert such that the core velocity is fully utilised for atomisation. However, this would cause a loss of kinetic energy within the gas jet through the reduction of the effective gas volume flow rate available for atomisation. In this study, IDL was held constant at 1.5 × 10⁻³ m.

3.2. Nozzle Configurations

Figure 6 illustrates atomisation attempts of NC No. 4 at varying ALR. The corresponding data is presented in

Table 4. Operating parameters during image acquisition, corresponding to Figure 6.

Index Figure 6	NC	FPS s−1	${\mathit{\eta }}_{\mathit{L}}^0$ Pa s	ALR -	${\dot{\mathit{V}}}_{\mathit{G}}\times {10}^3$ std m3/s	${\dot{\mathit{m}}}_{\mathit{L}}\times {10}^3$ kgs−1
1	4	60	11.1	3849	83.33	21.00
2	4	5000	11.1	4875	105.56	21.00
3	4	10,000	11.1	6143	52.78	8.33

. The spray pattern of the nozzle configurations listed in Table 3 were investigated 100 × 10⁻³ m below the atomiser and high speed recordings using the shadow photography method were made, according to Section 2.3.

NC No. 9, supporting a typical apex angle (30°) used in atomisation processes for low-viscosity liquids, resulted in the production of fibrous droplets. A conglomerated drop of silicone oil, increasing in size, accumulated at the nozzle tip and was torn off as gravitational forces became dominant. A periodic manner was noticed but not further investigated, as atomisation did not occur.

As a result, nozzle configurations with increased apex angles were tested. Nozzle configurations No. 4 and 10, both with an apex angle of 90°, atomised the liquid equally well when observed visually. Using high speed image recording, however, it turned out that atomisation quality was significantly better at NC No. 4 compared to NC No. 10. Nozzle configuration No. 3, No. 5, and No. 9 with apex angles of 60°, 120°, and 30°, respectively, revealed the production of a larger fibrous droplet content compared to NC No. 4, as can be seen in Figure 7. The optimal apex angle was therefore found to be 90°.

With the apex held constant at 90°, different hole counts were investigated. NC No. 1 was unable to atomise the liquid and resulted in the production of fibre. NC No. 2 allowed for adequate atomisation, while NC No. 4 provided better results. A small $s/d_G$ ratio therefore seemed preferable at first; however, this was counterbalanced by the inability to resist decreasing gas velocity down to the gas jet core due to the decreasing air jet diameter as the number of gas jet holes increased. The atomisation quality therefore decreased at some critical $s/d_G$-ratios with decreasing $s/d_G$. The decline in atomisation quality became evident through the formation of large fibrous structures, as demonstrated in Figure 7. This was the case for all tested configurations with $s/d_G$ ratios below 3. The optimal nozzle configuration (ONC) was therefore found to be NC No. 4.

3.3. Droplet Velocity

The averaged droplet velocity as well as the corresponding standard deviation were determined for NC No. 4, as explained in Section 2.3. The measurement points and the corresponding results are specified by

Table 5. Spray velocity measurements at recording positions (AX) for liquid viscosity ${\eta }_L^0=12.3\mathrm{Pa}\mathrm{s}$.

NC	MP	AX m × 103	ALR -	Avg. Velocity ms−1	Std. Velocity ms−1
No. 4	1	100 (12.5 × $d_L$)	12,286	86.2	29.6
No. 4	2	500 (62.5 × $d_L$)	12,286	71.1	24.3
No. 4	3	700 (87.5 × $d_L$)	12,286	61.3	24.6
No. 4	4	1050 (131.25 × $d_L$)	12,286	14.8	6.8

. Figure 8 gives a graphical representation of those measurement points (MP). A quadratic interpolation was fitted into the first three evaluated MPs.

A liquid velocity of 24.9% of the sonic gas velocity was determined at MP 1. We attempted to analyse the droplet distribution at MP 1 with the Sony RX10M3; however, this resulted in the capture of motion blurred droplets.

A significant deviation between the interpolated averaged droplet velocity and measured droplet velocity is found at MP 4. This suggests a strong deceleration at ground level, as the air velocity at the liquid surface must be zero due to the no slip condition. Given the comparatively low droplet velocities at MP 4, this position was selected as the primary measurement point for evaluating droplet size distributions.

3.4. ALR

Table 6. Calculated gas flow properties at gas nozzle exit for measured ${\dot{V}}_G$ and $T_A$.

NC	${\dot{\mathit{V}}}_{\mathit{G}}\times {10}^3$ std m3/s	${\mathit{T}}_{\mathit{A}}$ K	Ma -	$\mathit{p}\times {10}^{-5}$ Pa
No. 4	52.78	298	0.9	1
No. 4	105.56	288	1.0	1.8

shows two gas flow rates used in Figure 6, for which the following physical properties were calculated. Although the Mach numbers and gas velocities at the nozzle exit show minimal variation across different gas volume flows for the given NC, a significant discrepancy is predicted in the gas pressure at the gas nozzle exit based on calculations regarding standard thermodynamic law for isentropic flows.

Subsequently, we varied the liquid flow rate while the volume gas flow rate was held constant at 105.56 × 10⁻³ Nm³s⁻¹. High-speed image recordings at varying liquid flow rates were analysed to minimise the formation of fibre-like droplets. The videos were shot 100 × 10⁻³ m (upper images) and 1050 × 10⁻³ m (lower images) below the nozzle exit, or $12.5\times d_L$ and $131.25\times d_L$, respectively. Example images are shown in Figure 9. At $12.5\times d_L$, fibre-like structures are found for all investigated mass flow rates. At $131.25\times d_L$, however, the number of captured fibre-like structures decreased noticeably with decreased liquid mass flow rate. It was found that a liquid mass flow rate above 16 × 10⁻³ kg s⁻¹ led to an increased production of fibrous droplets with equivalent diameters above 1 × 10⁻³ m. Liquid flow rates of 16 × 10⁻³ kg s⁻¹ or below ensured that the amount of produced fibre was kept sufficiently low, and, therefore, a minimum ALR of 6856 was determined for a corresponding zero-shear viscosity of 12.3 $\mathrm{Pa}$ $\mathrm{s}$.

3.5. Atomisation Quality

The atomisation quality of NC No. 4 was evaluated by the determination of the Sauter mean diameter and cumulative droplet size distribution. Figure 10 illustrates the cumulative droplet size distribution at the measurement positions MP 2 and MP 4 and the corresponding process parameters and Sauter mean diameters are obtained from

Table 7. Droplet size distributions for NC No. 4 categorised by dataset (DS) 0 and 1.

DS	NC	AX m	${\mathit{\eta }}_{\mathit{L}}^0$ Pa s	ALR -	${\dot{\mathit{m}}}_{\mathit{L}}\times {10}^3$ kgs−1	${\mathit{d}}_{32}$ × ${10}^6$ m
0	4	62.5 × $d_L$	12.3	12,286	8.33	367
1	4	131.25 × $d_L$	12.3	12,286	8.33	259

. Based on the data in Table 7, secondary atomisation had not fully progressed at $AX=62.5\times d_L$, as reflected by a further reduction in SMD at $AX=131.25\times d_L$.

Table 8. Sauter mean diameter and corresponding operating conditions.

DS	NC	AX m	${\mathit{\eta }}_{\mathit{L}}^0$ Pa s	ALR -	${\dot{\mathit{m}}}_{\mathit{L}}$ × ${10}^3$ kgs−1	${\mathit{d}}_{32}$ × ${10}^6$ m
0	4	62.5 × $d_L$	12.3	12,286	8.33	367
1	4	131.25 × $d_L$	12.3	12,286	8.33	259
2	4	131.25 × $d_L$	16.7	20,477	5.00	343
3	4	131.25 × $d_L$	15.9	11,376	9.00	372
4	4	131.25 × $d_L$	15.9	8532	12.00	570

lists the operating conditions for the liquid mass flow rate and viscosity variations and the corresponding droplet size distributions are illustrated in Figure 11. Liquid mass flow was increased from Dataset 2 to 4. At constant viscosity and AX, decreasing the ALR resulted in higher SMD values and coarser droplet size distributions.

The results in Table 7 and Table 8, along with Figure 10 and Figure 11, highlighted the influence of key operating parameters—namely, axial distance AX, air-to-liquid ratio ALR, liquid viscosity ${\eta }_L^0$, and mass flow rate ${\dot{m}}_L$ on atomisation performance, as quantified by the Sauter mean diameter $d_{32}$.

A qualitative sensitivity analysis suggests that ALR exerts the strongest influence on droplet size. For example, comparing Datasets 3 and 4 in Table 8, a reduction of ALR from 11,376 to 8532, by increasing ${\dot{m}}_L$ from 9.00 to 12.00 g/s at constant ${\dot{V}}_G$, lead to an increase in $d_{32}$ from 372 × 10⁻⁶ m to 570 × 10⁻⁶ m, indicating a strong sensitivity of droplet size to the air-to-liquid ratio. A further observation concerns the broad droplet size distribution produced by the ONC, potentially limiting its applicability in processes that demand narrow spray spectra, as shown in Figure 11.

In contrast, changes in viscosity at relatively high ALR (cf. Datasets 1 and 3, Table 8) showed a less pronounced effect: an increased ${\eta }_L^0$ from 12.3 $\mathrm{Pa}$ $\mathrm{s}$ to 15.9 $\mathrm{Pa}$ $\mathrm{s}$ resulted in a rise in $d_{32}$ from 259 × 10⁻⁶ m to 373 × 10⁻⁶ m. While high viscosity inhibits atomisation by dampening fluid instability waves, the overall effect appeared less pronounced than expected. As shown in a study of PDMS AK 1,000,000 [41], viscosity is strongly dependent on both temperature and shear rate. Under high shear, the viscosity differences between differently tempered silicone oils, however, decrease, resulting in reduced impact on the atomisation outcome. Comparable data for Wacker AK 10,000 are, to the best of the authors’ knowledge, not available; however, a similar qualitative behaviour may be expected due to the analogous polymeric structure of the fluid.

In addition, the axial measurement position influenced the observed SMD. As shown in Figure 10, a downstream shift from $AX=62.5\times d_L$ to $AX=131.25\times d_L$ resulted in a notable reduction in droplet size, indicating continued secondary atomisation. An extended breakup distance was expected for high-viscosity liquids, as an elevated Ohnesorge number has been shown to delay the onset of liquid column deformation and ligament breakup [42]. High-viscosity liquids were typically characterised by Oh > 1 [21]. The surrogate fluid used in this study, Wacker AK 10,000, exhibits an Oh number exceeding 19 under an estimated local shear rate of 50,000 s⁻¹ in the near-nozzle region (see Table 1). Further downstream measurements could have revealed a continued decrease in SMD; however, such investigations were not feasible due to vertical space limitations in the test facility. Interestingly, a downstream distance of 0.35$\mathrm{m}$ was selected as the measurement zone in a previous study [14], corresponding to the ignition zone of CWS with viscosities of 0.8 $\mathrm{Pa}$ $\mathrm{s}$ to 0.9 $\mathrm{Pa}$ $\mathrm{s}$. The observation implies for CWS with viscosities in the range of 0.8 $\mathrm{Pa}$ $\mathrm{s}$ to 0.9 $\mathrm{Pa}$ $\mathrm{s}$ that secondary atomisation had sufficiently progressed by that point. In contrast, the delayed droplet break up observed in the present study is consistent with the higher viscosity and Oh number of the fluid. Secondary atomisation was found to progress notably between the measurement positions at 0.5$\mathrm{m}$ and 1.05$\mathrm{m}$ downstream.

It is worth noting that stable atomisation was consistently achieved across ambient temperatures, ranging from approximately 0 °C (winter conditions) to 25 °C (summer conditions), suggesting a certain degree of operational redundancy with respect to external environmental factors. The robustness was further confirmed by the fact that repeatable atomisation could be achieved in all trials using the ONC.

Several aspects, however, remain unresolved and merit further investigation. The influence of varying characteristic atomiser distances, in particular the liquid impingement distance (IDL) and the gas impingement distance (IDG), on droplet size distribution has not yet been evaluated. IDL and IDG are expected to impact droplet size distribution due to altered velocity gradients. Moreover, the present study was limited to sonic gas velocities. It remains an open question how supersonic gas flow conditions would alter the atomisation performance. Overall, the ONC configuration demonstrates promising atomisation characteristics. Broader validation, however, is required to enable its practical implementation in resource recovery applications. One of the primary limitations lies in the scalability and adaptability of the nozzle to real high-viscosity sludges, given their stronger fouling tendencies, compositional heterogeneity, and higher solids content. Ensuring long-term operational stability, resistance to clogging, and easy maintenance under industrial conditions represents a key technical challenge that needs to be addressed in future studies. The shadow photography method used in this study was subject to limitations due to the rapid contamination of the acrylic glass containment by droplets, necessitating cleaning after each trial. As a result, only a limited number of droplets could be captured per run. Incorporating advanced diagnostic tools such as Phase Doppler anemometry could provide more accurate measurements of droplet size and velocity distributions; however, the test rig would require modification to accommodate Phase Doppler anemometry measurements.

4. Conclusions

The twin fluid atomisation of silicone oil, mimicking a specific target sewage sludge, was studied. The investigated single-stage, free-fall atomiser configurations did not produce atomisation due to flow instabilities that deflected the high-viscosity liquid stream prior to reaching the designed impingement location. In such a design, a method to stabilise the free-falling liquid must be identified.

Two-step atomisation, as shown in [36], may present a promising solution to this problem. Testing a two-stage free-falling nozzle design, however, was not feasible due to the geometrical constraints of the current nozzle design. This limitation arose from the excessive radial distance between the vertical gas streams ($\theta$ = 0°) and the coaxially flowing liquid. A nozzle insert was introduced into the atomiser to mitigate the encountered issues.

It turned out that relatively few, but large-diameter, discrete gas nozzle holes achieved the best atomisation results for the investigated atomiser design. This behaviour is attributed to larger-diameter free jets retaining their kinetic energy over extended distances (IDG) along the jet core. The gas velocity is therefore maintained at a maximum within the jet core. It was found that at least four discrete and equally distant gas jet orifices were necessary to enable atomisation. An atomiser design comprising six discrete and equally distant gas orifices, each 6 × 10⁻³ m in diameter, was identified as optimal (ONC).

Ambient temperature fluctuations caused variations in the viscosity of the surrogate liquid. A minimum feasible ALR of 8532 was determined for the ONC at a zero-shear viscosity of 15.9 $\mathrm{Pa}$ $\mathrm{s}$, corresponding to a SMD of 570 × 10⁻⁶ m. ALR was found to depend on the viscosity: an increase from 15.9 $\mathrm{Pa}$ $\mathrm{s}$ to 16.7 $\mathrm{Pa}$ $\mathrm{s}$ led to an ALR rise from 11,376 to 20,477 in order to achieve comparable SMD values.

This study aimed to investigate the feasibility of atomising high-viscosity, shear-thinning sewage sludge by employing a surrogate with comparable properties. Atomisation efficiency was found to improve through the optimisation of the orifice arrangement and apex angle. The findings contribute to the optimisation of atomiser designs for high-viscosity fluids exhibiting comparable characteristics to the surrogate, as encountered in a wide range of resource recovery applications. This is particularly relevant, since conventional nozzle designs are based on low-viscosity atomisation, which may limit their efficient applicability to high-viscosity fluids. The ONC demonstrated atomisation for silicone oil with a zero-shear viscosity of 10 $\mathrm{Pa}$ $\mathrm{s}$ at 25 °C, a result not previously reported in the literature, highlighting the potential of this design for challenging fluids.

Nevertheless, several challenges remain before industrial application can be realised. These include scalability to real sludges with more complex composition and fouling tendencies, as well as ensuring long-term operational stability. Another challenge lies in the broad droplet size distribution observed with the ONC, limiting its applicability in scenarios demanding uniform spray characteristics. Future work should address the influence of characteristic atomiser dimensions (IDL, IDG) and explore atomisation under supersonic gas flows. Improved diagnostics such as Phase Doppler anemometry are additionally recommended to enhance droplet characterisation.