Complete breakup of liquids into ultrafine droplets by grid turbulence

doi:10.21203/rs.3.rs-3873446/v1

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Complete breakup of liquids into ultrafine droplets by grid turbulence

https://doi.org/10.21203/rs.3.rs-3873446/v1

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Ultrafine droplets play an important role in materials processing and nanotechnology, with crucial applications in nanoparticle preparation, molecular spraying, water evaporation, nanodrug delivery, nano-printing/coating, among numerous others. While the potential of turbulent gas flow to enhance liquid breakup is acknowledged, the construction of turbulence-driven atomizers for generating ultrafine droplets remains a significant challenge. Herein, we report the innovation of grid-turbulence atomization (GTA), which employed a rotating mesh to deliver liquid and an air knife to spray ultrafine droplets. The airflow across the mesh transitions from laminar to grid-turbulence, leading to complete liquid breakup with three-stages: bag formation, stretching, and turbulence-induced breakup. Ultrafine water droplets with a 4.8 µm Sauter mean diameter have been achieved through GTA. The GTA system demonstrates versatility in atomizing various liquids including those with high viscosities of ~ 1000 cP. We further achieved high-quality production of ultrafine powders including milk, coffee, sugar, polymers, and ceramics, based on the combination of GTA and spray-drying. Our strategic methodology establishes pivotal link between turbulence characteristics and materials processing, influencing a wide range of applications and sparking further innovation in the field.

Physical sciences/Materials science/Nanoscale materials

Physical sciences/Chemistry/Chemical engineering

Liquid atomization holds fundamental importance as a cornerstone for various scientific and industrial processes. This phenomenon has been extensively studied not only for its direct applications but also for its potential to enhance the efficiency and effectiveness of diverse processes, including fuel combustion¹, disinfectant and pesticide spraying^2,3, drug delivery^4–6, environmental humidification and purification^7,8, seawater desalination⁹, cooling¹⁰, and food industry¹¹, among many others. Specifically, the significance and importance of liquid atomization are pronounced in the realm of material processing and nanotechnology. Completely breaking up bulk liquid into ultrafine droplets is especially critical in this domain, playing a vital role in the production of nano-medicine, aerosol and nanomaterials using methods such as spray drying¹², spray pyrolysis¹³, molecular coating¹⁴, water microdroplet chemistry¹⁵, and nanoscale printing¹⁶. In these sophisticated applications, the size of liquid droplets is paramount, and minimizing liquid droplet size has long been recognized as a critical goal. Consequently, given the important role that ultrafine droplets play in diverse materials processing and nanotechnology contexts, effectively breaking up bulk liquid into such ultrafine droplets poses a significant scientific challenge that calls for innovative solution.

Current industrial liquid atomization is commonly achieved through the use of high-speed airflow; such process involves complex interactions between gas and liquid flow. The fundamental understanding of this gas-liquid interaction has been a persistent research focus, encompassing both substantial scientific challenges and practical implications that extend across scales ranging from the complexities of the global water cycle to the intricate atomization processes^17–22. A prominent illustration of the gas-liquid interactions is found in the widely applied technique of pneumatic two-fluid nozzle atomization. This method harnesses high-speed airflow to efficiently break up liquids. Owing to its straightforward design, rapid operational speed, and ability to atomize high-temperature liquids, including molten metals, this technology has achieved considerable success in various engineering applications. Its simplicity, combined with versatility and efficiency, especially in handling challenging materials, positions it as a cornerstone technology in these fields^23–25. However, two-fluid nozzle atomization provides limited shear force to break up the bulk liquid and typically yields droplets ranging from tens to hundreds of micrometers^23,26. The spraying of sub-10-µm droplets, crucial in applications such as aerosol medications due to their high surface area-to-volume ratio as well as superior penetration and dispersion, remains challenging using conventional two-fluid nozzle atomization. Ultrasonic atomization has been applied to generate ultrafine droplets with sizes down to a few micrometers, but it often struggles with atomizing liquids of high viscosity. Moreover, the relatively low flow rate and high operating cost of ultrasonic atomization hinder its broad industrial adoption^27–29. Electrostatic spraying has also been developed to generate mists but is contingent upon the use of liquids that have appropriate conductivity and/or low viscosity, and it tends to provide very limited processing efficiency^29–31. The absence of a versatile method capable of producing high-quality, ultrafine droplets is a notable limitation in both fundamental science and practical applications. Consequently, development of new strategies for high-performance atomization assumes critical importance. This endeavor becomes particularly significant in the context of traditional pneumatic two-fluid atomization. Reforming and enhancing this established method to consistently generate sub-10-µm ultrafine droplets would not only be a remarkable technological breakthrough but also a major leap forward in meeting the advanced needs of various industrial processes.

The physics of turbulence and the interactions between turbulent gas and liquid droplets have been intensively studied as one of the most challenging and valuable research topics in both science and engineering³². During the global COVID-19 pandemic, scientists conducted urgent research on how coughing and sneezing spread viruses, revealing that the effect strongly depends on the turbulent flow dynamics of human airflows. Bourouiba et al. reported experimental observations and the physical mechanisms of ultrafine droplet formation during sneezing³³. It was found that sneezes feature turbulent multiphase flows that may contain pathogen-bearing droplets of mucosal fluid (Fig. 1a). During sneezing, air expelled at high velocity can fragment mucus and saliva into tiny droplets laden with solid or semi-solid particles. These droplets evaporate swiftly in the turbulent setting, quickly morphing into aerosols that can travel considerable distances^33–36. This effect is particularly pronounced when wearing a mask, as the “thin meshes” play a significant role in reducing the size of saliva droplets³⁷. Although the “sneezing” itself may not generate ultrafine droplets in a uniform, continuous, and stable manner, this phenomenon provides insightful observations into its scientific mechanisms, suggesting that gas turbulence could be a fundamental factor in facilitating the process of ultrafine atomization. This correlation opens up potential avenues for research, where the dynamics observed in natural processes like sneezing could inform and inspire innovative approaches in atomization technology, particularly in achieving ultrafine droplet production.

Herein, we were inspired by “sneezing” and its mechanisms to establish a grid-turbulence atomization (GTA) system for rapid and ultrafine liquid spraying. In general, the breakup of droplets in high-speed airflow is predominantly governed by the Weber number (We), which represents the ratio of fluid inertial forces to the surface tension forces of the droplets. The Weber number is defined as $\:We={\rho\:}_{g}{U}^{2}D/\sigma\:\:,$where $\:{\rho\:}_{g}$ is air density, U is the slip velocity between droplet and flow, D is the droplet size and $\:\sigma\:$ is the interfacial tension. As Weber number increases, the droplets undergo various breakup regimes³⁸: deformation and flattening (We < 12), bag breakup (12 < We < 80), boundary layer or “shear” breakup (We > 80), stretching and thinning breakup (80 < We < 350) and catastrophic breakup (We > 350). Theses regimes depend on the slip velocity and the droplet size. To accelerate the breakup of the droplets into ultrafine size, we designed and constructed a rapid rotating metal mesh to continuously deliver liquid that is sprayed out with a vertically blown grid-turbulence airflow, where the initial droplet size is constrained by the mesh size, resulting in a corresponding Weber number around O(10). The GTA setup initiates a bag formation process near the mesh. As the airflow continues to act on the liquid, the thin hollow bags begin to deform and stretch into elongated liquid threads. Additionally, the grid-induced turbulence further breaks up the droplets larger than the Kolmogorov scale, in accordance with Kolmogorov-Hinze theory^39,40. Due to the high-speed airflow through the mesh holes and the intense grid-induced turbulent flows, the droplets experience three typical stages of breakup: bag formation, stretching, and turbulence-induced breakup. Under this three-stage breakup mechanism, we demonstrated that GTA can be applied as a generalized strategy for effective atomization of liquids, achieving water droplets with a Sauter mean diameter (SMD) of 4.8 µm. Beyond water, high-viscosity liquids such as olive oil, lubricating oil, and methyl silicone oil (with a viscosity of 990.0 cP) can be atomized by GTA. This capability holds particular importance in fields such as heavy oil atomization for combustion processes and inkjet printing technology. In these areas, the precision in droplet control is not just a matter of enhanced efficiency but also crucial for maintaining high-quality outcomes. The ability to accurately manage droplet size and distribution is key to optimizing performance in these applications, thereby underscoring the importance of advanced atomization technologies. As a result of the high-quality solution spray through GTA, we successfully manufactured ultrafine and uniform powders including milk, coffee, sugar, polymers and ceramics by spray-drying. The GTA system exemplifies a sophisticated interplay between turbulent gas and liquids, achieving high-quality two-fluid atomization.

Grid turbulence is a specific type of turbulence generated when fluid flows pass through a grid or a mesh-like solid structure (lower Fig. 1a). It serves as a classic prototype for deepening our understanding of turbulence physics due to its reproducibility and simplicity^41,42. In this study, we designed a GTA system that combines grid turbulence with intensive liquid spraying, utilizing a continuously rotating mesh which carries liquid for rapid atomization (Fig. 1b, c and Supplementary Videos 1 and 2). The system consisted of a mesh fixed to a rotating shaft, a vessel containing liquid, and an air knife set above the mesh to provide high-speed gas blowing vertically.

Firstly, a slit in the bottom of the vessel allowed the liquid to flow out of it and be continuously and uniformly separated into the mesh cells as the mesh rotated (Fig. 1b, c). With such rotating grid system, before effective atomization, bulk liquids were separated and filled into grid cells of the mesh (Fig. 1d). Secondly, the liquid was subsequently ejected from each mesh cell by a high-speed airflow provided by a vertically oriented air knife, forming a mist of microdroplets that vibrated and moved at exceedingly high speeds and frequencies. A clear and uniform Tyndall phenomenon could be observed during the process, indicating a stable and ultrafine liquid spray (Fig. 1c and Supplementary Videos 2 and 3). To ensure full utilization of the airflow's speed and energy while avoiding significant resistance to the mesh rotation, the air knife was positioned very close to the mesh (typically ~ 1 millimeters) without making direct contact.

In the GTA process, the effective separation and filling of bulk liquids into the mesh grid cells are critically dependent on the wettability of the liquid on the mesh. This wettability is influenced by both the type of liquid and the material of the mesh. The meshes employed here were commercially available and economical, typically priced at ~ 3 US dollars per piece (7.5-inch size), showcasing the cost-effectiveness of the GTA system. Additionally, the GTA system offers extensive flexibility in terms of both mesh count and material, including but not limited to nylon, copper, and stainless steel, making the system highly adaptable for handling various liquids with different wetting properties (Fig. 1e and Supplementary Fig. 1). We tested the wettability of different liquids on stainless steel meshes (Supplementary Fig. 2) and the wettability of water on various material substrates (Supplementary Fig. 3). Liquids with good wettability tend to spread more easily on the mesh and infiltrate the mesh pores, which facilitates efficient atomization. For liquids with relatively poor wettability, to ensure rapid and even spreading on the mesh while it is rotating quickly, we placed the vessel containing the liquid adjacent to the mesh (typically ~ 1 millimeters). This setup not only supplied the liquid but also served as a scraper, effectively assisting in the application and distribution of the liquid across the mesh. This versatility, combined with the system's simplicity and financial practicality, underscores its utility in a diverse array of applications.

To demonstrate the universality of the GTA strategy, we sprayed various kinds of liquids, including water (H₂O), 3 wt% hydrogen peroxide in water (3 wt% H₂O₂), ethanol, isopropanol, kerosene, crude oil, ethylene glycol, peanut oil, olive oil, lubricating oil, and methyl silicone oil (Fig. 1f and Supplementary Fig. 4). The high-speed camera results showed that the atomization process for all liquids was stable. All liquids were ejected from the mesh by the gas flow, forming a mist followed by high-speed oscillations of the microdroplets (Supplementary Video 4). A notable aspect of our study is the broad range of liquid viscosities we successfully atomized, ranging from ~ 1–1000 cP (Supplementary Table 1 and Supplementary Video 5). This demonstrates the applicability of the GTA system in various scenarios, especially in critical areas such as fuel combustion. This versatility stands out, particularly when compared to a conventional ultrasonic atomizer equipped with a 1.7 MHz ultrasonic chip, which struggled with these higher-viscosity liquids (Supplementary Fig. 5 and Supplementary Table 1).

To better understand the mechanisms involved in liquid fragmentation and facilitate the production of ultrafine droplets, it is first very important to understand the formation of turbulent gas flow in our GTA system. High-fidelity computational fluid dynamics (CFD) simulations (see the “Computational fluid dynamics (CFD) simulations” section in the Methods and Supplementary Fig. 6) vividly illustrated the evolution of grid-generated turbulence as airflow progresses downstream of a grid. As the gas flow encounters the grid, the flow velocity field is significantly disturbed because of the obstacle of the grid. The flow forms a strong shear layer near the grid and produces shedding vortices immediately downstream of the grid. These vortices interact and break up into smaller scales, inducing a flow transition from laminar to turbulent as it moves downstream and forming homogeneous, isotropic turbulence (Fig. 2a, Supplementary Fig. 7a and Supplementary Video 6).

The simulation results were also found to be quantitatively consistent with experimental flow visualization using a smoke-wire system (Fig. 2b, Supplementary Fig. 7b and Supplementary Video 7. The details of flow visualization are provided in the “Flow Visualization” section in the Methods and Supplementary Fig. 8). The smoke streak lines, which visualized the flow process, showed that the original laminar flow began to destabilize after passing through the mesh, forming vortices that then broke down into smaller-scale turbulent eddies.

The turbulence intensity along the streamwise direction initially increased, indicating the augmentation of turbulence, and then gradually decayed, reflecting the decay of turbulence (the upper panel of Fig. 2c and the “Turbulence Intensity and Anisotropy” section in the Methods). As the mesh count increased, the distance from the meshes to the peak of turbulence intensity became shorter, and the turbulence decayed faster. This demonstrates the evolution of grid turbulence produced with different mesh counts. In the vorticity contour map with mesh of 150 counts, the flow field visibly became more chaotic at 0.5 mm distance from the edge of the mesh compared with meshes of 30 and 60 counts, indicating an earlier onset of turbulence (Fig. 2d and Supplementary Fig. 9). Meanwhile, the grid turbulence became isotropic before the turbulence intensity reached the peak (the lower panel of Fig. 2c and the “Turbulence Intensity and Anisotropy” section in the Methods). The isotropic turbulence has been found to promote heat and mass transfer, increasing the evaporation rate of droplets⁴³. As a comparison, the smoke streak lines still maintained uniform and straight indicating the laminar flow, when we removed the mesh from the sieve (Fig. 2e).

With such grid-turbulence flow field, we propose that the liquid underwent a three-stage process to achieve ultrafine atomization during GTA: bag formation, stretching, and turbulence-induced breakup. We used the Volume of Fluid (VOF) method to validate this process (the “Volume of Fluid (VOF) method” section in the Methods). First, during the early development of grid-generated turbulence, the high-speed airflow blew out from the grid, creating a significant velocity difference from the liquid spreading in the mesh cells. Such a velocity difference leads to the formation of thin, hollow liquid bags connected to the edge of the original droplets in the mesh cells (Fig. 3a). Correspondingly, the formation of these bags was observed experimentally using the high-speed camera (Fig. 3b and Supplementary Video 8).

Second, as the airflow continues to act on the liquid, the thin hollow bags begin to deform and stretch into elongated liquid threads. The VOF simulations demonstrated this stretching phase, where the liquid threads are pulled into long, thin filaments by the aerodynamic forces. During this stage, the liquid remains continuous and does not break into droplets (Fig. 3c).

Third, once droplets entered the turbulence region, they underwent turbulence-induced breakup (Fig. 3d). At this stage, the flow field evolved into turbulence after experiencing instability, resulting in multi-scale vortices. We employed the Q criterion (see the “Q criterion” in the Methods), which reflects the difference between the magnitudes of the fluid vorticity and strain rate to identify the vortices. The contours of pressure fluctuations and Q show that the generation of vortices was accompanied by pressure fluctuations (Fig. 3e). Lower pressure usually occurred in vorticity-dominant regions (Q > 0), whereas higher pressure typically arose in strain-dominant regions (Q < 0). Liquid droplets tended to concentrate in the strain-dominant regions due to the centrifugal effect (Supplementary Fig. 10 and Supplementary Video 9). These areas exhibited high pressure and strong stretching, leading to the breakup of droplets^44,45. Additionally, as turbulence evolved, large vortex structures disintegrated into finer vortices, with their energy cascading down to smaller scales. This process continued until reaching the dissipation scale, where the kinetic energy was ultimately dissipated (Fig. 3f)⁴⁶. This process forms multi-scale distribution of vortices from the large scale to the dissipation scale. Previous studies have shown that small droplets are influenced by these multi-scale vortices, resulting in their fragmentation into smaller droplets, following the Kolmogorov-Hinze (KH) theory^47,48. KH theory is the cornerstone of small droplet break up in turbulence, and identifies a Hinze scale to estimate the maximum droplet size for which the surface tension forces of the droplet can resist pressure fluctuations from turbulence^40,46. Based on the KH theory, the Hinze scale decreases with the increasing dissipation rate of turbulence, indicating that turbulence augmentation leads to forming finer droplets (Supplementary Note 1).

In a concise overview of the liquid atomization mechanism, the airflow passing through the mesh initiates a high-speed zone, resulting in the formation of thin, hollow liquid bags. The continued interaction with the liquid film causes these hollow bags to deform and stretch into elongated liquid threads. As the airflow progresses, it undergoes a gradual transition into turbulence, giving rise to vortices of varying scales with fluctuations in physical quantities. These turbulent conditions exert stress on the droplet surface, leading to further droplet breakup.

Taking advantages of the three-stage breakup mechanism, the GTA method proved highly effective in achieving superior atomization quality. The resulting water spray from the GTA method displayed a uniform particle size distribution, with the Sauter mean diameter (SMD) reaching 4.8 µm (Fig. 3g, measured using laser diffraction analysis, see the “Spray particle size measurement” section in the Methods). This closely rivals the particle sizes attained by commercial ultrasonic atomization, for which we tested frequencies of 1.7 MHz, 2.4 MHz, and 3.0 MHz, with the smallest droplet size achieved being 6.28 ± 0.25 µm at 3.0 MHz (Supplementary Fig. 11). The GTA method also demonstrated remarkable atomization effectiveness across various liquids, achieving droplet sizes with a SMD of around 3.9 µm for ethanol, kerosene, and isopropanol (Fig. 3h and Supplementary Fig. 12). Additionally, the GTA method showcased its capability for ultrafine atomization of a range of high-viscosity liquids, as demonstrated in the atomization of glycerol and water mixtures with varying ratios (Fig. 3i). These liquids have similar surface tensions but significantly different viscosities (Supplementary Table 2). The droplet diameters remained consistently fine across different viscosities, which is challenging for ultrasonic atomization²⁹. These results underscore that grid turbulence substantially augments gas-liquid interactions, thereby facilitating finer atomization.

Liquid atomization, as a method for fluid disintegration, has been widely employed in various industrial applications, including spray drying, coating, incineration, emulsion preparation, and medical devices.

Spray drying has been widely applied in industrial processing to fabricate uniform, spherical, and low-cost powder particles composed of a wide array of materials from polymers to ceramics⁴⁹. Based on the development of GTA strategy, we have successfully demonstrated its high-performance application in spray drying for the production of ultrafine powders across various substances, including sugar, coffee, milk, phosphor, NaCl, polyvinyl alcohol (PVA), and tartrazine (Fig. 4a and Supplementary Fig. 13). Additionally, GTA facilitated the production of certain oxides, such as silica, alumina, zirconia, lithium cobalt nickel manganese oxide (LiNi_0.8Co_0.1Mn_0.1O₂) and lithium lanthanum zirconium oxygen (Li₇La₃Zr₂O₁₂), by precursor spray drying followed by sintering (Supplementary Figs. 14–16). All these powders exhibited a uniform morphology and particle size distribution (Fig. 4b and Supplementary Fig. 17), showcasing the GTA method's potential in diverse fields, from food processing to battery material manufacturing. Its formidable capacity for high-quality, ultrafine atomization positions GTA as a versatile and efficient solution across a broad application spectrum.

Additionally, we have demonstrated the superior performance of the GTA method in rapid humidification. Humidity control is critical in both industrial and living environments, with industrial humidification systems playing a vital role in regulating moisture levels and preventing production issues⁵⁰. Comparative humidification experiments revealed that GTA achieves a fast humidification rate, highlighting its promising potential for industrial applications (Supplementary Fig. 18).

In summary, we have developed a highly efficient and nozzle-free GTA strategy that enables fast, uniform and ultrafine atomization of diverse liquids based on the principle of grid turbulence. The elevated airflow velocities and turbulent fluctuations associated with grid turbulence facilitated breakup and atomization of the liquid, promoting the creation of water droplets with an SMD of 4.8 µm. We emphasize the flexibility of the GTA platform, particularly in its capability to atomize a wide range of liquids including those with high viscosity. This adaptability makes the GTA system extensively applicable across various domains. Its versatility in breaking up liquids of different viscosities to product ultrafine droplets not only demonstrates its technical superiority but also expands its potential applications, making it an invaluable tool in industries where precise and efficient atomization of diverse liquids is critical.

The GTA platform significantly enhances the capabilities and applications of atomization technologies. Additionally, our strategic approach in linking turbulence characteristics with flow manipulation, contributing to a deeper understanding of control paradigms within fluid dynamics. This advanced comprehension of turbulent gas-liquid interactions paves the way for a host of prospective developments in practical applications. These include but are not limited to, improved fuel injection systems, more effective disinfection methods for public spaces, and the atomization of molten metal to produce ultrafine metal powders, an essential component in the evolving technology of 3D printing. Each of these applications demonstrates the far-reaching impact and potential of the GTA system in both scientific research and industrial innovation.

High-speed camera observation

A high-speed camera (Os7, IDT Vision, USA) equipped with two F-mount lenses (ATX 16–28 mm and 100 mm, Tokina, Japan) was used for the direct observation of the flow visualization process. A 100 W LED lamp (LED-100-T, Visico, China) was used to continuously illuminate the observed area, which enabled the acquisition of clear images with a short exposure time of the high-speed camera. The high-speed images were captured at different frame rates, including 2700, 4000, and 8000 fps. The analysis of the videos obtained was carried out using the Motion Studio software. All the high-speed videos were played at a frame rate of 30 fps using the images obtained at different frame rates.

Computational fluid dynamics (CFD) simulations

In this study, we examined the transition from a uniform laminar airflow to turbulence induced by a grid structure, a phenomenon pivotal in the breakup of droplets. To accurately replicate this transition, a series of comprehensive three-dimensional direct numerical simulations (DNSs) were conducted. These simulations employed an in-house CFD code, which integrates the finite difference method (FDM) and the immersed boundary method (IBM), as detailed in previous works^51,52. The computational model and domain are illustrated in Supplementary Fig. 4, where D is the separation between wire centerlines, s denotes the distance from the inlet to the central plane of the grid structure, L is the streamwise domain length, and W and H specify the width and the height of the computational domain, respectively.

In the present study, the velocity range of interest for the airflow is considerably below the speed of sound. Consequently, the airflow dynamics are governed by incompressible and isothermal Naiver-Stokes equations as follows,

$$\:\begin{array}{c}\frac{\partial\:\varvec{u}}{\partial\:\text{t}}+\left(\varvec{u}\cdot\:\nabla\:\right)u=-\frac{1}{{\rho\:}_{f}}\nabla\:p+\nu\:{\nabla\:}^{2}u+f \left(1\right)\end{array}$$

$$\:\begin{array}{c}\nabla\:\cdot\:u=0\:. \left(2\right)\end{array}$$

Here, $\:\varvec{u}$ is the velocity of airflow, $\:{\rho\:}_{f}$ represents the density of air, p is the pressure, $\:\nu\:$ is the kinematic viscosity of air, and $\:\varvec{f}$ encapsulates the additional forces exerted on the fluid by the grid structure.

To model the effect of the grid structure within the airflow, IBM was utilized to model the boundary of the grid structure. The surface of the grid structure was discretized into a uniform grid, with the discretization points denoted as X, located on the fixed boundary of the grid structure. Concurrently, a set of immersed boundaries (IB) points $\:{\varvec{X}}_{ib}$ were employed to passively trace the flow, originating from the locations at X. To constraint IB points $\:{\varvec{X}}_{ib}$ to the fixed points X, a weak coupling scheme was imposed by exerting IB forces $\:{\varvec{F}}_{L}$on the surface of the grid structure, as expressed in the following equation,

$$\:\begin{array}{c}{\varvec{F}}_{L}=-\gamma\:\left[{\int\:}_{0}^{t}\left({\varvec{U}}_{ib}-\varvec{U}\right)dt+{\Delta\:}t\left({\varvec{U}}_{ib}-\varvec{U}\right)\right], \left(3\right)\end{array}$$

where $\:\gamma\:$ is a large constant, $\:\varDelta\:t$ is the time interval of the simulation, $\:{\varvec{U}}_{ib}$ and $\:\varvec{U}$ represent velocities of IB points $\:{\varvec{X}}_{ib}$ and fixed points $\:\varvec{X}$ on boundary, respectively. Note that $\:\varvec{U}$ is set to zero during computation adhering to the no-slip velocity condition at the boundary, while $\:{\varvec{U}}_{ib}$ is computed by interpolating the local fluid velocity from adjacent Eulerian grid points $\:\varvec{x}$, as follows,

$$\:\begin{array}{c}{\varvec{U}}_{ib}=\sum\:u{\delta\:}_{h}\left(\varvec{X}-\varvec{x}\right)\varDelta\:V. \left(4\right)\end{array}$$

Here, u represents the fluid velocity at the Eulerian grid points x. The term $\:\varDelta\:V={h}^{3}$ represents the volume of each grid cell, where h is the cell size. Note that the Cartesian grids encompassing the surface of grid structure are uniformly sized with h in all three spatial directions. Furthermore, the delta function $\:{\delta\:}_{h}$ is formulated as

$$\:\begin{array}{c}{{\delta\:}}_{\text{h}}\left(x\right)=\frac{1}{{h}^{3}}\varphi\:\left(\frac{x}{h}\right)\varphi\:\left(\frac{y}{h}\right)\varphi\:\left(\frac{z}{h}\right), \left(5\right)\end{array}$$

where

$$\:\begin{array}{c}\varphi\:\left(r\right)=\left\{\begin{array}{c}\frac{1}{8}\left(3-2\left|r\right|+\sqrt{1+4\left|r\right|-4{r}^{2}}\right),\:\:\:\:\:\:\:0\le\:\left|r\right|<1,\\\:\frac{1}{8}\left(5-2\left|r\right|-\sqrt{-7+12\left|r\right|-4{r}^{2}}\right),\:1\le\:\left|r\right|<2,\\\:0,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:2\le\:\left|r\right|\end{array}\right. \left(6\right)\end{array}$$

denotes a four-point smoothed delta function⁵³.

Similarly, $\:\varvec{f}$ at the Eulerian grids is derived by interpolating the forces $\:{\varvec{F}}_{L}$ exerted on the surface of the grid structure, i.e.,

$$\:\begin{array}{c}f=\sum\:{\varvec{F}}_{L}{{\delta\:}}_{\text{h}}\left(\varvec{x}-\varvec{X}\right)\varDelta\:V \:\left(7\right)\end{array}$$

For the flow solver, we adopted an implicit velocity decoupling procedure on staggered Cartesian grid system to solve the incompressible Navier-Stokes equations, as delineated by Kim et al⁵⁴. The computational domain of the entire fluid field is set as $\:15D\times\:9D\times\:9D$ for $\:L,W$ and $\:H$, respectively. The characteristic length scale is defined by the distance between the centerlines of nearby wires, with D being 25.4mm divided by the mesh count. The distance between the inlet and the center plane of the grid structure s is equal to D. This study employs a grid resolution of 32 uniform grids per length D, resulting in a total grid number of approximately 40 million. Periodic boundary conditions for velocity and pressure are imposed in both the $\:y$ and z directions. The inlet velocity is uniform, expressed as $\:\varvec{u}={U}_{g}{\varvec{e}}_{x}$, where $\:{U}_{g}$ is the airflow velocity and $\:{\varvec{e}}_{x}$ is the unit vector in the streamwise direction. At the outlet, a convective boundary condition is implemented. The kinematic viscosity of airflow is 1.48$\:\times\:{10}^{-5}{m}^{2}/s$, and the inlet airflow velocity is around 18 m/s. Three different grid structures with mesh counts of 30, 60, and 150 were simulated, yielding Reynolds numbers based on D of $\:Re={U}_{g}D/{\nu\:}_{g}=1100$, 550 and 220, respectively.

Volume of Fluid (VOF) method

The Volume of Fluid (VOF) method⁵⁵ is one of the most commonly used interface capturing methods for simulating multiphase flows due to its mass conserving property, and ease in handling large interfacial deformations. In VOF framework, the different fluid phases interfaces are identified by an indicator fraction, α, which is chosen to be the fluid volume fraction on the Eulerian mesh. The fluid volume fraction α is given by

$$\:\begin{array}{c}\alpha\:=\left\{\begin{array}{c}0,\:\:for\:fluid\:A\\\:0<\alpha\:<1,\:\:mixing\:region\:between\:fluid\:A\:and\:B\:\\\:1,\:\:for\:fluid\:B\end{array}\right. \left(8\right)\end{array}$$

In VOF method, the fluid interface is reconstructed by the above fluid volume fraction, which is advected with the flow. The evolution of fluid volume fraction is modeled by

$$\:\begin{array}{c}\frac{\partial\:\alpha\:}{\partial\:t}+\nabla\:\cdot\:\left(\varvec{u}\alpha\:\right)+\nabla\:\cdot\:\left[\alpha\:\left(1-\alpha\:\right){\varvec{U}}_{r}\right]=0 \left(9\right)\end{array}$$

in which, U_r is the artificial compression velocity on the fluid interface to guarantee the sharpness of the fluid interface⁵⁶.

The effect of the surface tension of the two-phase flow is determined by the Continuum Surface Model (CSF)⁵⁷ in the momentum equation and continuity equation.

$$\:\begin{array}{c}\frac{\partial\:\rho\:\varvec{u}}{\partial\:t}+\nabla\:\cdot\:\left(\rho\:\varvec{u}\varvec{u}\right)=-\nabla\:{p}_{\text{r}\text{g}\text{h}}-\left(\mathbf{g}\cdot\:\mathbf{x}\right)\nabla\:\rho\:+\nabla\:\cdot\:\left[\mu\:\left(\nabla\:\varvec{u}+{\left(\nabla\:\varvec{u}\right)}^{T}\right)\right]+\sigma\:\kappa\:\nabla\:\alpha\: \left(10\right)\end{array}$$

$$\:\begin{array}{c}\nabla\:\cdot\:u=0\:. \left(11\right)\end{array}$$

where ρ and µ are the average density and viscosity weighted by the fluid volume fraction α, respectively. p_rgh is the pressure excluding hydrostatic pressure, g is the gravity acceleration, σ is the surface tension coefficient, and κ is the mean curvature of the fluid interface.

The mathematical models are also utilized to simulate the grid-turbulence atomization proposed in the present study. Moreover, the above multiphase flow model is solved with an open-source CFD platform, i.e., OpenFOAM. The grid structures, mesh resolution, and inlet airflow velocity are the same as those used in single-phase airflow simulation.

Q Criterion

The Q criterion is used to distinguish the vorticity-dominant region (Q > 0) and strain-dominant region (Q < 0). It is defined by the formula,

$$\:\begin{array}{c}Q=\frac{1}{2}\left(Tr\left({\varvec{\varOmega\:}}^{2}\right)-Tr\left({\varvec{S}}^{2}\right)\right), \left(12\right)\end{array}$$

where $\:\varvec{\varOmega\:}$ is the fluid rotation tensor, and expressed as,

$$\:\begin{array}{c}\varOmega\:=\frac{1}{2}\left(\nabla\:\varvec{u}-\nabla\:{\varvec{u}}^{\text{T}}\right), \left(13\right)\end{array}$$

and $\:\varvec{S}$ is the fluid strain-rate tensor as follows,

$$\:\begin{array}{c}S=\frac{1}{2}\left(\nabla\:\varvec{u}+\nabla\:{\varvec{u}}^{\text{T}}\right). \left(14\right)\end{array}$$

Note that $\:\nabla\:\varvec{u}$ is the fluid velocity gradient tensor, $\:Tr(\cdot\:)$ represents an operator of the trace.

Turbulence Intensity and Anisotropy

Turbulence intensity at a given position x is calculated using the following formula,

$$\:\begin{array}{c}I\left(x\right)=\frac{{{u}^{{\prime\:}}\left(x\right)}_{rms}}{⟨U\left(x\right)⟩}. \left(15\right)\end{array}$$

Here, $\:{u}^{{\prime\:}}{\left(x\right)}_{rms}$ represents the root-mean-square of the velocity fluctuations in y-z plane at position x, and $\:⟨U\left(x\right)⟩$ is the ensemble-averaged velocity in y-z plane at the same position x. Note that $\:⟨\cdot\:⟩$ represents the ensemble-averaging in y-z plane.

Turbulence anisotropy $\:\eta\:$ is a measure used to estimate the anisotropy of Reynolds stress in turbulent flows. The Reynolds stress in y-z plane at position x is denoted as $\:⟨{u}_{i}^{{\prime\:}}{u}_{j}{\prime\:}⟩$, where $\:{u}_{i}{\prime\:}$ is the component of fluid velocity fluctuation. The anisotropy factor $\:\eta\:$ is defined as the second invariant of a normalized tensor$\:{b}_{ij}$, which is calculated as,

$$\:\begin{array}{c}{b}_{ij}=\frac{⟨{u}_{i}^{{\prime\:}}{u}_{j}{\prime\:}⟩}{⟨{u}_{k}^{{\prime\:}}{u}_{k}{\prime\:}⟩}-\frac{1}{3}{\delta\:}_{ij}, \left(16\right)\end{array}$$

namely $\:\eta\:={b}_{ij}{b}_{ji}$. When $\:\eta\:$ approaches $\:0$, the Reynolds stress becomes more isotropic, indicating the same statistics of fluid in any direction. Conversely, a higher $\:\eta\:$ indicates a more anisotropic state of Reynolds stress.

Flow Visualization

Flow visualization was realized using a smoke-wire system in a wind tunnel (Supplementary Fig. 6), which is composed of a smoke-wire controller (SW02, Dalian Hanghua Science & Technology Co., Ltd, China), a resistance wire with a diameter of 0.1 mm, a flashlamp, and a digital camera (Canon 850D). In the experiment, paraffin oil was coated on the resistance wire to produce a smoke line under the control of the controller. The smoke line was blown forward in the wind tunnel and captured by the camera. The flashlamp was used to illuminate the flow field. Photographs of the smoke line's trajectory characterized the flow characteristics and vortex dynamics.

Spray Particle Size Measurement

The spray particle sizes, specifically the volume distribution of the droplets, were measured using a spray laser particle size analyzer (PW180-B, Shandong NKT Analytical Instrument Co., Ltd, China). The measuring axial distance was approximately 100 mm. The instrument was able to measure sprays of diverse substances by leveraging a built-in database containing material parameters. Data analysis was conducted using accompanying software provided by the manufacturer.

To determine the average diameter of the droplets, the Sauter Mean Diameter (SMD) was used, calculated using the formula:

$$\:\begin{array}{c}SMD=\frac{\sum\:\left({d}_{i}^{3}{n}_{i}\right)}{\sum\:\left({d}_{i}^{2}{n}_{i}\right)}, \left(17\right)\end{array}$$

where $\:{d}_{i}$ represents the diameter of individual droplets, and $\:{n}_{i}$ is the number of droplets with that diameter.

Evaluation of Humidification Efficiency of the Atomization System

To gauge the efficiency of the atomization system, a humidification experiment was conducted in an enclosed room of dimensions 2m × 3m × 4m (Supplementary Fig. 18a). The ambient humidity was initially reduced to 20% using a dehumidifier. Once this was achieved, the dehumidifier was turned off and the atomization system was activated. A digital hygrometer was employed to monitor and record the rise in humidity in real-time.

Morphology and structure Characterizations

The morphological properties and elementary composition of particles were measured by a field-emission scanning electron microscope (FE-SEM, LEO-1530, Zeiss, Germany) equipped with energy-dispersive X-ray spectroscopy (EDS). The diameter distribution of the particles was measured with a laser particle sizer (Mastersizer 3000, Malvern, UK). Crystal structure of SiO₂, Al₂O₃, ZrO₂, Li₇La₃Zr₂O₁₂, and LiNi_0.8Co_0.1Mn_0.1O₂ powder were determined by XRD (D/Max 2,500, Rigaku, Japan), where the X-ray was Cu-Kα radiation, scanning speed was 5°/min, and the scanning range was 10° − 80°.

Data availability

All relevant data are contained in the manuscript, Supplementary Information, and source data.

Code availability

Custom code used in the study is available from the corresponding authors upon reasonable request.

Acknowledgments

This work was supported by the Basic Science Center Program of the National Natural Science Foundation of China (NSFC) under grant No. 52388201, NSFC under grant No. 52325312, 123881019, 2252104, 92252204, and 12302285, the China Postdoctoral Science Foundation (CPSF) under grant No. 2022M721849, and the Postdoctoral Fellowship Program of CPSF under grant No. GZB20230360.

Author contributions

H.W. conceived the idea and supervised the research. H.W. and Z.W.L. designed the experiments. Z.W.L. and Z.K.C designed and construct the experimental system. L.H.Z., Y.S.L, Z.W.C., and S.J.L. performed the modeling and simulations. Z.W.L., S.Y.Z., Y.H., H.Y.W., Y.C.F., Y.Q.Z, P.D., S.L., and H.W. synthesized the specimens and performed the analysis of different characterizations. Z.W.L., Z.W.C., L.H.Z., and H.W. contributed to writing the manuscript.

Corresponding authors

Correspondence to Hui Wu or Lihao Zhao.

Competing interests

A patent (application number: CN202211013454.3, application date: 23 August 2022, patent status: under substantive examination) for the atomization method has been applied for on behalf of Tsinghua University. H.W. and Z.L. are listed as inventors. The invention discloses an atomization system, its usage method, and applications, which correlated with the research. The other authors declare no competing interests.

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Complete breakup of liquids into ultrafine droplets by grid turbulence

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Abstract

Figures

Introduction

Design and working mechanisms of GTA

Three stages of liquid breakup

Ultrafine atomization for applications

Conclusion and outlook

Methods

High-speed camera observation

Computational fluid dynamics (CFD) simulations

Volume of Fluid (VOF) method

Q Criterion

Turbulence Intensity and Anisotropy

Flow Visualization

Spray Particle Size Measurement

Evaluation of Humidification Efficiency of the Atomization System

Morphology and structure Characterizations

Declarations

References

Additional Declarations

Supplementary Files

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