Interpreting Liquid Atomization Efficiency
Miguel R Oliveira Panão*
Department of Mechanical Engineering, University of Coimbra, Portugal
*Corresponding author: Miguel R Oliveira Panão, Assistant Professor, ADAI, LAETA, Department of Mechanical Engineering, University of Coimbra, Pólo II – Rua Luis Reis Santos, 3030-788 Coimbra, Portugal
Received: September 17, 2021 Accepted: September 30, 2021 Published: October 08, 2021
Citation: Oliveira Panão MR. Interpreting Liquid Atomization Efficiency. Int J Eng Tech & Inf. 2021;2(5):121‒124. DOI: 10.51626/ijeti.2021.02.00024
Liquid atomization involves several mechanisms transforming a bulk of liquid into small droplets. The atomization eﬃciency usefulness is questionable considering its low values (0.01-1%). This work presents a general deﬁnition for atomization efficiency and explains why the Sauter mean diameter is the appropriate characteristic drop size (and no other mean diameter value). Finally, future directions are suggested for developing injector design tools from atomization efficiency.
In liquid atomization, the production of small droplets from a liquid bulk is a physical event dominated by surface energy transfer. The liquid atomization eﬃciency relates the interfacial energy change between the initial liquid bulk and the spray droplets, with the input energy available depending on the atomization strategy. However, Jedelsky et al.  showed that surface energy represents a small portion of the input energy at the nozzle inlet considering all friction losses, the kinetic energy transported by the liquid, air, and their interaction, and the energy associated with acoustic and thermal eﬀects during atomization. Therefore, the scales for the atomization eﬃciency range between relatively low values of 0.01-1%.
In their reference textbook on “Atomization and Sprays,” Lefebvre et al.  associated the quality or ﬁneness of liquid atomization to the characterization of atomizer performance but do not analyze the atomization eﬃciency or interpret it. Most works reported on spray characterization consider the atomization eﬃciency as one of the parameters inside empirical correlations developed to predict the spray droplets’ mean diameter. And the most used mean quantities are the Sauter Mean Diameter and the Arithmetic Mean Diameter But, while the SMD is “the most widely”  used parameter for these correlations, Lefebvre et al.  do not explain the reason. And while several researchers argue the reason is “obvious,” such affirmation still needs grounding in a physical explanation. This mini-review explores this reason.
Furthermore, Lefebvre  is among the ﬁrst works containing the fundamental insights into a systematic characterization of the atomization eﬃciency, introducing the physical analysis of the surface atomizing energy between a ﬂat-sheet or plain-jet liquid bulk and the spray droplets, but lacks a general treatment to any hydrodynamic structure of the liquid bulk. Therefore, this work attempts to develop a general definition of atomization eﬃciency followed by its interpretation. Additionally, one assesses this definition as a performance index, comparing with previous work for an air-assisted multiple impinging jets spray. And, finally, one presents future directions for atomization efficiency as a design tool to explore new liquid atomization strategies.
What is Liquid Atomization’s General Definition?
Liquid atomization concerns the change in surface energy between the total surface energy in the initial hydrodynamic structure of a bulk liquid and the surface energy of the spray droplets after atomization as the liquid (L) surface tension, AL as the bulk liquid surface area, and Ad as the total surface area of the spray droplets.
The total surface energy of the bulk liquid before atomization depends on its geometry. Namely, it could be a cylinder, a sheet, or any other liquid structure. The interfacial change of surface energy in the atomization of a bulk liquid is the difference between the final and initial stages: In general, considering the energy initially available for liquid atomization as the atomization eﬃciency results in:
Assuming the mass of this initial liquid structure one can divide each term in Eq. (1) by the atomized mass and obtain the atomization efficiency as a function of specific energy. In the numerator, the atomization specific energy depends on the difference between the final and initial specific surface area of the spray droplets and bulk liquid, respectively.
What Insight Liquid Atomization Provides about the Physical Meaning of the Sauter Mean Diameter?
Any mean drop size expresses the equivalence between the polydispersed sizes of droplets in a spray and a spray made of single-size (or monodispersed) droplets. Kowalczuk et al.  give a step forward and associate the physical meaning of the SMD as the representative size of a monodispersed spray with the same surface energy as the polydispersed spray. However, this physical meaning is not directly related to the liquid atomization physical process.
In the earlier work of Evers , similarly to Lefebvre , the author analyzes atomization from energy conservation. And while defining the specific surface area of the spray droplets, Evers  arrives at an expression involving a characteristic diameter related to the liquid volume and states the «Sauter mean diameter (SMD) is by definition the diameter of a droplet having the same ratio of volume to surface area as the entire spray.» However, a physical link between this definition and atomization efficiency is still missing. The formulation in Eq. (5) is the same as Lefebvre  and Evers , but these authors used a general variable D as a representative diameter and then stated that the Sauter mean diameter is the best choice by its definition. However, linking with the atomization efficiency implies it is not a choice but an outcome.
Figure 1: Comparison between atomization efficiency and performance (left); Sauter Mean Diameter as ALR function in Pizziol et al. .
Panão et al.  explain why choosing a mean diameter in spray characterization is inherent to the nature of the research question. In the case of following the interpretation of Sowa , it is the mean diameter of an area-weighted drop size distribution. Therefore, if the change in surface energy is the underlying physical process described by the atomization eﬃciency, it is reasonable to consider as the appropriate characteristic size of droplets in a spray. However, while defining the atomization efficiency in Eq. (5), one notices the appearance of the Sauter mean diameter as a result of the interfacial energy of droplets in a spray, justifying why it is a result, not a choice.
Future Directions for the Atomization Efficiency as a Design Tool
Most research works on spray characterization present information on mean drop sizes, especially the Sauter Mean Diameter (SMD), without an apparent reason. Once we establish a physical link between the atomization efficiency and SMD, we aim to develop empirical correlations to predict it, as thoroughly covered in textbooks such as Lefebvre . These empirical correlations include the atomization efficiency, itself correlated with other parameters derived from geometrical features of the atomizer or based on the atomization strategy (e.g., the ALR). However, a mean diameter of a surface-weighted drop size distribution does not enable retrieving any reliable information on the polydispersion of the spray and subsequently measured drop size distributions. The SMD is enough to quantify the atomization efficiency or compare different atomization strategies with similar efficiencies, but predicting the SMD of a spray from the knowledge of the atomization efficiency explains little about its drop size distribution. And without the drop size distribution, it is hard to simulate the spray transport, its footprint if it impacts a surface, and many other applications. Therefore, establishing a link between the atomization efficiency and the original drop size distribution is a topic for future research.
Finally, there is still scarce research on the reasons for such low-efficiency values of liquid atomization. Most new atomization strategies focus on the best way to break up challenging liquids into droplets, for example, considering applications such as sludge drying or the need to produce sprays in small constricted environments. But developing new atomization strategies from the atomization efficiency point of view, paying particular attention to the technology used for the input energy, is also a challenging direction for future research where a proper interpretation of the atomization efficiency is valuable.
The author would like to acknowledge project UIDB/50022/2020 and UIDP/50022/2020 of ADAI for the financial support for this publication.
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