Primary break-up and atomization characteristics of a nasal spray

The primary objective of this research was to extract the essential information needed for setting atomization break up models, specifically, the Linear Instability Sheet Atomization (LISA) breakup model, and alternative hollow cone models. A secondary objective was to gain visualization and insight into the atomization break up mechanism caused by the effects of viscosity and surface tension on primary break-up, sheet disintegration, ligament and droplet formation. High speed imaging was used to capture the near-nozzle characteristics for water and drug formulations. This demonstrated more rapid atomization for lower viscosities. Image processing was used to analyze the near-nozzle spray characteristics during the primary break-up of the liquid sheet into ligament formation. Edges of the liquid sheet, spray break-up length, break-up radius, cone angle and dispersion angle were obtained. Spray characteristics pertinent for primary breakup modelling were determined from high speed imaging of multiple spray actuations. The results have established input data for computational modelling involving parametrical analysis of nasal drug delivery.

1. The use of several advanced data treatments (detailed image analysis, Canny edge detection, a brief introduction using the Weber number to describe air-surface tension relationships) is included in the manuscript, but insufficient information regarding how these can be/will be used to parameterize the proposed LISA model is described. The reviewer is left to question whether a follow-up publication reporting on the development of the LISA model to describe these results is planned. The limited quantitative evaluation of the results or their application to a broader set of nasal sprays provided in the manuscript is a significant weakness.

Response:
We agree that certain details were not provided in detail to highlight and showcase some of the innovations of the study -one that was missing is the technique of backlighting for shadowgraphy at high frame rates which has not been performed before. We also agree that the link between the measured data and LISA model was not as strong as could be, and that the details on how the results from this study apply to spray modelling have not been sufficiently provided in the manuscript. To improve this, we have added further discussion on the novel experimental technique and LISA model requirements. Its application towards the follow-up computational study of spray atomization using the LISA model is now discussed under a subsection "Implementation in CFD modelling" which relates the spray characteristics with quantitative data required in the LISA model and hollow cone injection approach of a nasal spray modelling.

Implementation in CFD modelling
Spray modelling has been well understood and validated for high-pressure applications such as industrial and combustion fuel sprays (De Villiers et al., 2004;Dos Santos et al., 2011). However, there are limited studies with accurate validation of low-pressure applications such as nasal sprays. The available primary break-up models, such as Huh and LISA (Huh, 1991;Senecal et al., 1999), were modelled for combustion sprays operating under high injection and combustion chamber pressure.
The current study aims to provide insight into the external and near-nozzle spray characteristics of a low-pressure nasal spray atomizing in atmospheric pressure. The high speed imaging was processed to obtain quantitative data to serve as a reference for initial conditions required for computational atomizer breakup models, such as the LISA model and an alternative approach involving explicitly defining the droplet parcels at the disintegration/break-up length (liquid core length) based on our measurements from a nasal spray. Secondary break-up would be achieved through the Taylor-Analogy-Breakup (TAB) model which is suitable for low Weber number applications. The LISA breakup model requires a spray cone and dispersion angle as inputs. The spray cone angle describes the spray plume development whereas the dispersion angle describes the liquid sheet fluctuation from the mean cone spray angle. The dispersion angle is an important parameter in the LISA break-up model, as it leads to the radial droplet dispersion from the mean cone spray angle. This parameter has not been reported for nasal spray applications and past studies have used a dispersion angle of 3°  by tuning the parameter to match a droplet size distribution. For engine sprays, the dispersion angle was generally set to 10° (Baumgarten, 2006;Suh et al., 1999). Our measured results showed an angle of 8.65 o ± 0.64 o .
An alternative to atomizer breakup models is to explicitly define the initial droplet conditions, which includes a choice of hollow-cone, ring cone and solid-cone, as well as a custom user-defined cone. The most likely choice of cone to best represent pressure-swirl atomizers would be the hollow cone model . In this approach the primary break-up (eg: LISA, Huh models) is not modelled, but rather the droplet conditions in the near-nozzle are defined. This information can be extracted from measurements, that includes droplet location at the break-up length where the liquid sheet disintegration occurs, and spray cone angle. The droplets are distributed on a hollow circular ring at a break-up length from the nozzle, and a droplet size distribution would be imposed based on an empirical Rosin Rammler distribution function within the nasal spray droplet size distribution range.
A fully-resolved model of spray atomization is computationally intensive and challenging. Our measurement data of near-nozzle characteristics includes spray cone angle, break-up length, ligament diameter (break-up diameter), and dispersion angle and aims to contribute to the existing dataset for spray atomization CFD model setup." 2. The authors conducted a somewhat limited study regarding spray formation using a single spray device containing a commercially-available formulation or water sprayed from the same device. The report would be strengthened by the inclusion of specific information about the spray actuator system used in the product tested (manufacturer, model, any performance or design specifications available) and about the properties of the specific formulation tested. The authors, instead, rely on the description of a range of formulation variables obtained from the literature (Table 1). This results in the inability to build upon and potentially generalize beyond the specific results provided.

Response a):
Information on the spray actuator system used in the product test has now been added in the "Materials and methods" section of the manuscript.
"A schematic of the experimental setup is shown in Fig 1a which

Response: The dimensions of the spray bottle and the length of the dip tube have now been added in the section "Materials and Methods" as:
The measured length of the dip tube was 3 cm and the diameter of the bottle was 2.9 cm totaling the volume of the liquid to 20 mL in a bottle.
In addition, volume of the liquid and corresponding length of the dip tube immersed in the liquid is provided in a new table (Table1).  (Chung et al., 1998). This phenomenon was identified in the current study when the drug formulation, which was comparatively more viscous compared to water, had a somewhat longer break-up length (longer by ≈ 0.5mm).
The formulation in the nasal spray used contains oxymetazoline hydrochloride 0.05% and exhibits thixotropic behaviour due to its viscosity-enhanced formulations. Its rheologic behaviour is demonstrated by its viscosity at resting state which is high (3761cP (Doughty et al., 2010)) but, under shear forces, its viscosity reduces, and hence the requirement that some nasal sprays must be shaken to reduce viscosity so the formula can easily pass through the atomizer. During spray atomization, the formulation stretches and swirls as it exits the nozzle orifice, thinning out and shearing into ligaments and later, into droplets. However, after depositing on the nasal mucosa, the formulation increases in viscosity in order to enhance its residence time on the surface and create the 'no drip' effect.
A lower surface tension liquid has higher tendency to disintegrate. The drug formulation has a lower surface tension than water. However, the effect of formulation on sprays can be described with the Ohnesorge number (Oh) which characterizes the effect of viscous to inertial and surface forces. Comparison of Oh numbers for the drug formulation and water indicate a greater influence of viscosity (Ohdrug=2-12Ohwater) with the assumption that inertial force is the same (ΔP=5bar actuation force). The liquid properties also influence secondary break-up as they affect the liquid core length and ligament diameter. An increase in formulation viscosity (with similar surface tension) is expected to reduce plume angle and produce both larger and more variable droplets irrespective of the nasal spray devices tested. However, studies have shown that plume angles were identical and had no influence on droplet size distribution when fluid with varying surface tension was used (with similar viscosity) and irrespective of the nasal devices tested (Dayal et al., 2004;Foo, 2007;Kooij et al., 2018).
5. The manuscript needs careful copy editing prior to the next submission. There are numerous typos, grammatical errors and generally careless mistakes in figure descriptors. The references are also poorly edited, especially with respect to consistency in journal names.