Table I.

Factors expected to influence dispersion of the aerosol.

Factor name and symbol	Equation	Units	Interpretation
Flow Field Parameters
Volume-averaged turbulent kinetic energy of the flow field (k_field)	$k_{field}^{} = \frac{1}{V o l} \int_{V o l}^{} k dvol$ Where Vol is the volume of the DAC unit and k is the turbulent kinetic energy at each location in the volume.	m²/s²	Turbulent kinetic energy arises from turbulent velocity fluctuations and is directly proportional to turbulent strength or intensity. It is expected that high k will break apart aggregates thereby reducing MMAD and will also help remove particles from the walls.
Volume-averaged specific dissipation rate of the flow field (ω_field)	$ω_{field}^{} = \frac{1}{V o l} \int_{V o l}^{} ω dvol$ Where Vol is the volume of the DAC unit and ω is the specific dissipation rate at each location in the volume.	1/s	The specific dissipation rate is defined as $\frac{k^{1 / 2}}{C_{μ}^{1 / 4} l}$ where l is the turbulent length scale and C_μ is a constant. High values of ω indicate elevated k together with small l. Longest et al. (14) interpreted this as high k in small eddies and proposed that this was ideal for maximizing small particle deaggregation using turbulence.
Non-dimensional turbulent kinetic energy of the flow field (k*_field)	$k_{field}^{*} = k_{field} \frac{1}{V_{inlet}^{2}} ∙ 10^{4}$ Where V_inlet is the mean velocity of the inlet air jet.	Non-dimensional	V_inlet has an inverse relation with expected particle residence time. Therefore, high V_inlet reduces the exposure time to the turbulent field and is expected to reduce deaggregation. A multiplier of 10⁴ is used to increase values to O(10).
Non-dimensional specific dissipation rate of the flow field (ω*_field)	$ω_{field}^{*} = ω_{field} t_{inlet}$ Where $t_{inlet} = {V o l}^{\frac{1}{3}} / V_{inlet}$ and provides a representative exposure time of particles to the flow field.	Non-dimensional	Longer exposure time is expected to improve deaggregation. The resulting parameter is similar to the non-dimensional specific dissipation (NDSD) proposed by Longest et al. (14) and shown to correlate with deaggregation of airborne particles moving through a 3D array of rods.
Non-dimensional eddy viscosity (k_field / ω_field)	$\frac{k_{field}^{}}{ω_{field}^{}} = \frac{k_{field}}{ω_{field}} \frac{1}{V_{inlet}^{2} t_{inlet}}$	Non-dimensional	Represents turbulent or eddy viscosity, which significantly increases shear stress on the particles. The mean value represents eddy viscosity throughout the flow field.
k_field x ω**_field	$k_{field}^{} ω_{field}^{} = k_{field} \frac{ω_{field} t_{inlet}}{V_{inlet}^{2}}$	Non-dimensional	Does not have a physical interpretation like the eddy viscosity. Instead, it represents a modified version of ω_field where k is increasingly important and represented as $\frac{k^{3 / 2}}{C_{μ}^{1 / 4} l}$
Wall shear stress (WSS)	$W S S = \int_{A}^{} μ_{total} \frac{d u}{d n} d A$ Where A is the surface area of the DAC unit, μ_total is the total viscosity at the wall including both laminar and turbulent components, u is the local velocity parallel to the wall and n is the local wall-normal coordinate.	N/m²	The WSS is an area-averaged value computed over the wall surface of the DAC unit. High WSS is expected to remove particles from the wall and therefore correlate with emitted dose.
Particle Trajectory Parameters
Average particle residence time (t_part)	$t_{part} = \frac{1}{n} \sum_{i = 1}^{n} \int_{trajectory}^{} d t$ Where n particles are considered and the integral is performed for each particle from its starting point through the DAC outlet.	s	Average particle residence time within the DAC unit geometry based on particle number.
Average particle turbulent kinetic energy (k_part)	$k_{part} = \frac{1}{n} \sum_{i = 1}^{n} \int_{trajectory}^{} k d t$ Where k is the local turbulent kinetic energy experienced by each particle along its trajectory.	(m²/s²)s or Nm or Joules	Represents the history of k a particle experiences over its trajectory through the system. Both k and exposure time to k are expected to be directly proportional to deaggregation. Units represent work (J) performed by turbulence on the particle.
Non-dimensional particle turbulent kinetic energy (k*_part)	$k_{part}^{*} = k_{part} \frac{1}{V_{inlet}^{2}} \frac{1}{t_{inlet}}$	Non-dimensional	Of the available time scales, use of t_inlet provided the strongest correlation with the experimental data.
Average particle specific dissipation rate (ω_part or ω*_part)	$ω_{part}^{*} = \frac{1}{n} \sum_{i = 1}^{n} \int_{trajectory}^{} ω d t$ Where ω is the local specific dissipation rate experience by each particle along its trajectory.	Non-dimensional	Represents the history of ω a particle experiences over its trajectory through the system. Both ω and exposure time to ω are expected to be directly proportional to deaggregation.
Non-dimensional ω_part / t_part	${(\frac{ω_{part}}{t_{part}})}^{*} = \frac{ω_{part}}{t_{part}} t_{inlet}$	Non-dimensional	Allows for consideration of ω_part without the influence of t_part. Inclusion of t_part may be confounding if deaggregation occurs quickly.