Effect of a barrier on spatial distribution of respiratory particles in a room

Figures & data

Figure 1. Experimental layout, including x–y plane of room (top pane) and x–z plane of room (bottom pane); nebulizer outlet attached to tripod with outlet at x = 0.3 m, y = 0 m, z = 1.5 m. Sampling points located at intersections of all dashed lines. In the experiments including the barrier, the barrier is located at x = 0.76 m. The barrier, represented by the long-dashed line, is 0.91 m wide (centered at y = 0 m) and is 1.83 m tall (as measured from the floor).

Table 1. Length of experiment (including nebulizer run time), PSL concentration in tube received from manufacturer (Polysciences, Inc, PA, USA) and volume added to nebulizer (diluted to a final volume of 5 mL in nanopure water).

PSL microsphere diameter	Experiment duration, h (without barrier, with barrier)	PSL microsphere stock concentration (Ci), # mL^−1	Volume added to nebulizer (Volneb), mL	Final concentration in nebulizer, # mL^−1
0.5 µm	23.5, 23.1	3.64 × 10^11	0.05	3.64 x 10^9
1 µm	23.9, 24.0	4.55 x 10^10	2.5	2.28 x 10^10
6 µm	18.0, 21.3	2.10 x 10^8	0.5	2.10 x 10^7
10 µm	3.4, 3.2	4.55 x 10^7	0.5	4.55 x 10^6
20 µm	1.3, 1.5	5.68 x 10^6	0.5	5.68 x 10^5

Table 2. Total microsphere numbers observed (N_tot) and quantification limits for each microsphere size. Too few to count (TFTC) was set to N/N_tot = 2 × 10⁻⁴ and not detectable (ND) was set to N/N_tot = 1 × 10⁻⁴.

PSL microsphere diameter (µm)	Experimental setup	NTOT (no. of particles)	TFTC	ND
			N (no. of particles per sample)	N (no. of particles per sample)
0.5	No barrier	2.8 × 10^6	N/A	N/A
	Barrier	1.3 × 10^7
1	No barrier	5.6 × 10^7	N/A	N/A
	Barrier	8.6 × 10^6
6	No barrier	4.1 × 10^4	8.2	4.1
	Barrier	2.1 × 10^4	4.2	2.1
10	No barrier	2.7 × 10^3	< 1	< 1
	Barrier	0^a
20	No barrier	1.0 × 10^2	< 1	< 1
	Barrier	0^a

^a No microspheres were observed during the 10 and 20 µm barrier experiments; all samples were either TFTC or ND, therefore, N_tot could not be calculated.

N/A indicates that no samples were below the quantification limit and no samples were classified as TFTC or ND.

Table 3. List of variables used in modeling.

Variable name	Units	Description	Value
Vt	m s^−1	Settling velocity	$\frac{\mathrm{g}{\mathrm{ }*\mathrm{ }\mathrm{D}}_{\mathrm{p}}^2\mathrm{ }*\mathrm{ }\mathrm{(}{\mathrm{\rho }}_{\mathrm{p}}-\mathrm{ }{\mathrm{\rho }}_{\mathrm{f}}\mathrm{)}\mathrm{ }*\mathrm{ }{\mathrm{C}}_{\mathrm{c}}}{18\mathrm{ }*\mathrm{ }{\mathrm{\mu }}_{\mathrm{f}}}$
${\mathrm{C}}_{\overline{\mathrm{a}}}$	No. of particles m^−3	Assumed concentration of PSL microspheres aerosolized in room	$\frac{{\mathrm{C}}_{\mathrm{i}}\text{ * }{\text{Vol}}_{\text{neb}}}{{\text{Vol}}_{\text{room}}}$
Ci	No. of particles mL^−1	PSL microsphere stock concentration	See Table 1
Volneb	mL	Volume of PSLs added to nebulizer	See Table 1
Volroom	m^3	Volume of room	42.4
Q	m^3 s^−1	Volumetric flow rate	λ$\mathrm{*}\mathrm{ }$ Volroom
λ	s^−1	Air exchange rate	1.6 × 10^−4
Afloor	m^2	Area of floor	16.4
Aslide	m^2	Area of microscope slide	1.9 × 10^−3
t	s	Settling time	Independent variable^a
g	m s^−2	Acceleration due to gravity	9.81
Dp	m	PSL microsphere diameter	0.5, 1, 6.2, 10.2, 20.2 (× 10^−6)
ρp	kg m^−3	Density of PSL microspheres	1050
ρf	kg m^−3	Density of air in room	1.2
µf	kg m^−1 s^−1	Dynamic viscosity of air	1.85 × 10^−5
Cc		Slip correction coefficient (for Dp < 5 µm)	$1+\text{Kn}\mathrm{ }[1.257+0.4\mathrm{ }*\mathrm{ }\hspace{0.17em}\exp \hspace{0.17em}\left(\frac{-1.1}{\text{Kn}}\right)]$
Kn	–	Knudson number	$\frac{2\mathrm{ }*\mathrm{ }0.065}{{\mathrm{D}}_{\mathrm{p}}}$
Cavg	No. of particles m^−3	Average airborne concentration at each sampling location	Equation (5)(5) $$C_{\mathit{\text{avg}}}=\frac{N}{V_t t_e A_{\mathit{\text{slide}}}}$$(5)
N	No. of particles	Number of observed particles per microscope slide	Determined experimentally
te	s	Exposure time (time for 3 air changes or time to settle 1.5 m)	0.5 µm: 1.8 × 10^4 1 µm: 1.8 × 10^4 6 µm: 1.3 × 10^3 10 µm: 470 20 µm: 120

^aSettling time was the independent variable used in Equations (3)(3) $$C\left(t\right)=C_{\overline{a}} \hspace{0.17em}\exp \hspace{0.17em}\left[-\left(\frac{Q+V_{\mathit{\text{t }}}{A}_{\mathit{\text{floor}}}}{{\mathit{\text{Vol}}}_{\mathit{\text{room}}}}\right)*t\right]$$(3) and (4)(4) $$\text{Flux}=V_t\mathit{\text{ C}}=V_t{\mathit{\text{ C}}}_{\overline{a}} * \hspace{0.17em}\exp \hspace{0.17em}\left[-\left(\frac{Q + V_{\mathit{\text{t }}}{A}_{\mathit{\text{floor}}}}{{\mathit{\text{Vol}}}_{\mathit{\text{room}}}}\right)*t\right]$$(4) , and therefore different values were used when calculating flux.

Figure 2. Distribution of 0.5 µm microspheres in the room with no barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points and star represents location of nebulizer outlet. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 3. Distribution of 0.5 µm microspheres in the room with barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points and star represents location of nebulizer outlet. Solid line at x = 0.76 m represents location of barrier. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 4. Distribution of 1 µm microspheres in the room with no barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points and star represents location of nebulizer outlet. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 5. Distribution of 1 µm microspheres in the room with barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points and star represents location of nebulizer outlet. Solid line at x = 0.76 m represents location of barrier. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 6. Distribution of 6 µm microspheres in the room with no barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, the star represents location of nebulizer outlet, and triangles represent sampling locations that were classified as “too few to count”. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 7. Distribution of 6 µm microspheres in the room with barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, the star represents location of nebulizer outlet, and triangles represent sampling locations that were classified as “too few to count”. Solid line at x = 0.76 m represents location of barrier. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 8. Distribution of 10 µm microspheres in the room with no barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, star represents location of nebulizer outlet, triangles represent sampling locations classified as “too few to count” and x’s represent those that were classified as “not detectable”. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 9. Distribution of 10 µm microspheres in the room with barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, star represents location of nebulizer outlet, triangles represent sampling locations classified as “too few to count” and x’s represent those classified as “not detectable”. Solid line at x = 0.76 m represents location of barrier. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 10. Distribution of 20 µm microspheres in the room with no barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, star represents location of nebulizer outlet, triangles represent sampling locations classified as “too few to count” and x’s represent those classified as “not detectable”. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.

Figure 11. Distribution of 20 µm microspheres in the room with barrier in place. (a) x–y plane at z = 0 m level; (b) x–y plane at z = 1.5 m level; and (c) x–z plane at y = 0 m level. Closed dots represent sampling points, star represents location of nebulizer outlet, triangles represent sampling locations classified as “too few to count” and x’s represent those classified as “not detectable”. Solid line at x = 0.76 m represents location of barrier. N represents the total observed microspheres settled on each 25 × 75 mm microscope slide and N_tot represents the total microspheres observed on all slides during this experiment.