The dependence of pool scrubbing decontamination factor on particle number density: modeling based on bubble mass and energy balances

Figures & data

Figure 1. Schematic diagram of the experimental apparatus

Figure 2. Measured DF plotted against water depth for different initial particle number densities

Figure 3. Measured (a) void fraction and (b) bubble Sauter mean diameter distributions

Figure 4. Conceptual picture of temperature and vapor concentration distributions in the bubble

Table 1. Calculation parameters

	Base case	Case 1	Case 2
Water temperature ${\mathrm{T}}_{\mathrm{w}}$ (K)	284
Water depth (m)	2.4
Bubble rise velocity (absolute) ${\mathrm{U}}_{\mathrm{b}}$ (m s^−1)	0.9
Bubble relative velocity to water ${\mathrm{U}}_{\mathrm{b}}^{\ast }$ (m s^−1)	0.24
Bubble diameter ${\mathrm{d}}_{\mathrm{b}}$ (m)	5 × 10^−3
Initial particle diameter ${\mathrm{d}}_{\mathrm{p},0}$ (µm)	0.5	2.0	0.5
Bubble Schmidt (Nusselt) Num. $\mathrm{S}{\mathrm{h}}_{\mathrm{b}}\left(\mathrm{N}{\mathrm{u}}_{\mathrm{b}}\right)$ (-)	16	16	8

Figure 5. Calculation results (base case) of (a) degree of supersaturation ${\mathrm{s}}^{\ast }$, (b) particle diameter and (c) DF

Figure 6. Sensitivity calculation result of DF for case 1 with larger initial particle diameter of 2.0 µm

Figure 7. Sensitivity calculation result of DF for case 2 with half bubble heat and mass transfer coefficients of the base case

Table

$\mathrm{a}$: thermal diffusivity (m^2 s^−1)

${\mathrm{C}}_{\mathrm{c}}$: Cunnigham slip correction factor (-)

${\mathrm{C}}_{\mathrm{v}}$: specific heat at constant volume (J kg^−1 K^−1)

$\mathrm{d}$: diameter (m)

$\mathrm{D}$: molecular diffusion coefficient (m^2 s^−1)

$\mathrm{E}$: internal energy (J)

$\mathrm{g}$: gravitational acceleration (m s^−2)

$\mathrm{h}$: heat transfer coefficient (W m^−2 K^−1)

$\mathrm{j}$: superficial velocity (m s^−1)

$\mathrm{k}$: mass transfer coefficient (m s^−1)

$\mathrm{L}$: latent heat (J kg^−1)

$\mathrm{l}$: mean free path (m)

$\mathrm{M}$: molecular mass (kg mol^−1)

$\mathrm{m}$: mass (kg)

$\dot{m}$: mass flow rate (kg s^−1)

$\mathrm{n}$: particle number density (m^−3)

$\mathrm{N}$: total particle number (-)

$\mathrm{p}$: pressure (Pa)

$\dot{q}$: heat flow rate (W)

$\mathrm{R}$: gaseous constant (J mol^−1 K^−1)

$\mathrm{s}$: saturation ratio (-)

$\mathrm{S}$: surface area (m^2)

$\mathrm{t}$: time (s)

$\mathrm{T}$: temperature (K)

$\mathrm{U}$: velocity (m s^−1)

$\mathrm{V}$: volume (m^3)

$\mathrm{z}$: height (m)

Greek

$\alpha$: void fraction (-)

$\rho$: density (mass concentration) (kg m^−3)

$\nu$: kinematic viscosity (m^2 s^−1)

$\mu$: dynamic viscosity (Pa s)

$\lambda$: heat conductivity (W m^−1 K^−1)

$\sigma$: surface tension (N m^−1)

$\tau$: relaxation time (s)

$\theta$: angle (-)

Subscript

0: initial value

1: bubble surface

2: particle surface

$\mathrm{a}$: air

$\mathrm{b}$: bubble

$\mathrm{p}$: particle

$\mathrm{s}\mathrm{a}\mathrm{t}$: saturation

$\mathrm{s}\mathrm{m}$: Sauter mean

$\mathrm{t}$: total

$\tau$: tangential

$\mathrm{v}$: vapor

$\mathrm{w}$: liquid water

Superscript

*: relative or equivalent

Nondimensional number

$\mathrm{K}\mathrm{n}$: Knudsen number

$\mathrm{N}\mathrm{u}$: Nusselt number$=\mathrm{h}\mathrm{d}/\lambda$

$\mathrm{P}\mathrm{e}$: Peclet number$=\mathrm{U}\mathrm{d}/\mathrm{a}$ (heat) and $\mathrm{U}\mathrm{d}/\mathrm{D}$ (mass)

$\mathrm{R}\mathrm{e}$: Reynolds number$=\mathrm{U}\mathrm{d}/\nu$

$\mathrm{S}\mathrm{h}$: Sherwood number $=\mathrm{k}\mathrm{d}/\mathrm{D}$