${\tilde{\mathit{B}}}_{\mathit{\alpha }}$	concentration of active cells in the αth phase, $\left[\mathbf{cells}·c{m}^{-\mathbf{3}}\right]$;
${\tilde{\mathit{B}}}_{\mathit{\lambda }\mathit{\beta }}$	interfacial concentration of active cells, $\left[\mathbf{cells}·c{m}^{-\mathbf{2}}\right]$;
$Bi$	Biot number, $Bi={\mathit{H}}_{\mathit{A},\mathit{\upsilon }/\mathit{\beta }}{\tilde{\mathit{R}}}_{\mathit{P}}{\tilde{\mathit{k}}}_{\mathit{p}/\mathit{\upsilon }}/{\tilde{\mathit{D}}}_{\mathit{A}\mathit{\beta }}=\left({\mathit{H}}_{\mathit{A},\mathit{\upsilon }/\mathit{\beta }}/{\mathsf{\Lambda }}_{\mathit{A}\mathit{\beta }}\right)S{h}_{\mathit{p}/\mathit{\upsilon }}/\mathbf{2}$;
${\tilde{\mathit{c}}}_{\mathit{A}\mathit{\alpha }}$	mass concentration of oil in the αth phase, $\left[\mathbf{g}·c{m}^{-\mathbf{3}}\right]$, dimless ${\mathit{c}}_{\mathit{A}\mathit{\alpha }}={\tilde{\mathit{c}}}_{\mathit{A}\mathit{\alpha }}/{\tilde{\mathit{c}}}_{\mathit{A},\mathit{\lambda }/\mathit{\alpha }}$;
${\tilde{\mathit{c}}}_{\mathit{A},\mathit{\lambda }/\mathit{\alpha }}$	solubility of oil in the αth phase, $\left[\mathbf{g}·c{m}^{-\mathbf{3}}\right]$;
$\langle {\tilde{\mathit{c}}}_{\mathit{A}\mathit{\beta }}\rangle$	volume averaged concentration of oil in the β-phase, Equation (35), $\left[\mathbf{g}·c{m}^{-\mathbf{3}}\right]$;
${\tilde{\mathit{D}}}_{\mathit{A}\mathit{\alpha }}$	diffusion coefficient of the A solute in the αth phase, $\left[c{m}^{\mathbf{2}}·s^{-\mathbf{1}}\right]$;
$D{a}_{\mathit{\alpha }}$	Damköhler number in the αth phase, $D{a}_{\mathit{\alpha }}={\tilde{\mathit{k}}}_{\mathbf{1}\mathit{\alpha }}{\tilde{\mathit{R}}}_{\mathit{P}}^{\mathbf{2}}/{\tilde{\mathit{D}}}_{\mathit{A}\mathit{\alpha }}$;
${\tilde{\mathit{D}}}_{\mathit{c},\mathit{t}}$	diameter of the oily core, $\left[cm\right]$, dimless ${\mathit{D}}_{\mathit{c},\mathit{t}}={\tilde{\mathit{D}}}_{\mathit{c},\mathit{t}}/{\tilde{\mathit{D}}}_{\mathit{P},\mathbf{0}}$;
${\tilde{\mathit{D}}}_{\mathit{P},\mathit{t}}$	diameter of the compound particle, $\left[\mathbf{cm}\right]$, dimless ${\mathit{D}}_{\mathit{P},\mathit{t}}={\tilde{\mathit{D}}}_{\mathit{P},\mathit{t}}/{\tilde{\mathit{D}}}_{\mathit{P},\mathbf{0}}$;
$\tilde{\mathit{g}}$	gravitational acceleration, $\left[cm·s^{-\mathbf{2}}\right]$;
${\mathit{H}}_{\mathit{A},\mathit{\upsilon }/\mathit{\beta }}$	solubility ratio, ${\mathit{H}}_{\mathit{A},\mathit{\upsilon }/\mathit{\beta }}={\tilde{\mathit{c}}}_{\mathit{A},\mathit{\lambda }/\mathit{\upsilon }}/{\tilde{\mathit{c}}}_{\mathit{A},\mathit{\lambda }/\mathit{\beta }}$;
$Ha$	Hatta modulus, $Ha=\mathbf{2}\sqrt{D{a}_{\mathit{\upsilon }}}/S{h}_{\mathit{p}/\mathit{\upsilon }}^{\mathbf{0}}$;
${\mathit{h}}_{\mathit{T}}$	Thiele number in the biofilm shell, ${\mathit{h}}_{\mathit{T}}={\tilde{\mathit{R}}}_{\mathit{P}}\sqrt{{\tilde{\mathit{k}}}_{\mathbf{1}\mathit{\beta }}/{\tilde{\mathit{D}}}_{\mathit{A}\mathit{\beta }}}=\sqrt{D{a}_{\mathit{\beta }}}$;
${\tilde{\mathit{J}}}_{\mathit{A}\mathit{\alpha }}$	mass flux of oil in the αth phase, $\left[g·c{m}^{-\mathbf{2}}·s^{-\mathbf{1}}\right]$, dimless ${\mathit{J}}_{\mathit{A}\mathit{\alpha }}={\tilde{\mathit{J}}}_{\mathit{A}\mathit{\alpha }}/({\tilde{\mathit{D}}}_{\mathit{A}\mathit{\alpha }}{\tilde{\mathit{c}}}_{\mathit{A},\mathit{\lambda }/\mathit{\alpha }}/{\tilde{\mathit{R}}}_{\mathit{P}})$;
${\tilde{\mathit{k}}}_{\mathbf{1}\mathit{\alpha }}$	first-order reaction rate constant in the αth phase, Equation (4), $\left[s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{k}}}_{\mathit{p}/\mathit{\upsilon }}^{\mathbf{0}}$	mass transfer coefficient for external mass transfer with $D{a}_{\mathit{\upsilon }}=\mathbf{0}$, Equation (21), $\left[cm·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{k}}}_{\mathit{p}/\mathit{\upsilon }}$	mass transfer coefficient for external mass transfer, Equation (24), $\left[cm·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{k}}}_{\mathit{\lambda }/\mathit{\beta }}$	mass transfer coefficient for the dissolution of the oily core, Equation (33), $\left[cm·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{k}}}_{\mathit{d}\mathit{i}\mathit{s}}$	droplet shrinking rate caused by dissolution, Equation (50b), $\left[cm·s^{-\mathbf{1}}\right]$, dimless Equation (54);
${\tilde{\mathit{k}}}_{\mathit{g}\mathit{r}\mathit{t}}$	biofilm expansion rate due to growth, Equation (50c), $\left[cm·s^{-\mathbf{1}}\right]$, dimless Equation (54);
${\tilde{\mathit{k}}}_{\mathit{s}\mathit{r}\mathit{n}}$	droplet shrinking rate caused by direct uptake, Equation (50a), $\left[cm·s^{-\mathbf{1}}\right]$, dimless Equation (54);
${\tilde{\mathit{K}}}_{\mathit{S},\mathit{\alpha }}$	half-saturation constant for the A solute in the αth phase, $\left[g·c{m}^{-\mathbf{3}}\right]$;
$n_{\mathit{\alpha }\mathit{\omega }}$	unit normal vector on the αω-interface pointing from the α-phase to the ω-phase;
$\tilde{\mathit{r}}$	radial coordinate, $\left[cm\right]$, dimless $\mathit{r}=\tilde{\mathit{r}}/{\tilde{\mathit{R}}}_{\mathit{P}}$;
${\tilde{\mathit{r}}}_{\mathit{A},\mathit{\alpha }}$	oil consumption rate in the αth phase, $\left[g·c{m}^{-\mathbf{3}}·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{r}}}_{\mathit{c},\mathit{\alpha }}$	microbial cell proliferation rate in the αth phase, $\left[\mathbf{cells}·c{m}^{-\mathbf{3}}·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{r}}}_{\mathit{\beta }}$	biofilm production rate, ${\tilde{\mathit{r}}}_{\mathit{\beta }}={\tilde{\mathit{r}}}_{\mathit{c},\mathit{\beta }}/{\mathit{Y}}_{\mathit{c}/\mathit{\beta }}$, $\left[g·c{m}^{-\mathbf{3}}·s^{-\mathbf{1}}\right]$;
$P{e}_{\mathit{\alpha }}$	Péclet number in the αth phase, $P{e}_{\mathit{\alpha }}={\tilde{\mathit{R}}}_{\mathit{P}}\tilde{\mathit{U}}/{\tilde{\mathit{D}}}_{\mathit{A}\mathit{\alpha }}$;
${\tilde{\mathit{R}}}_{\mathit{c}}$	radius of the oily core, $\left[cm\right]$, dimless ${\mathit{R}}_{\mathit{c}}={\tilde{\mathit{R}}}_{\mathit{c}}/{\tilde{\mathit{R}}}_{\mathit{P}}$;
${\tilde{\mathit{R}}}_{\mathit{P}}$	radius of the compound particle, $\left[cm\right]$, dimless ${\mathit{R}}_{\mathit{P}}={\tilde{\mathit{R}}}_{\mathit{P}}/{\tilde{\mathit{R}}}_{\mathit{P}}=\mathbf{1}$;
${\tilde{\mathit{S}}}_{\mathit{\beta }\mathit{\upsilon }}$	area of the compound particle surface, ${\tilde{\mathit{S}}}_{\mathit{\beta }\mathit{\upsilon }}=\mathbf{4}\mathit{\pi }{\tilde{\mathit{R}}}_{\mathit{P}}^{\mathbf{2}}$, $\left[c{m}^{\mathbf{2}}\right]$;
${\tilde{\mathit{S}}}_{\mathit{\lambda }\mathit{\beta }}$	area of the oily core surface, ${\tilde{\mathit{S}}}_{\mathit{\lambda }\mathit{\beta }}=\mathbf{4}\mathit{\pi }{\tilde{\mathit{R}}}_{\mathit{c}}^{\mathbf{2}}$, $\left[c{m}^{\mathbf{2}}\right]$;
$S{h}_{\mathit{p}/\mathit{\upsilon }}^{\mathbf{0}}$	Sherwood number for external mass transfer with $D{a}_{\mathit{\upsilon }}=\mathbf{0}$, Equation (22);
$S{h}_{\mathit{p}/\mathit{\upsilon }}$	Sherwood number for external mass transfer, Equation (24);
$S{h}_{\mathit{\lambda }/\mathit{\beta }}$	overall Sherwood number for the dissolution of the oily core, Equation (34);
$\tilde{\mathit{U}}$	undisturbed velocity of the approaching fluid, $\left[cm·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{V}}}_{\mathit{\beta }}$	volume of the biofilm shell, ${\tilde{\mathit{V}}}_{\mathit{\beta }}=\mathit{\pi }({\tilde{\mathit{D}}}_{\mathit{P}}^{\mathbf{3}}-{\tilde{\mathit{D}}}_{\mathit{c}}^{\mathbf{3}})/\mathbf{6}$, $\left[c{m}^{\mathbf{3}}\right]$;
${\tilde{v}}_{\mathit{\upsilon }}$	velocity of the aqueous fluid, $\left[cm·s^{-\mathbf{1}}\right]$, dimless $v_{\mathit{\upsilon }}={\tilde{v}}_{\mathit{\upsilon }}/\tilde{\mathit{U}}$;
${\mathit{Y}}_{\mathit{c}/\mathit{\beta }}$	number of active cells per unit biofilm mass, [cells/mg-biofilm];
${\mathit{Y}}_{\mathit{c}/\mathit{A},\mathit{\alpha }}$	yield coefficient of cells in the αth phase, [cells/mg-oil];
${\mathit{Y}}_{\mathit{\beta }/\mathit{A}}$	biofilm yield coefficient, ${\mathit{Y}}_{\mathit{\beta }/\mathit{A}}={\mathit{Y}}_{\mathit{c}/\mathit{A},\mathit{\beta }}/{\mathit{Y}}_{\mathit{c}/\mathit{\beta }}$, [mg-biofilm/mg-oil];
${\tilde{\mathit{W}}}_{\mathit{A},\mathit{p}/\mathit{\upsilon }}$	external mass transfer rate: from the particle surface to the υ-phase, Equation (26), $\left[g·s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{W}}}_{\mathit{A},\mathit{\lambda }/\mathit{\beta }}$	overall dissolution rate at the surface of the oily core, Equation (32), $\left[g·s^{-\mathbf{1}}\right]$;
Greek letters
${\tilde{\mathit{\delta }}}_{\mathit{\beta }}$	thickness of the biofilm shell, ${\tilde{\mathit{\delta }}}_{\mathit{\beta }}={\tilde{\mathit{R}}}_{\mathit{P}}-{\tilde{\mathit{R}}}_{\mathit{c}}$, $\left[cm\right]$;
${\mathit{\delta }}_{\mathit{\beta }}$	dimless thickness of the biofilm shell, ${\mathit{\delta }}_{\mathit{\beta },\mathit{t}}={\tilde{\mathit{\delta }}}_{\mathit{\beta },\mathit{t}}/{\tilde{\mathit{R}}}_{\mathit{P},\mathit{t}}=\mathbf{1}-{\tilde{\mathit{R}}}_{\mathit{c},\mathit{t}}/{\tilde{\mathit{R}}}_{\mathit{P},\mathit{t}}$;
$\Delta \tilde{\mathit{\rho }}$	excess density, $\Delta \tilde{\mathit{\rho }}=\left|{\tilde{\mathit{\rho }}}_{\mathit{\upsilon }}-{\tilde{\mathit{\rho }}}_{\mathit{P}}\right|$, $\left[g·c{m}^{-\mathbf{3}}\right]$;
${\tilde{\mathit{\mu }}}_{m,\mathit{\alpha }}$	maximum specific growth rate of active cells, $\left[s^{-\mathbf{1}}\right]$;
${\tilde{\mathit{\mu }}}_{\mathit{\upsilon }}$	viscosity of the υ-phase, $\left[g·c{m}^{-\mathbf{1}}·s^{-\mathbf{1}}\right]$;
${\mathsf{\Lambda }}_{\mathit{A}\mathit{\beta }}$	diffusivity ratio, ${\mathsf{\Lambda }}_{\mathit{A}\mathit{\beta }}={\tilde{\mathit{D}}}_{\mathit{A}\mathit{\beta }}/{\tilde{\mathit{D}}}_{\mathit{A}\mathit{\upsilon }}$;
${\tilde{\mathit{\rho }}}_{\mathit{\alpha }}$	density of the αth phase, $\left[g·c{m}^{-\mathbf{3}}\right]$, dimless ${\mathit{\varrho }}_{\mathit{\alpha }}={\tilde{\mathit{\rho }}}_{\mathit{\alpha }}/{\tilde{\mathit{\rho }}}_{\mathit{\upsilon }}$;
${\tilde{\mathit{\tau }}}_{\mathit{D}}$	scaled characteristic diffusion time, Equation (52), $\left[s\right]$;
$\mathit{\tau }$	dimless time,$\mathit{\tau }=\tilde{\mathit{t}}/{\tilde{\mathit{\tau }}}_{\mathit{D}}$;
${\mathsf{\Phi }}_{\mathit{b}\mathit{r}\mathit{n}}$	mass fraction of oil biodegraded within the biofilm shell, Equation (63a);
${\mathsf{\Phi }}_{\mathit{d}\mathit{i}\mathit{s}}$	mass fraction of oil released into the aqueous phase, Equation (63b);