List of Symbols
a	radius of the soft particle (m)
C	concentration of total electrolytes (1/m3)
Dj	diffusivity of ionic species j (m2/s)
D1	diffusivity of cation in binary electrolyte solution (m2/s)
D2	diffusivity of anion in binary electrolyte solution (m2/s)
e	elementary charge of an electron (1.6 × 10−19 coul)
Fd	magnitude of the hydrodynamic drag force exerted on the droplet (Nt)
Fe	magnitude of the electric force exerted on the droplet (Nt)
fj	molar flux of ionic species j (mole/m2/s)
${\mathrm{G}}_{\mathrm{j}}^{*}$	one-dimensional shape function representing the extra non-concentric concentration perturbation of ionic species j (volt)
gj	shape function representing the extra non-concentric concentration perturbation of ionic species j (volt)
kB	Boltzmann constant (1.38 × 10−23 joul/K)
nj	number density of ionic species j (1/m3)
n10	bulk concentration of cations (1/m3)
n20	bulk concentration of anions (1/m3)
Pej	Peclet number of ionic species j (Pej = U0a/Dj) representing the reciprocal of its diffusivity in a dimensionless form
p	pressure (Nt/m2)
r	r-coordinate in spherical coordinates (r, θ, φ)
${\mathrm{r}}^{*}$	dimensionless r-coordinate in spherical coordinates, defined as r/a
U	diffusiophoretic velocity of the droplet under consideration
U0	characteristic velocity in diffusiophoretic motion defined as $\frac{\mathsf{\epsilon }}{{\mathsf{\eta }}_{\mathrm{r}}a}{\left(\frac{\mathrm{kT}}{{\mathrm{z}}_1\mathrm{e}}\right)}^2$
U*	dimensionless diffusiophoretic velocity of the droplet in [42] defined as $\frac{3\left({\mathsf{\eta }}_{\mathrm{D}}+{\mathsf{\eta }}_{\mathrm{m}}\right)}{3{\mathsf{\eta }}_{\mathrm{D}}+2{\mathsf{\eta }}_{\mathrm{m}}}\mathsf{\beta }{\mathsf{\varphi }}_{\mathrm{r}}$ following the definitions of symbols here
v	velocity vector
zj	charge valence of ion species j
β	dimensionless diffusivity difference between the cations and the anions in symmetric binary electrolyte solutions defined as $\mathsf{\beta }=\frac{{\mathrm{D}}_1-{\mathrm{D}}_2}{{\mathrm{D}}_1{+\mathrm{D}}_2}$
δnj	perturbation of the number density
δρ	perturbation of the space charge density
${\mathsf{\delta }\mathsf{\Phi }}^{*}$	one-dimensional perturbation of the electric potential
δϕ	perturbation of the electric potential
ε	electric permittivity (coul/volt/m)
η	viscosity of the fluid (kg/m/s)
ηD	viscosity of the conducting droplet interior fluid (kg/m/s)
${\mathsf{\eta }}_{\mathrm{fr}}$	viscosity ratio defined as ${\mathsf{\eta }}_{\mathrm{D}}$/${\mathsf{\eta }}_{\mathrm{m}}$
ηm	viscosity of the ambient solution (kg/m/s)
θ	θ-coordinate in spherical coordinates (r, θ, φ)
κ	Debye length defined as $\left(\sqrt{{\displaystyle \sum _{\mathrm{j}=1}^2{\mathrm{n}}_{\mathrm{j}0}{\left(\mathrm{e}{\mathrm{z}}_{\mathrm{j}}\right)}^2}/\epsilon {\mathrm{k}}_{\mathrm{B}}\mathrm{T}}\right)$
μ	diffusiophoretic mobility of the particle defined as $\raisebox{1ex}{$\mathrm{U}$}\!\left/ \!\raisebox{-1ex}{$\nabla \mathrm{C}$}\right.$
μ*	dimensionless diffusiophoretic mobility of the particle defined as μ* = $\frac{\mathsf{\mu }}{\frac{{\mathrm{U}}_0}{\left(\raisebox{1ex}{${\mathsf{\varphi }}_0$}\!\left/ \!\raisebox{-1ex}{$\mathrm{a}$}\right.\right)}}$
ρ	space charge density (coul/m3)
ρfix	uniform charge density in the outer porous layer of the soft particle (coul/m3)
σ	surface charge density (coul/m2)
σ*	dimensionless surface charge density defined as $\frac{\mathsf{\sigma }\mathrm{a}}{{\mathsf{\epsilon }}_{\mathrm{m}}{\mathsf{\varphi }}_0}$
Φ	one-dimensional version of the electric potential distribution (volt)
φ	φ-coordinate in spherical coordinates (r, θ, φ)
${\mathsf{\Psi }}^{*}$	one-dimensional version of the stream function
$\mathsf{\psi }$	stream function
ϕ	electric potential (volt)
ϕ0	thermal potential in a binary electrolyte solution (ϕ0 = kT/z1e)
${\mathsf{\zeta }}^{*}$	dimensionless surface potential of the particle (ϕr = ϕ/ϕ0)
Operators
An	${\mathrm{A}}_{\mathrm{n}}\left(\mathrm{x}\right)\equiv {{\displaystyle \int }}_1^{\infty }\left(\frac{\mathrm{t}}{{\mathrm{r}}^{*}{}^{5-\mathrm{n}}}+\frac{1}{{\mathrm{r}}^{*}{}^{6-\mathrm{n}}}\right){\mathrm{E}}_5\left[\left(\mathrm{x}\right){\mathrm{r}}^{*}\right]e^{-\left(\mathrm{x}\right){\mathrm{r}}^{*}}{\mathrm{dr}}^{*},\mathrm{n}\in \mathrm{integer}$
C	$\mathrm{C}\equiv \frac{1}{2}{\mathrm{E}}_5\left(\mathsf{\kappa }\mathrm{a}\right)+{\mathrm{E}}_{-1}\left(\mathsf{\kappa }\mathrm{a}\right)$
E2	operator defined as E2 = $\frac{{\partial }^2}{\partial r^2}+\frac{\sin \theta }{r^2}\frac{\partial }{\partial \theta }\left(\frac{1}{\sin \theta }\frac{\partial }{\partial \theta }\right)$ in spherical coordinates (r, θ, φ)
E4	E4 = E2·E2
${\mathrm{E}}_{1\mathrm{D}}^{*}{}^2$	one-dimensional E2
${\mathrm{E}}_{1\mathrm{D}}^{*}{}^4$	${\mathrm{E}}_{1\mathrm{D}}^{*}{}^2·{\mathrm{E}}_{1\mathrm{D}}^{*}{}^2$
${\mathrm{E}}_{\mathrm{n}}$	${\mathrm{E}}_{\mathrm{n}}\left(\mathrm{t}\right)\equiv {{\displaystyle \int }}_1^{\infty }\frac{e^{-\left(\mathrm{t}\right)\mathrm{x}}}{{\mathrm{x}}^{\mathrm{n}}}\mathrm{dx},\mathrm{n}\in \mathrm{integer}$
N	$\mathrm{N}\equiv e^{\mathsf{\kappa }\mathrm{a}}\left[\left(\mathsf{\kappa }\mathrm{a}\right){\mathrm{E}}_{-1}\left(2\mathsf{\kappa }\mathrm{a}\right)+2{\mathrm{E}}_0\left(2\mathsf{\kappa }\mathrm{a}\right)+\frac{2}{\mathsf{\kappa }\mathrm{a}}{\mathrm{E}}_1\left(2\mathsf{\kappa }\mathrm{a}\right)+\left(\frac{\left(\mathsf{\kappa }\mathrm{a}\right)}{2}+\frac{1}{{\left(\mathsf{\kappa }\mathrm{a}\right)}^2}\right){\mathrm{E}}_2\left(2\mathsf{\kappa }\mathrm{a}\right)+\frac{1}{2}{\mathrm{E}}_3\left(2\mathsf{\kappa }\mathrm{a}\right)\right]$
Wn	${\mathrm{W}}_{\mathrm{n}}\left(\mathrm{x}\right)\equiv -{\mathrm{A}}_{\mathrm{n}}\left(\mathrm{x}\right)+{\mathrm{E}}_{3-\mathrm{n}}\left(2\mathrm{x}\right)+\frac{2}{\mathrm{x}}{\mathrm{E}}_{4-\mathrm{n}}\left(2\mathrm{x}\right)+\frac{1}{{\mathrm{x}}^2}{\mathrm{E}}_{5-\mathrm{n}}\left(2\mathrm{x}\right)$ $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\left[\frac{1}{2}{\mathrm{E}}_5\left(x\right)+{\mathrm{E}}_{-1}\left(x\right)\right]\left[{\mathrm{xE}}_{4-\mathrm{n}}\left(\mathrm{x}\right)+{\mathrm{E}}_{5-\mathrm{n}}\left(\mathrm{x}\right)\right],\mathrm{n}\in \mathrm{integer}$
$\nabla$	gradient operator
${\nabla }^2$	Laplacian operator
$\nabla ·$	divergence operator
${\nabla }_{\mathrm{r}}^{*}{}^2$	r-directional Laplacian operator
${\nabla }_{1\mathrm{D}}^{*}{}^2$	one-dimensional Laplacian operator
Superscripts
*	dimensionless variable
Subscripts
1	cation
2	anion
D	the contributions from the chemiphoresis component
DL	the contributions from a “Droplet”
E	the contributions from the electrophoresis component
e	equilibrium state
HS	the contributions from a “Hard Sphere”
j	jth ionic species