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List of Symbols

Symbol	Explanation	Unit
α	thermal diffusivity	mm² s⁻¹
α	correction factor
β	artificial compressibility factor
Γ	Gamma function
γ	surface tension	mN m⁻¹, J m⁻²
γ	free surface energy	J m⁻², N m⁻¹
γ_c	critical surface tension	mN m⁻¹, mJ m⁻²
δ	delta function
δ	gas dilution factor
∆G⁰	free standard enthalpy of reaction	kJ mol⁻¹
$Δ G_{f}^{0}$ $Δ G_{f}^{0}$	free standard enthalpy of formation	kJ mol⁻¹
∆H	reaction enthalpy	kJ mol⁻¹
∆H⁰	standard reaction enthalpy	kJ mol⁻¹
$Δ H_{f}^{0}$ $Δ H_{f}^{0}$	standard enthalpy of formation	kJ mol⁻¹
∆H_vap	enthalpy of vaporization	kJ mol⁻¹
	roughness height	m
	depth of the potential well in the Lennard-Jones potential	J
ζ	Riemann zeta function
η	viscosity	mPa s, cP
η	residual function
Θ	contact angle	°
Θ	Heaviside function
Θ_a	advancing contact angle	°
Θ_r	receding contact angle	°
κ	curvature	m⁻¹
κ	conductivity	S, Ω ⁻¹ m⁻¹
λ	mean free path of a gas molecule before experiencing a collision	m
λ	thermal conductivity	W m⁻¹ K⁻¹
λ	wavelength	m
µ	chemical potential	J
ν	frequency	s⁻¹
ν	kinematic viscosity	m² s⁻¹
ρ_m	density per length	g cm⁻⁴, kg m⁻⁴
ρ	specific resistance	Ω m
ρ	mass concentration	g L⁻¹
ρ	density	kg m⁻³
ρ_el	charge density	A s m⁻³, C m⁻³
σ	diffusion or transport mobility	kg s⁻¹
σ	atom distance for which the Lennard-Jones potential is 0	m
σ	normal stress	Pa, N mm⁻²
τ	shear stress	Pa, N mm⁻²
Ψ	dissipation coeﬃcient	s⁻²
Ψ	gravitational potential	m² s⁻²
ω	relaxation parameter
ω	angular frequency, angular velocity	s⁻¹
a, $\vec{a}$ $\vec{a}$	acceleration vector, in Cartesian coordinates composed of the x-component a_x, y-component a_y and z-component a_z	m s⁻²
A	area	m²
b	molality	mol kg⁻¹
B	Bernoulli number
Bo	Bond number, relates buoyancy forces to surface tension
c	molar concentration	mol L⁻¹
C	capacitance	F
$C$ $C$	compactness factor
c_eq	equivalent concentration	mol L⁻¹
c_p	isobaric heat capacity	J kg⁻¹ K⁻¹
c_s	speed of sound	m s⁻¹
c_v	isochoric heat capacity	J kg⁻¹ K⁻¹
Ca	Capillary number, relates viscous forces to surface tension
c	constant
d	diameter	m
d	thickness	m
D	spring constant	N m⁻¹
D	diffusion coeﬃcient	m² s⁻¹
d_H	hydraulic diameter	m
e	specific energy	J kg⁻¹
E	energy	J
E, $\vec{E}$ $\vec{E}$	electric field	V m⁻¹
e_V	volume-specific energy	J m⁻³
E_d	bond energy	J
E⁰	Standard reduction potentials	V
Ec	Eckert number, relates kinetic energy to enthalpy
Eo	Eötvös number, relates buoyancy forces to surface tension
erf	error function
erfc	complementary error function
f	Darcy friction factor
F, $\vec{F}$ $\vec{F}$	force	N
F	function value f (x) at discreet value of x	any physical unit
f_eq	equivalence factor
Fr	Froude number, relates inertia forces to gravity forces
G	Gibbs (free) energy	J
h	step width	any physical unit
$\dot{h}$ $\dot{h}$	specific enthalpy flow	J kg⁻¹ s⁻¹
h, H	height	m
h	specific enthalpy	J kg⁻¹
H	enthalpy	J
$\dot{H}$ $\dot{H}$	enthalpy flow	J s⁻¹
h_c	capillary height	m
I, I	Identity matrix
I	electrical current	A
I_ν, I	modified Bessel function of order ν of the first kind
J	mass flux	kg m⁻² s⁻¹
J, J	Jacobian matrix, commonly used for coordinate system transformation
J_ν, J	Bessel function of order ν of the first kind
k	proportionality factor; constant
k	damping constant	N s m⁻¹
k	wavenumber $k = \frac{2 π}{λ}$ $k = \frac{2 π}{λ}$
k, $\vec{k}$ $\vec{k}$	volume force	N m⁻³
K_ν, K	modified Bessel function of order ν of the second kind
$K_{p}^{0}$ $K_{p}^{0}$	equilibrium constant at standard conditions referred to the partial pressures, which are proportional to the molar concentrations
K_c	equilibrium constant, referred to the molar concentrations
$K_{c}^{0}$ $K_{c}^{0}$	equilibrium constant at standard conditions, referred to the molar concentrations
K_p	equilibrium constant referred to the partial pressures, which are proportional to the molar concentrations
Kn	Knudsen number, relates the mean free path to a characteristic length of a problem, allows determining if the continuum hypothesis is valid
l	length	m
l_c	circumference	m
L_c	capillary length	m
L_s	slip length	m
L_char	characteristic length scale of a problem	m
Le	Lewis number, relates mass transport to energy transport
m	mass	kg
$\dot{m}$ $\dot{m}$	mass flow	kg s⁻¹
M	molecular weight or molar mass	g mol⁻¹
M	torque	N m
M	Mach number, relates the flow velocity to the speed of sound, allows determining if a gas can be considered as being incompressible
Ma	Marangoni number, relates Marangoni forces (due to temperature gradients) to viscous forces
n	amount of substance	mol
n	speed of rotation	min⁻¹
N	number of molecules
n_eq	equivalent amount of substance	mol
n_D	number density, i.e., the number of molecules per volume	m⁻³
O	error function
Oh	Ohnesorge number, relates viscous forces to the produce of inertia and surface tension forces
p	momentum	kg m s⁻¹
P	electrical power	W
p₀	standard pressure	Pa
Pe	mass transport related Péclet number, relates convective to diffusive transport
pH	pH value
pI	isoelectric point
s, $\vec{s}$ $\vec{s}$ , x	position vector, path, in Cartesian coordinates composed of the x-component s_x, y-component s_y and z-component s_z	m
Pr	Prandtl number, relates momentum transport to heat transport
p, $\tilde{p}$ $\tilde{p}$	pressure	Pa, bar
q	specific heat	J kg⁻¹
$\dot{q}$ $\dot{q}$	specific heat flow	J kg⁻¹ s⁻¹
$\dot{q} A$ $\dot{q} A$	area-specific heat flow	J m⁻² s⁻¹
Q	heat	J
Q	flow rate	m³ s⁻¹
Q	electrical charge	C
$\dot{Q}$ $\dot{Q}$	heat flow	J s⁻¹
q_V	volume-specific heat	J m⁻³
r, R, $\tilde{R}$ $\tilde{R}$	radius	m
r	aspect ratio
R	ohmic resistance	Ω
$R$ $R$	residual
R_n,hyd	normalized hydraulic resistance	kg m⁻⁵ s⁻¹
R_hyd	hydraulic resistance	kg m⁻⁴ s⁻¹
R_A,hyd	cross-section hydraulic resistance	mPa s m⁻¹
R_A,geom	geometric hydraulic resistance	kg m⁻⁵ s⁻¹ mPa⁻¹ s⁻¹, m⁻³ mm⁻¹
R_S	specific gas constant	J kg⁻¹ mol⁻¹
r_m	atom distance for which the Lennard-Jones potential is minimal	m
Re	Reynolds number, relates the inertial forces to the viscous forces, allows determining if a flow can be considered to be laminar
s	specific entropy	J K⁻¹ kg⁻¹
s	arclength	m
$\vec{s}$ $\vec{s}$	vector to the point S in space
S	spreading parameter	J m⁻²
S	entropy	J K⁻¹
$\dot{S}$ $\dot{S}$	entropy flow	J K⁻¹ s⁻¹
S⁰	standard entropy	J mol⁻¹
Sc	Schmidt number, relates momentum transport to mass transport
sign	signum function
w	specific work	J kg⁻¹
$\dot{s}$ $\dot{s}$	specific entropy flow	J kg⁻¹ s⁻¹
t, $\tilde{t}$ $\tilde{t}$	time	s
T	period length	s
T	trial function
T_ν, T	Chebyshev polynomial of order ν of the first kind
T_b	boiling temperature	K, C
T	temperature	K
u	specific internal energy	J kg⁻¹
U	internal energy	J
U	voltage	V
U_ν, U	Chebyshev polynomial of order ν of the second kind
u_V	volume-specific internal energy	J m⁻³
$v, \vec{v}, \tilde{v}, \tilde{\vec{v}}$ $v, \vec{v}, \tilde{v}, \tilde{\vec{v}}$	velocity vector, in Cartesian coordinates composed of the x-component v_x, y-component v_y and z-component v_z	m s⁻¹
v	specific volume	m³ kg⁻¹
$\dot{V}$ $\dot{V}$	volume flow	kg m⁻³
V	volume	m³
V_LJ	Lennard-Jones potential	J
w	mass fraction	kg kg⁻¹
$\dot{w}$ $\dot{w}$	specific work flow	J kg⁻ ¹ s⁻¹
w, W	width	m
$\dot{W}$ $\dot{W}$	work flow	J s⁻ ¹
W	work	J
We	Weber number, relates inertia forces to surface tension
x	molar fraction	mol mol⁻¹
X	value of the derivative $\frac{d f}{d x} (x)$ $\frac{d f}{d x} (x)$ of the function f (x) at discreet value of x	any physical unit
Y_ν, Y	Bessel function of order ν of the second kind; Weber function of order ν
z	number of charges transferred in an electrochemical reaction