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 |
γc | 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 |
ΔG0f | free standard enthalpy of formation | kJ mol−1 |
∆H | reaction enthalpy | kJ mol−1 |
∆H0 | standard reaction enthalpy | kJ mol−1 |
ΔH0f | standard enthalpy of formation | kJ mol−1 |
∆Hvap | 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 | |
Θa | advancing contact angle | ° |
Θr | 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 |
ρm | 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 |
ρel | 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, a→ | acceleration vector, in Cartesian coordinates composed of the x-component ax, y-component ay and z-component az | 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 | compactness factor | |
ceq | equivalent concentration | mol L−1 |
cp | isobaric heat capacity | J kg−1 K−1 |
cs | speed of sound | m s−1 |
cv | 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 |
dH | hydraulic diameter | m |
e | specific energy | J kg−1 |
E | energy | J |
E, E→ | electric field | V m−1 |
eV | volume-specific energy | J m−3 |
Ed | 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, F→ | force | N |
F | function value f (x) at discreet value of x | any physical unit |
feq | equivalence factor | |
Fr | Froude number, relates inertia forces to gravity forces | |
G | Gibbs (free) energy | J |
h | step width | any physical unit |
h. | specific enthalpy flow | J kg−1 s−1 |
h, H | height | m |
h | specific enthalpy | J kg−1 |
H | enthalpy | J |
H. | enthalpy flow | J s−1 |
hc | capillary height | m |
I, I | Identity matrix | |
I | electrical current | A |
Iν, 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 | |
Jν, J | Bessel function of order ν of the first kind | |
k | proportionality factor; constant | |
k | damping constant | N s m−1 |
k | wavenumber k=2πλ | |
k, k→ | volume force | N m−3 |
Kν, K | modified Bessel function of order ν of the second kind | |
K0p | equilibrium constant at standard conditions referred to the partial pressures, which are proportional to the molar concentrations | |
Kc | equilibrium constant, referred to the molar concentrations | |
K0c | equilibrium constant at standard conditions, referred to the molar concentrations | |
Kp | 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 |
lc | circumference | m |
Lc | capillary length | m |
Ls | slip length | m |
Lchar | characteristic length scale of a problem | m |
Le | Lewis number, relates mass transport to energy transport | |
m | mass | kg |
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 | |
neq | equivalent amount of substance | mol |
nD | 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, s→, x | position vector, path, in Cartesian coordinates composed of the x-component sx, y-component sy and z-component sz | m |
Pr | Prandtl number, relates momentum transport to heat transport | |
p, p˜ | pressure | Pa, bar |
q | specific heat | J kg−1 |
q. | specific heat flow | J kg−1 s−1 |
q.A | area-specific heat flow | J m−2 s−1 |
Q | heat | J |
Q | flow rate | m3 s−1 |
Q | electrical charge | C |
Q. | heat flow | J s−1 |
qV | volume-specific heat | J m−3 |
r, R, R˜ | radius | m |
r | aspect ratio | |
R | ohmic resistance | Ω |
R | residual | |
Rn,hyd | normalized hydraulic resistance | kg m−5 s−1 |
Rhyd | hydraulic resistance | kg m−4 s−1 |
RA,hyd | cross-section hydraulic resistance | mPa s m−1 |
RA,geom | geometric hydraulic resistance | kg m−5 s−1 mPa−1 s−1, m−3 mm−1 |
RS | specific gas constant | J kg−1 mol−1 |
rm | 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 |
s→ | vector to the point S in space | |
S | spreading parameter | J m−2 |
S | entropy | J K−1 |
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 |
s. | specific entropy flow | J kg−1 s−1 |
t, t˜ | time | s |
T | period length | s |
T | trial function | |
Tν, T | Chebyshev polynomial of order ν of the first kind | |
Tb | boiling temperature | K, C |
T | temperature | K |
u | specific internal energy | J kg−1 |
U | internal energy | J |
U | voltage | V |
Uν, U | Chebyshev polynomial of order ν of the second kind | |
uV | volume-specific internal energy | J m−3 |
v,v→,v˜,v→˜ | velocity vector, in Cartesian coordinates composed of the x-component vx, y-component vy and z-component vz | m s−1 |
v | specific volume | m3 kg−1 |
V. | volume flow | kg m−3 |
V | volume | m3 |
VLJ | Lennard-Jones potential | J |
w | mass fraction | kg kg−1 |
w. | specific work flow | J kg− 1 s−1 |
w, W | width | m |
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 dfdx(x) of the function f (x) at discreet value of x | any physical unit |
Yν, Y | Bessel function of order ν of the second kind; Weber function of order ν | |
z | number of charges transferred in an electrochemical reaction | |