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. 2023 Feb 11;13(4):698. doi: 10.3390/nano13040698
C&T work from Coulaloglou and Tavlarides [8]
DSD drop size distribution
DDSD daughter drop size distribution
PBE population balance equation
RRMSD relative root-mean-square deviation
TEM transmission electron microscopy
w/o water-in-oil
2D two-dimensional
Symbols Used
A [m2] area
a [-] constant in beta distribution
B˙ [m4s1] birthrate in PBE
b [-] constant in beta distribution
C [-] measure of the width of the normal distribution
c [-] fitparameter in PBE submodels
cnp,c [-] dimensionless damping factor in coalescence efficiency
cdes [J1] fitparameter in the energybarrier modell
d [m] drop diameter (d and d are used to differentiate between drops)
d32 [m] Sauter mean diameter
D˙ [m4s1] death rate in PBE
D [m] tank diameter
E [J] energy
F [m3s1] coalescence rate
f [m4] density function of number
fd [-] ratio of daughter drop volume to mother drop volume
g [s1] breakage rate
h [m] height
H [m] height
n [s1] stirring speed
np [-] number of particles in the system
nd [-] desorbed number of particles
P [Js1] power
q       [m1] density function
Q [-] cumulative function
r [m] radius
s [m] strength
t [s] time
T [K] temperature
V [m3] volume
w [-] mass fraction
w [m] wide
Greek Symbols
β [-] daughter drop size distribution
η [Pas] dynamic viscosity
ϵ [Wkg1] mass specific energy dissipation rate
ε [-] voidage
λ [-] coalescence efficiency
κ [Sm1] electrical conductivity
ν [-] number of daughter drops
φ [-] dispersed-phase volume fraction
ρ [kgm3] density
γ [Nm1] interfacial tension
γ˙ [s1] shear rate
σ [m3] standard deviation
μ [m] mean value
θ [] contact angle
Θ [-] interface coverage degree by particles
ξ [m3s1] coalescence frequency
ζ [V] zeta potential
Subscripts
ads adsorption
b breakage
b baffle
c continous phase
c coalescence
cov covered
d dispersed phase
d desorbed
d daughter
des desorption
eff effective
exp experimental
e/s between endoscope and stirrer
g gap
in initial
m mother
max maximum
min minimum
np nanoparticle
o organic phase
o,w oil/water interface
p particle
sb stirrer blades
sim simulated
st stirrer
stat in steady-state
tot total
3 volume-based