|
η
m
|
polymer viscosity of matrix |
|
η
d
|
polymer viscosity of droplet |
|
γ
|
shear rate |
| Γ |
interfacial tension |
|
R
|
droplet radius |
|
D
0
|
droplet diameter |
|
Ca
|
capillary number |
|
Ca
crit
|
critical capillary number |
|
p
|
viscosity radio |
|
G
|
ellipsoid droplet tensor |
|
L
|
velocity gradient tensor |
|
Df
|
droplet deformability |
|
L
|
major axis of droplet |
|
B
|
minor axis of droplet |
|
W
|
width of droplet |
|
θ
|
orientation angle of droplet |
|
τ
r
|
surface-tension relaxation time |
|
e
ij
|
deformation rate tensor |
|
w
ij
|
vorticity tensor |
|
f
1
|
MM model parameter |
|
f
2
|
MM model parameter |
|
k* |
simplified capillary number |
|
d
|
diameter of the split sub-droplet |
|
d* |
critical diameter of fiber breakup |
|
t
b
|
time required for droplet breakup |
|
N
d
|
total number of droplets of volume V |
|
X
m
|
main wave number |
|
p
coll
|
collision probability |
|
t
loc
|
local residence time |
|
p
exp
|
liquid film discharge probability |
|
h
c
|
critical thickness of the liquid film for breakup |
|
D
eq
|
diameter at equilibrium |
|
|
diameter at zero component |
|
R* |
radii of droplets after coalescence |
|
nk
|
number of droplets of volume kV1
|
|
C(i, j) |
coalescence coagulation kernel |
|
F(i) |
overall breakup frequency |
|
nf(i) |
number of fragments formed at breakup of a droplet of volume iV1 |
|
ω(i, j) |
probability that a fragment formed by the breakup of a droplet of volume jV1 will have volume iV1 |
|
η
αp
|
apparent viscosity of the blend |
|
EDK
|
volume energy |
|
R
0
|
droplet radius for ϕ = 0 |
|
tB* |
dimensionless breakup time |
|
R
c
|
critical value for breakup |
|
R* |
ratio of R and Rc |
|
D
|
diffusion coefficient |
|
μ
|
chemical potential |
|
c
|
concentration of the fluid |
|
ξ
|
thermal noise |
|
fσ,α(x,t) |
particle probability distribution function |
|
eα
|
discrete particle velocity |
|
G(|eα|) |
interaction function of pseudo-potential lattice Boltzmann method |
|
|
interaction constant |
|
w(|eα|2) |
weight function of LBM |
|
ρ
|
density |
|
u
|
velocity |
|
P
|
pressure |
|
T
|
temperature |
|
c
p
|
specific heat |
|
λ
|
heat conductivity |
|
η
|
viscosity |
|
A
|
area tensor |
| dim |
dimension |
|
v
σ
|
kinematic viscosity of component σ |
|
ρ
σ
|
density of component σ |
|
τ
σ
|
relaxation time of component σ |
|
j
σ
|
momentum flux of component σ |