Page 10 - 81Sulfonation-Sulfation Processing Technology for Anionic Surfactant Manufacture_opt

Sulfonation/Sulfation Processing Technology for Anionic Surfactant Manufacture 277

 C SO    C SO  d
v z 3   (D SO  D T ) 3   r δ ≤ y ≤ (1)
z  y   3 y   2

 C    C 
v A  (D  D ) A  r 0 ≤ y ≤ δ (2)
z  A T 
z  y   y  
As discussed by Knaggs, (2004), even if the liquid film is turbulent and does wavy flow then
turbulent diffusivity cannot be neglected, this and turbulent viscosity in the liquid phase can
be taken of work suggested by Yih & Liu (1983).
0,5
  0,5 2 
D   2    y   ( / )   
T   0,5 0,5 1 0,64(y )   1 exp  w   f  (3)

 
 T   w    A      
  
3   
     y 
w  1   L  (4)
   G   L       
 
Turbulent Schmidt number is evaluated from the Cebeci’s modification of the van Driest
model and is further modified as:

v T 1 exp( y    ( / w ) 0,5 / A  )
Sc   (5)
T  0,5 

D 1 exp( y   ( / ) /B )
T w
5 i 1

B  Sc  0,5 C i   10 log Sc (6)
i 1
with A + = 25,1; C 1 = 34,96; C 2 = 28,97; C 3 = 13,95; C 4 = 6,33 and C 5 = –1,186. For non–volatile
liquids such as methyl stearate, the vapor pressure is zero at working temperatures. At the
interface, it is assumed that Henry and Raoult’s laws are applicable to determine the SO 3
solubility. The Henry constant m, is determined from the SO 3 vapor pressure:
N G  k  C G  mC i (7)
SO 3 G SO 3 SO 3 
k  0,704
G  0,8Sc (McCready & Hanratty, 1984) (8)
u
where the turbulent velocity is defined as:
0,5
  
u   G  (9)
  G 

4.2 Momentum balance
Axial liquid velocity v z, can be found from the momentum equation after neglecting the
pressure gradient and axial terms (Figure 9). The flow profile of the liquid falling is

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