Model of Prince and Blanch (1990). The coalescence rate is calculated by. More...
Public Member Functions  
TypeName ("PrinceBlanch")  
Runtime type information. More...  
PrinceBlanch (const populationBalanceModel &popBal, const dictionary &dict)  
virtual  ~PrinceBlanch () 
Destructor. More...  
virtual void  precompute () 
Precompute diameter independent expressions. More...  
virtual void  addToCoalescenceRate (volScalarField &coalescenceRate, const label i, const label j) 
Add to coalescenceRate. More...  
Public Member Functions inherited from coalescenceModel  
TypeName ("coalescenceModel")  
Runtime type information. More...  
declareRunTimeSelectionTable (autoPtr, coalescenceModel, dictionary,(const populationBalanceModel &popBal, const dictionary &dict),(popBal, dict))  
coalescenceModel (const populationBalanceModel &popBal, const dictionary &dict)  
autoPtr< coalescenceModel >  clone () const 
virtual  ~coalescenceModel () 
Destructor. More...  
Additional Inherited Members  
Static Public Member Functions inherited from coalescenceModel  
static autoPtr< coalescenceModel >  New (const word &type, const populationBalanceModel &popBal, const dictionary &dict) 
Protected Attributes inherited from coalescenceModel  
const populationBalanceModel &  popBal_ 
Reference to the populationBalanceModel. More...  
Model of Prince and Blanch (1990). The coalescence rate is calculated by.
with the coalescence efficiency
the turbulent collision rate
the buoyancydriven collision rate
and the laminar shear collision rate
The rise velocity of bubble i is calculated by
the equivalent radius by
the collision cross sectional area by
and the shear strain rate by
Note that in equation 2, the bubble radius has been substituted by the bubble diameter, which leads to a different coefficient in equation 8. Also the expression for the equivalent radius, equation 19 was corrected.
=  Turbulent collision rate [m3/s]  
=  Buoyancydriven collision rate [m3/s]  
=  Laminar shear collision rate [m3/s]  
=  Coalescence efficiency []  
=  Equivalent radius [m]  
=  Density of continuous phase [kg/m3]  
=  Surface tension [N/m]  
=  Initial film thickness [m]  
=  Critical film thickness [m]  
=  Continuous phase turbulent dissipation rate [m2/s3]  
=  Diameter of bubble i [m]  
=  Diameter of bubble j [m]  
=  Rise velocity of bubble i [m/s]  
=  Collision cross sectional area [m2]  
=  Gravitational constant [m/s2]  
=  Continuous phase shear strain rate [1/s]  
=  Continuous phase velocity field [m/s] 
Reference:
Prince, M. J., & Blanch, H. W. (1990). Bubble coalescence and break‐up in air‐sparged bubble columns. AIChE journal, 36(10), 14851499.
Property  Description  Required  Default value 

C1  coefficient C1  no  0.356 
h0  initial film thickness  no  1e4m 
hf  critical film thickness  no  1e8m 
turbulence  Switch for collisions due to turbulence  yes  none 
buoyancy  Switch for collisions due to buoyancy  yes  none 
laminarShear  Switch for collisions due to laminar shear  yes  none 
Definition at line 259 of file PrinceBlanch.H.
PrinceBlanch  (  const populationBalanceModel &  popBal, 
const dictionary &  dict  
) 
Definition at line 55 of file PrinceBlanch.C.
References Foam::dimLength, Foam::dimVelocity, populationBalanceModel::mesh(), dimensioned< Type >::name(), coalescenceModel::popBal_, IOobject::time(), and Foam::Zero.

inlinevirtual 
Destructor.
Definition at line 302 of file PrinceBlanch.H.
TypeName  (  "PrinceBlanch"  ) 
Runtime type information.

virtual 
Precompute diameter independent expressions.
Reimplemented from coalescenceModel.
Definition at line 115 of file PrinceBlanch.C.
References Foam::fvc::grad(), Foam::mag(), Foam::sqrt(), and Foam::symm().

virtual 
Add to coalescenceRate.
Implements coalescenceModel.
Definition at line 125 of file PrinceBlanch.C.
References Foam::cbrt(), sizeGroup::dSph(), Foam::exp(), Foam::log(), Foam::mag(), sizeGroup::phase(), Foam::constant::mathematical::pi(), Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), and Foam::sqrt().