Abstract
The work presents a new modeling technique designed for transporting selected property while simultaneously tracking particular value of certain field variable. The model addresses the problem of transportation of superficial properties according to fluid/fluid interface evolution. Such problem arises when some superficial variable needs to be attached to the evolving interface or front defined. Several multiphase models in CFD technique lack such ability. The model proposed is illustrated by the experimental two phase system of toluene/water with surfactant specie (sodium dodecylsulfate SDS). The selected superficial property that is important to be tracked according to interface evolution is Gibbs surface excess. The computation was performed using Ansys/Fluent software with proposed models created and attached using C programming language.
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Abbreviations
- A :
-
Area (m\(^{2}\))
- \(A_\mathrm{sz}\) :
-
Szyszkowski isotherm coefficient (mol/m\(^{3}\))
- \(B_\mathrm{sz}\) :
-
Szyszkowski isotherm coefficient (–)
- c :
-
Concentration (mol/m\(^{3}\))
- D :
-
Diffusion coefficient (m\(^{2}\)/s)
- F :
-
Force (N)
- g :
-
Acceleration due to gravity (m/s\(^{2}\))
- G :
-
Gibbs free energy (J)
- J :
-
Mass flux (mol/m\(^{2}\)s)
- k :
-
Coefficient for modified Weibull function (1/s)
- m :
-
Mass (kg)
- n :
-
Unit normal vector
- \(N_\mathrm{f}\) :
-
Number of cell faces
- P :
-
Pressure (Pa)
- R :
-
Curvature radius (m)
- S :
-
General volumetric source term [mol (units of ø)/(m\(^{3}\) s)]
- t :
-
Time (s)
- u, w, v :
-
Velocity components of its magnitude (m/s)
- u :
-
Coefficient for modified Weibull function (mol/m\(^{2}\)s)
- v :
-
Coefficient for modified Weibull function (mol/m\(^{3}\))
- V :
-
Volume (m\(^{3}\))
- We :
-
Weber number
- ø :
-
General scalar quantity
- \(\alpha \) :
-
Phase volume fraction
- \(\eta \) :
-
Viscosity (Pa s)
- \(\varGamma \) :
-
Gibbs surface excess (mol/m\(^{2}\))
- \(\gamma \) :
-
Interfacial tension (N/m)
- \(\kappa \) :
-
Local interface curvature (1/m)
- \(\lambda \) :
-
Coefficient for modified Weibull function (mol/m\(^{3}\))
- \(\rho \) :
-
Phase density (kg/m\(^{3}\))
- \(\tau \) :
-
Viscous stress tensor (Pa)
- \(\upsilon \) :
-
Velocity (vector) (m/s)
- \(\varTheta \) :
-
Contact angle (\(^\circ \))
- \(\omega \) :
-
Angular velocity component (1/rad)
- ads :
-
Refers to adsorptive
- cell :
-
Refers to single cell
- f :
-
Refers to face centered value
- ø :
-
Refers to general scalar quantity
- p :
-
Refers to \(p\mathrm{th}\) phase
- q :
-
Refers to \(q\mathrm{th}\) phase
- s :
-
Refers to surface value
- x, y, z :
-
Cartesian coordinates
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The work described in this paper was supported by Politechnika Poznańska (Grant No. 03/32/DSPB/0807).
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Staszak, M. Superficial transportation model using finite volume method. Theor. Comput. Fluid Dyn. 32, 689–711 (2018). https://doi.org/10.1007/s00162-018-0473-1
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DOI: https://doi.org/10.1007/s00162-018-0473-1