Development of transport equations for multiphase system—I

Zanotti, Federica; Carbonell, Ruben G.

doi:10.1016/0009-2509(84)80026-3

Cited by 97 publications

(34 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They show that these are equivalent under steady state conditions and "effectively indistinguishable when the rate-controlling process is either external mass transfer or internal mass transfer" under transient conditions. From a more fundamental perspective, Zanotti and Carbonell showed in [39] that, for the non-reactive case, two-equation models have a time-asymptotic behavior which can be described in terms of a one-equation model. The demonstration is based on the moments matching principle at long times and does not assume local mass equilibrium.…”

Section: A One-equation Non-equilibrium Modelmentioning

confidence: 98%

Modeling non-equilibrium mass transport in biologically reactive porous media

Davit

Debenest

Wood

et al. 2010

Advances in Water Resources

View full text Add to dashboard Cite

Section: A One-equation Non-equilibrium Modelmentioning

confidence: 98%

Modeling non-equilibrium mass transport in biologically reactive porous media

Davit

Debenest

Wood

et al. 2010

Advances in Water Resources

View full text Add to dashboard Cite

“…In this study in order to aid in the solution of the (solute) species continuity equation [15], the method of spatial (area) averaging is used [16][17][18][19][20]. In particular, this methodology states that any variable of interest, h(x, y, z), can be decomposed into a simple addition of two expressions, i.e., the cross-sectional area average, 7 e h(x, y, z)8, and a "deviation" function from such an average value, h (x, y, z).…”

Section: Introductionmentioning

confidence: 99%

Role of geometrical dimensions in electrophoresis applications with orthogonal fields

Oyanader¹,

Arce²

2005

Electrophoresis

View full text Add to dashboard Cite

The role of geometrical dimensions in electrophoresis applications with axial and orthogonal (secondary) electric fields is investigated using a rectangular capillary channel. In particular, the role of the applied orthogonal electrical field in controlling key parameters involved in the effective diffusivity and effective (axial) velocity of the solute is identified. Such mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been studied. Moreover, explicit analytical expressions are derived for the effective parameters, i.e., diffusivity and convective velocity as functions of the applied (orthogonal) electric field. Previous attempts (see Sauer et al., 1995) have only led to equations for these parameters that require numerical solution and, therefore, limited the use of such results to practical applications. These may include, for example, the design of separation processes as well as environmental applications such as soil reclamation and wastewater treatment. An illustration of how a secondary electrical field can aid in reducing the optimal separation time is included.

show abstract

“…In this contribution and in order to aid in the solution of the (solute/analyte) species continuity equation [23], the method of spatial (area) averaging is used [14,16,[24][25][26]. In particular, this methodology states that any variable of interest, h(x,y,z), can be decomposed into a simple addition of two expressions, i.e.…”

Section: System Descriptionmentioning

confidence: 99%

Optimal separation times for electrical field flow fractionation with Couette flows

et al. 2008

View full text Add to dashboard Cite

The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. Mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field.

show abstract

Development of transport equations for multiphase system—I

Cited by 97 publications

References 25 publications

Modeling non-equilibrium mass transport in biologically reactive porous media

Modeling non-equilibrium mass transport in biologically reactive porous media

Role of geometrical dimensions in electrophoresis applications with orthogonal fields

Optimal separation times for electrical field flow fractionation with Couette flows

Contact Info

Product

Resources

About