Partial wetting model

The partial wetting model was adapted by Lee and Smith [40] to yield criteria for determining conditions under which negligible transport or partial wetting would obtain. To assure no pore diffusion limitations, it was found that the conventional criteria... 

Figure 3.3.1. Partial wetting model predictions for reaction by a...

Turek [80] using a simplified partial wetting model was able to reconcile measurements from a slurry, two stirred "basket reactors and a trickle bed. The reaction was glucose hydrogenation. 

The following partial wetting model of Bondi (1971), modified by Satterfield (1975), was used to correlate the apparent rate constant, Kpp.nos, with the superficial liquid mass velocity, G p, and the intrinsic rate constant, k HDs ... 

Reaction temperature and H2/oil ratio are other two process variables that favor catalyst wetting efficiency and are not considered explicitly in the partial wetting model. The theoretical curve of Figure 8.20 is valid only for specific conditions of reaction temperature and H2/oil ratio. Increasing any of these variables, particularly reaction temperature, will displace upward the zone in which catalyst wetting efficiency is a strong function of liquid velocity. 

The theory of seaweed formation does not only apply to solidification processes but in fact to the completely different phenomenon of a wettingdewetting transition. To be precise, this applies to the so-called partial wetting scenario, where a thin liquid film may coexist with a dry surface on the same substrate. These equations are equivalent to the one-sided model of diffusional growth with an effective diffusion coefficient which depends on the viscosity and on the thermodynamical properties of the thin film. 

The adsorption of block copolymers from a selective solvent was considered by Ligoure (1991). He predicted the existence of surface micelles (see Fig. 3.22) in the case when the block interacting unfavourably with the solvent only partially wets the surface. The model predicts a critical surface micellar concentration (csmc) that differs from the bulk cmc. When the contact angle, which characterizes the interfacial interactions between the copolymer, adsorbing surface, and solvent is lower than some universal value, surface micelles were predicted to appear at a lower copolymer concentration than bulk ones. Experimental results on surfaces are discussed in Section 3.8.4. 

Malek A, Li K, and Teo WK. Modeling of microporous hollow fiber membrane modules operated under partially wetted conditions. Ind. Eng. Chem. Res. 1997 36 784-793. 

Iliuta, L Larachi, F. Al-Dahhan, M.H. Doubleslit model for partially wetted trickle flow hydrodynamics. Am. Inst. Chem. Eng. J. 2000, 46, 597. 

The developed dynamic reactor model for the simulation studies of the unsteady-state-operated trickle-flow reactor is based on an extended axial dispersion model to predict the overall reactor performance incorporating partial wetting. This heterogeneous model consists of unsteady-state mass and enthalpy balances of the reaction components within the gas, liquid and catalyst phase. The individual mass-transfer steps at a partially wetted catalyst particle are shown in Fig. 4.5. 

Gessinge GH, Fischmei HF, Lukas HL (1973) Model for second-stage liquid-phase sintering with a partially wetting liquid. Acta MetaU 21 715-724... 

The Bravo and Fair correlation (122). This correlation is based on the two-film model, that assumes resistance to mass transfer in both the vapor and liquid phases. The correlation treats the mass transfer coefficient independently from the interfadal area, and accounts for effects of partial wetting, The correlation is based on extensive commercial and pilot scale efficient measurements for first generation packings and Psill rings, and applies to random packings only. 

The Cassie-Baxter-Wenzel theory [44, 47,48] defines the critical contact angle value on the smooth surface above this value, the Cassie-Baxter model is more stable wetting state and below this value the Wenzel model is the most stable wetting state. If the measured contact angle on a smooth surface is lower than this critical value and if the superhydrophobic behaviour is observed, the transition between the two models should be possible like, for example, with the LDPE surface treated in both plasmas. In this case, the roughness factor is 1.043, the contact angle on the dried surface reaches a value of 171° and the contact angle on the same surface partially wetted with water vapour or dipped in water is only 140°. 

Several authors have reported modelling of multi-phase membrane reactors and, in particular, of three-phase catalytic membrane reactors. Harold and Watson (1993) have considered the situation of a porous catalytic slab partially wetted by a liquid from one side and by a gas phase on the other side, and they have pointed out the complexity of the problem in presence of an exothermic reaction, capillary condensation and vaporization. 

Hydrodesulfurization is technically performed either in the gas phase or in a trickle bed reactor, that is, in a three-phase system with gaseous H2, liquid oil, and a solid catalyst. Trickle bed reactors are more complicated with respect to hydrodynamics and partial wetting of the catalyst that is unwanted but has to be considered, for example, for reactor modeling. Based on the above given reaction conditions, we can easily determine which feedstock has to be desulfurized in a trickle bed reactor and which feedstock completely forms a gas phase (vapor). The molar ratio of hydrogen (fresh and recycled) to oil (for a mean carbon number of about 20) is about two. Thus the partial pressure that the oil has to build up to be completely vaporized is about 3 of the total pressure. 

More recent modeling mainly follows the approach outlined in Sections 14.2.4 and 14.2.5. Mills and Dudukovic [1983] applied a generalized dispersion model with partially wetted pellets. A review by Gianetto and Specchia [1992] and the text books of Ramachandran and Chaudhari [1983] and of Shah [1979] provide further insight into the modeling of trickle bed reactors. 

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