Thickness of liquid film

Zl is the thickness of liquid film through which diffusion occurs, and Dl is the diffusivity in the liquid phase. 

There have been numerous studies of the effects of gas streams on the thicknesses of liquid films flowing in contact with them. Cases studied in the literature refer mainly to gas/film flow in vertical tubes or channels or horizontal pipes. The latter case will not be considered here. The gas/film flows may be countercurrent, cocurrent upwards, or cocurrent downwards. Only the most important studies can be discussed here. 

In spite of these apparently seriously restricting assumptions, Dukler (D15) has shown that his theory for downward cocurrent flow is in agreement with experimental gas/film thickness data reported by Charvonia (C4) and McManus (M3). Hewitt et al. (H10) and Collier and Hewitt (C13) have carried out analyses of numerous experimental data on the thicknesses of liquid films in upward cocurrent flow in terms of the Dukler theory and other simpler theories such as those due to Anderson and Mantzouranis (A5) and Calvert and Williams (C2) (Section III, F, 4). The experimental and calculated values are in moderate agreement in the case of the Dukler and the Anderson and Mantzouranis treatments. The discrepancies are probably due to the simplifying assumptions made in the theoretical treatments. 

From the remarks above, it can be seen that, although there are many experimental data available on the thicknesses of liquid films in the presence of gas streams, further work, both experimental and theoretical, will be required before film thicknesses can be predicted accurately under such conditions. 

C4. Charvonia, D. A., A study of the mean thickness of liquid films and surface characteristics in annular two-phase flow in a vertical pipe. Purdue Univ., Lafayette, Indiana, Jet Propulsion Lab., Rept. 1-59-1, May 1959. 

In practice, the thickness of liquid films in trickle beds has been estimated to vary between 0.01 and 0.2 mm (0.004 and 0.008 in). The dynamic liquid holdup fraction is 0.03 to 0.25, and the static fraction is 0.01 to 0.05. The high end of the static fraction includes the liquid that partially fills the pores of the catalyst. The effective gas-liquid interface is 20 to 50 percent of the geometric surface of the particles, but it can approach 100 percent at high liquid loading. This results in an increase of reaction rate as the amount of wetted surface increases (i.e., when the gas-solid reaction rate is negligible). 

The border cross-section shape (border profile) was determined photographically. The size of the balloon was chosen so that at the instant of contact with dodecahedron faces a sufficiently high inflection (> 300%) was ensured. This was done to diminish the possible anisotropy of rubber balloon elements. Thus, further deformation of the balloon during its transformation into a polyhedron would not be more than 10 - 30%. To check whether the balloon regions deformed, differently the position of control points situated in the centre of films and in the middle of borders was monitored. When the dodecahedron faces were wetted, the relative deformation of the balloon regions was practically identical and the shape of the border cross-section surface was spherical. The thickness of liquid films between the dodecahedron faces and the balloon surface was determined conductometrically. 

Case A Small concentration of solids or large particle size compared to the thickness of liquid film In this case, solid dissolution during diffusion of species C in the liquid film can be neglected. The solid dissolution and chemical reaction can be assumed to be processes in series. 

Various methods for estimating KLs are described by Satterfield.150 The most conservative estimate of KLS is obtained as KI S = D/<5,, where D is the molecular diffusivity of the reactant in the liquid phase and <5L the average thickness of liquid film surrounding the particles. This estimation assumes no turbulence in the liquid film. The average thickness of the liquid film can be obtained from a knowledge of the dynamic liquid holdup and the outside area of catalyst particles per unit volume of the reactor, os. For example, if the dynamic liquid holdup is 50 percent of the void volume e, then <5L = e/2as. Various methods for estimating fcL and Ks under trickle-flow conditions are described in Chap. 6. 

Comonomers mixture 73.4% of triethylene glycol (TEGDA) and 26.6% of UVE74 (Setacure AP570). Belt speed 8 m/min. Photoinitiator concentration 0.1 moll" in terms of photoreactive groups. Thickness of liquid film SOpm Number of passes under UV lamps required to cure the acrylic formulation Determined by H NMR analysis... 

The highest intensity of evaporation occurs in the zone II. The thickness of liquid film in the zone I is close to the size of molecular sorption film and there are no the favorable conditions for process of vaporization. In the zone III the liquid film is thick, so a thermal resistance is higher than in zone II. Thus the optimal conditions for intensive evaporation are in the zone II. There is great number of such zones over all porous surfaces, so the total area of evaporation is very large. Thus we have excellent condition for the intense heat transfer. 

Figures 3 and 4 show the variations in time of the thickness of liquid film for water and carbontetrachloride vapour. The experimental conditions are indicated in the figures. The initial thickness of the film is taken to be 11 nm for water vapour and 16 nm for carbontetrachloride vapour. The temperature parameter ot is taken to be 0.44675 for the both cases. These figures show that good conformity between the experiments and the theory is given for Oc = 0.10 (a = 0.35) in the case of water vapour and for Oc = 0.20 (a = 0.71) in the case of carbontetrachloride vapour. Theoretical values of c.p. and c.c., evaluated by Eqs.(5)> (6), and (7) are 0.14 and 0.50 respectively for water vapour and are 0.20 and 0.71 for carbontetrachloride vapour. The value of c.c. of water vapour is in rather good agreement with the Hatamiya and Tanaka s value [9]- The experimental and theoretical values of c.p. and c.c. of water vapour and carbontetrachloride vapour are significantly less than those for the complete capture of molecules on the condensed phases. The reason is the same as for methanol vapour.

J. F. Le Coz, C. Catalano, and T. Baritaud. Application of laser induced fluorescence for measuring the thickness of liquid films on trasparent walls. In 7th Int. Symposium on application of laser techniques to fluid mechanics, 1997. 

E Generalized entry coefficient g Gravitational constant h Thickness of liquid film hi . Thickness of film i... 

Critical rupture thickness of liquid film H Initial foam height without antifoam... 

Kos overspray part of suspension (-) thickness of liquid film (m) m mass (k ... 

In this contribution, the simphfication has been made and it was assumed that hquid film on particles has a constant thickness (Heinrich, 2001). To consider liquid film on particle surface correctly, the radius for contact detection of DEM has been increased by the thickness of liquid film. To detect collision between two wet particles with radii Ri and R2 the following criteria has been used ... 

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