Mears effect

Because of the Mears effect (wire corrodes faster per unit of area than more massive materials), galvanized wire corrodes some 10-80% faster than galvanized sheet (see Table 2.13 also see the series of Haynie et al. papers for explanations related to deposition rates of sulfur dioxide), and thin wire corrodes faster than thick wire. 

Sohd Catalysts Processes with solid catalysts are affected by diffusion of heat and mass (1) within the pores of the pellet, (2) between the fluid and the particle, and (3) axially and radially within the packed bed. Criteria in terms of various dimensionless groups have been developed to tell when these effects are appreciable. They are discussed by Mears (Ind. Eng. Chem. Proc. Des. Devel., 10, 541-547 [1971] Jnd. Eng. Chem. Fund., 15, 20-23 [1976]) and Satterfield (Heterogeneous Cataly.sls in Practice, McGraw-Hill, 1991, p. 491). 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Maaloum, M Pernodet, N Tinland, B, Agarose Gel Structure Using Atomic Force Microscopy Gel Concentration and Ionic Strength Effects, Electrophoresis 19, 1606, 1998. Mackie, IS Meares, P, The Diffusion of Electrolytes in a Cation-Exchange Resin Membrane I. Theortical, Proceedings of the Royal Society of London Series A 232, 498, 1955. 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

Effective thermal conductivities and heat transfer coefficients are given by De Wasch and Froment (1971) for the solid and gas phases in a heterogeneous packed bed model. Representative values for Peclet numbers in a packed bed reactor are given by Carberry (1976) and Mears (1976). Values for Peclet numbers from 0.5 to 200 were used throughout the simulations. 

For packed bed reactors, Carberry and Wendel (1963), Hlavacek and Marek (1966), and Carberry and Butt (1975) report that axial dispersion effects are negligible if the reactor length is sufficient. These and other researchers (Young and Finlayson, 1973 Mears, 1976) have developed criteria based on the reactor length for conditions where axial dispersion can safely be neglected. The criterion shown in Table V is a classic criterion for neglecting axial mass dispersion. The works by Young and Finlayson (1973) and Mears (1976) provide more detailed criteria to predict when axial dispersion is unimportant in nonisothermal packed bed reactors. 

V.K. Indusekhar and P. Mears, The effect of the diffusion layer on the ionic current from a solution into an ion-exchange membrane, in Physicochemical Hydrodynamics II, D. B. Spalding, ed., Advance Publications Limited, London, 1977, p. 1031. 

McCrum NG, Read BE and Williams G, "Anelastic and Dielectric Effects in Polymeric Solids", Wiley, New York, 1967. Meares P, "Polymers Structure and Bulk Properties", Van Nostrand, Princeton, 1965. 

The percentage desulfurization versus liquid flow rate (and, hence, length of the reactor, since LHSV was kept constant) data obtained with this catalyst are shown in Fig. 4-19. As one explanation for the effect shown in this figure, it has been suggested that the axial dispersion in shorter beds causes their poor performance. Is this a viable explanation Based on Mears criterion, what is the... 

According to Mears criterion, the minimum bed-length required to eliminate the axial dispersion effect can be expressed as... 

Mears,53 Paraskos et al.,66 Montagna and Shah,38 and Montagna et al.59 have recently shown that ineffective catalyst wetting can cause the reactor performance to be dependent on the liquid velocity. The y used a correlation of Puranik and Vogelpohl69 for the effectively wetted surface area of the packing to explain the effects ofliquid hourly space velocity and the length of the catalyst bed on the performance of bench-scale HDS reactors. 

The above criterion, which has been proposed by Gierman (2) is based on the argument that the temperature required for a given conversion in the test reactor should not exceed the theoretical one by more than 1 °C, which can be considered to be within the accuracy of temperature definition in practice. A similar, but more conservative criterion has been proposed earlier by Mears (5) based on a maximum increase of 5% in bed length or catalyst volume to effect the same conversion as in an ideal reactor. In the criterion of Mears, the coefficient 8 in Equation 1 should be replaced by 20. 

Effect of agitation on the rate of 2-propanol dehydrogenation to acetone at 355 K over Ni catalysts. [Rates are calculated at constant conversion level from the data in D. E. Mears and M. Boudart, AIChE J., 12 (1966) 313.] In this case, increasing the stirring speed increased the rate of acetone diffusion away from the catalyst pellet and decreased product inhibition. 

In accordance with the equation for the activation energy of diffusion proposed by Meares [31], cohesion energy density (CED) of the polymer has a significant effect on diffusion coefficients of lower hydrocarbons. This is especially typical of mbbery polymers an increase in CED results in reduction of diffusion coefficients. Similar dependencies also apply to glassy polymers [9,32]. For example, Figure 9.8a shows the dependence of diffusion coefficient of propylene on CED of both glassy and mbbery polymers. 

It can be concluded that ozone acts only very superficially on wet soft tissues. It is not able to penetrate deeply. This is confirmed by studies of Bohr and Mear (j ), who transfused blood of rabbits, poisoned by ozone, into normal rabbits without any harmful effect. These authors also ventilated only one lung of an animal (turtle or rabbit) with air containing ozone without harmful effects on the normal lung. 

This effect has been known for quite some time [76-81] and used to influence the reaction rate between the charged particles. Examples include some hydrolysis reactions [80] where a small addition of polyelectrolyte causes a dramatic acceleration of the chemical reaction between equally charged divalent counterions in solution. The effect of a polyelectrolyte on ion-ion collision frequencies has also been used to probe the distribution of ions around the polyion. For example, Meares and coworkers [82] probed the electrosta-... 

Closure After completing this chapter, the reader should be able to derive differential equations describing diffusion and reaction, discuss the meaning of the effectiveness factor and its relationship to the Thiele modulus, and identify the regions of mass transfer control and reaction rate control. The reader should be able to apply the Weisz-Prater and Mears criteria to identify gradients and diffusion limitations. These principles should be able to be applied to catalyst particles as well as biomaierial tissue engineering. The reader should be able to apply the overall effectiveness factor to a packed bed reactor to calculate the conversion at the exit of the reactor. The reader should be able to describe the reaction and transport steps in slurry reactors, trickle bed reactors, fluidized-besd reactors, and CVD boat reactors and to make calculations for each reactor. 

Using the methodology of Mears [19], the effect of axial dispersion on the performance of a tubular reactor can be ignored if the constraint given in Eq. (14) is satisfied ... 

An indication of the presence of bulk diffusion effects can be obtained by using the Mears criterion ... 

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