Particle tortuosity

The effective diffusivity De is a characteristic of the particle that must be measured for greatest accuracy. However, in the absence of experimental data, De may be estimated in terms of molecular diffusivity, Dab (for diffusion of A in the binary system A + B), Knudsen diffusivity, DK, particle voidage, p, and a measure of the pore structure called the particle tortuosity, Tp. 

Space time, reaction time (BR), residence time (PFR), Section 3.8.5 Residence time of a gas bubble Catalyst particle tortuosity... 

For catalyst particles, Satterfield (Heterogeneous Cataly.si.s in Frae-tiee, McGraw-Hill, 1980) recommends the use of a value of tp = 4 when no other information is available, and this can be used for many adsorbents. In general, however, it is more rehable to treat the tortuosity as an empirical constant that is determined experimentally for any particular adsorbent. 

For adsorbent materials, experimental tortuosity factors generally fall in the range 2-6 and generally decrease as the particle porosity is increased. Higher apparent values may be obtained when the experimental measurements are affected by other resistances, while v ues much lower than 2 generally indicate that surface or solid diffusion occurs in parallel to pore diffusion. 

The size distribution of the particles (with particles of a uniform size, there is increased voidage between the particles and a lower tortuosity, that is deviation from the linear path for the fluid flowing between the particles, making for improved filterability), and... 

The presence of particles in the fluid medium complicates diffusion in a sediment due to the effects of porosity, represented by n, and tortuosity. Since tortuosity of natural sediments is seldom known it is more convenient to use the term "formation factor" or "lithological factor," denoted L, which takes into account everything but porosity. Tick s diffusion constant D is replaced by the whole sediment diffusion constant Ds, where < D. 

For a system on nonconducting spherical particles of radius r, Boyack and Giddings found that the constriction and tortuosity factors are given by... 

For adsorbent materials, experimental tortuosity factors generally fall in the range 2-6 and generally decrease as the particle porosity is... 

In the special case of an ideal single catalyst pore, we have to take into account that diffusion is quicker than in a porous particle, where the tortuous nature of the pores has to be considered. Hence, the tortuosity r has to be regarded. Furthermore, the mass-related surface area AmBEX is used to calculate the surface-related rate constant based on the experimentally determined mass-related rate constant. Finally, the gas phase concentrations of the kinetic approach (Equation 12.14) were replaced by the liquid phase concentrations via the Henry coefficient. This yields the following differential equation ... 

The effective diffusivity is obtained from D, but must also take into account the two features that (1) only a portion of the catalyst particle is permeable, and (2) the diffusion path through the particle is random and tortuous. These are allowed for by the particle voidage or porosity, p, and the tortuosity, rp, respectively. The former must also be measured, and is usually provided by the manufacturer for a commercial catalyst. For a straight cylinder, rp = 1, but for most catalysts, the value lies between 3 and 7 typical values are given by Satterfield. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

X = Measure of the packing irregularities dp = Particle diameter, y = Tortuosity factor,... 

Pp Particle density of the adsorbent material, kg/m, subscript p for particle T Tortuosity factor, dimensionless... 

In this equation, RJR is the ratio of the solute s radius (RJ to the pore radius (R ), p is the particle porosity, t is the tortuosity factor, is the distribution coefficient for the solute, and D is the diffusion coefficient for the solute in free solution. By inserting different values for the... 

Dispersion The degree of dispersion of the nanoplatelets is determined by the degree of delamination of the clay. The fully delaminated (exfoliated) nanocomposite presents much higher values for the tortuosity factor and the aspect ratio in comparison with the partially delaminated (intercalated) nanocomposite. This means that the clay particles that grow as aggregates or books of sheets must be broken up or exfoliated into individual sheets that have a thickness of the order of 1 nm, with lengths and widths of the order of 500 nm. 

When the effective diffusivity of solutes D g can be approximated by the diffusivity in water, D, multiplied by a constant that includes the effects of particle porosity and tortuosity of pores in particles. Equation 14.3 can be written as follows ... 

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