Particle size slip correction factors

It was assumed that the motion of the fictitious particle within the above time steps is rectilinear. This simplification, which accelerates the computer calculation of the trajectories of the fictitious particle, has been show n to be justified (9). The Philips slip correction factor for an accommodation coefficient of unity (Eq. [4]) was used in the calculation of the diffusion coefficients of particles. The values of the dimensionless coagulation coefficients % obtained by the computer simulation for different particle sizes, are given in Table I. The statistical errors of the Monte Carlo simulation were estimated by the standard 3 a method (corresponding to a probability of 0.997) (13). The number of particle pairs that must be generated in order to lower the error to a reasonable level depends both on the initial distance of separation between... 

One of the assumptions of continuum fluid dynamics is that the velocity of the fluid at the surface of the particle surface is zero. However, as the size of the particles approaches molecular dimensions, this assumption becomes increasingly unreasonable. The first slip correction factors were developed by Cunningham to take this into account. The correction factor Cc is given by... 

The propenies of the solid-liquid or liquid-liquid interfaces are also important. often so important that their influence overshadows any other factor. The contribution of hydrodynamic driven phenomena such as slip Row, secondary flow, edge and end effects, viscous heating, and inertia may also play an important role (see Sec. IV). Good experimental and calculation procedures should ensure either that these factors are absent or that the data are corrected to eliminate their contribution. These will be discussed in Sec. IV. In the following sections, the main physicochemical factors that influence rheological behavior and viscosity are discussed. For the sake of clarity, a distinction will be made between the factors that are related to physical propeities such as composition and particle size, and physicochemical aspects, especially inteifacial properties. 

If the particle size is of the order of the mean free path of the gas, there may be slip at the particle surface between the fluid and the particle. To account for this effect, St is multiplied by a quantity Cc, called the Cunningham correction factor. For particles of 1 pm diameter at normal temperature and pressure, Cc is around 1.16 (Tien, 1989). 

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