Separation Mechanisms

Sedimentation processes lead to the formation of a concentration gradient. Fickian diffusion, Brownian motion, general entropic tendency and repulsive interactions counterbalance the concentration gradient formed. The sedimentation of an ensemble of particles progresses until an equilibrium concentration distribution is achieved due to the opposed sedimentation and dispersive fluxes. The equilibrium can be described by the differential transport equation:

-Ddc-Uc = 0 dx where c is the concentration of the sedimenting particles and dc/dx is the concentration gradient formed in the direction of the sedimentation. There exist some limits to the validity of this equation but the details are beyond the scope of this review. The ther-modynamic approach defines the equilibrium on the basis of the chemical potential of the sedimenting species mi(1 — vip(x))a>2xdx — Y -^dck = 0 k $ck where vi is the molar volume of the sedimenting species and w is the angular velocity of the centrifuge rotor. The concentration distribution of uniform-size particles at equilibrium in a homogeneous liquid is exponential. When different but uniform-size colloidal particles sediment separately by forming the exponential concentration distributions, the larger size particles are compressed close to the bottom of the sedimentation cell. This situation is demonstrated in Figure 13. On the other hand, the sedimentation of the colloidal particles exhibiting some PSD can lead to very different equilibrium concentration distributions of the particles of different sizes. Larger size particles can be compressed closer to the bottom of the sedimentation cell but they can form focused zones at higher levels as well. These two situations are demonstrated in Figure 14.

In the first case shown in Figure 14, two exponential concentration distributions corresponding to two different size particulate species are superposed. The lower part of the sedimentation cell contains a higher proportion of larger particles compared with the original mixture and vice versa for the upper part

Figure 13 Schematic representation of the sedimentation of different size particles. Concentration distribution is more compressed to the bottom of the sedimentation cell for larger size particles (left) and centre of gravity of the concentration distribution is closer to the bottom compared with smaller size particles (right).

Figure 13 Schematic representation of the sedimentation of different size particles. Concentration distribution is more compressed to the bottom of the sedimentation cell for larger size particles (left) and centre of gravity of the concentration distribution is closer to the bottom compared with smaller size particles (right).

of the sedimentation cell, and thus size fractionation exists. It is impossible, in principle, to achieve more complete size separation of particles by simple centrifugation.

In the second case shown in Figure 14, larger particles are focused in the density gradient due to the equilibrium exponential concentration distribution of smaller particles. The concentration distribution of larger focused particles approaches a Gaussian distribution function.

The two imaginary cases shown in Figure 14 demonstrate two limit situations which can appear in actual centrifugation experiments in a homogeneous suspending liquid. The focusing phenomenon is, of course, actively exploited in isopycnic (or more generally isoperichoric) focusing separations of particles. In such cases, a two- or multicomponent liquid is used to form the density gradient and larger particles are separated according to density differences.

The particle-particle interactions which limit the degree of freedom of the particle movements, and whose importance increases with increasing concentration, are the major factors imposing the particular concentration distribution of each sedimenting species of a polydisperse colloidal sample. Consequently, the results of the particle separation performed by any centrifugation method must be carefully evaluated.

Figure 14 Schematic representation of the sedimentation of a mixture of different size particles. The exponential concentration distribution of larger and smaller size particles can be either superposed (left) or larger size particles can be focused within the density gradient formed by the exponential concentration distribution of smaller particles (right).

Figure 14 Schematic representation of the sedimentation of a mixture of different size particles. The exponential concentration distribution of larger and smaller size particles can be either superposed (left) or larger size particles can be focused within the density gradient formed by the exponential concentration distribution of smaller particles (right).

Figure 15 Isoperichoric focusing of coloured polyaniline particles in the density gradient formed by colourless silica particles in thin-layer isoperichoric focusing (TLIF) cell in a centrifugation experiment.
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Solar Panel Basics

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