Fractal suspensions

Four novel approaches to contemporary studies of suspensions are briefly reviewed in this final section. Addressed first is Stokesian dynamics, a newly developed simulation technique. Surveyed next is a recent application of generalized Taylor dispersion theory (Brenner, 1980a, 1982) to the study of momentum transport in suspensions. Third, a synopsis is provided of recent studies in the general area of fractal suspensions. Finally, some novel properties (e.g., the existence of antisymmetric stresses) of dipolar suspensions are reviewed in relation to their applications to magnetic and electrorheolog-ical fluid properties. 

Available results pertinent to the hydrodynamics of fractal suspensions are sparse thus far, encompassing only three physical situations. Gilbert and Adler (1986) determined the Stokes rotation-resistance dyadic for spheres arranged in a Leibniz packing [Fig. 7(a)], With the gap between any two spheres assumed small compared with their radii, lubrication-type approximations suffice. In this analysis, the inner spheres are assumed to rotate freely, whereas external torques T( (i = 1, 2, 3) are applied to the three other spheres. For Stokes flow, these torques are linearly related to the sphere angular velocities by the expression... 

Fig. 7. Two examples of fractal suspensions (a) The spheres are arranged in a Leibnitz packing with the construction process illustrated to n = 2 sphere 4 is created during the generation n = 1, while spheres 5, 6 and 7 are created during step n = 2. (b) The spheres are arranged according to a modified Menger sponge, again the contruction stage is shown to n = 2.

Another fractal structure of interest is considered by Adler (1986). A three-dimensional fractal suspension may be constructed from a modified Menger sponge, as shown in Fig. 7(b). A scaling argument permitted calculating the effective viscosity of such a suspension however, this viscosity should be compared with numerical results for the solution of Stokes equations in such a geometry before this rheological result is accepted unequivocally. 

The original substrate structure used for our early photosensitization experiments was a fractal surface derived by hydrolysis of an organo-titanium compound, but this has since been replaced with a nanostructured layer deposited from a colloidal suspension of TiOi. This evidently provides for a much more reproducible and controlled high-surface-area nanotexture. Further, because it... 

Sampling in surface-enhanced Raman and infrared spectroscopy is intimately linked to the optical enhancement induced by arrays and fractals of hot metal particles, primarily of silver and gold. The key to both techniques is preparation of the metal particles either in a suspension or as architectures on the surface of substrates. We will therefore detail the preparation and self-assembly methods used to obtain films, sols, and arrayed architectures coupled with the methods of adsorbing the species of interest on them to obtain optimal enhancement of the Raman and infrared signatures. Surface-enhanced Raman spectroscopy (SERS) has been more widely used and studied because of the relative ease of the sampling process and the ready availability of lasers in the visible range of the optical spectrum. Surface-enhanced infrared spectroscopy (SEIRA) using attenuated total reflection coupled to Fourier transform infrared spectroscopy, on the other hand, is an attractive alternative to SERS but has yet to be widely applied in analytical chemistry. 

Light-scattering experiments on flocculating suspensions of silica colloids provided the data in the following table. (R is the average cluster radius.) Estimate the fractal dimension of the clusters formed and indicate whether the flocculation process is transport or reaction controlled. Hint Apply Eq. 6.1 and the concepts in Section 6.1.)... 

Measurements of the average floccule radius in a suspension of colloids, using light-scattering techniques, indicated the following time dependence R(t) = Ro(l + yty, where Ro = 5 nm, y = 9.3 s 1, and j8 = 0.56. Derive this equation, and estimate the initial number density of primary particles as well as the fractal dimension of the floccules formed. (Answer p0 = 7.5 x 1017 m 3 and D = 1.78.)... 

Aggregable suspensions were shown (Weitz and Oliveria, 1984 Schaefer et al., 1984) to yield fractal floes, a result which sheds new light on the old subject of coagulation and flocculation. 

In a metered dose inhaler, where fine drug particles are suspended in a propellent, stability and aggregation of the suspension are crucial for the performance of the inhaler. In an investigation into the aerosol formulation stability. Span 80 was added to a suspension of lactose to study the effect on deaggregation under shear.f An increase in shear stress was found to decrease aggregate size and boundary fractal dimension (Fig. 9), which was interpreted as a more compact aggregate. 

Ramadan, M.A. Tawashi, R. Effects of surface geometry and morphic features on the flow characteristics of microspheres suspensions. J. Pharm. Sci. 1990, 79 (10), 929-932. Suzuki, T. Yano, T. Fractal surface structure of food materials recognized by different molecules. Agric. Biol. Chem. 1991, 55 (4), 967-971. 

Perspectives. Ordered mesostnictured and mesoporous silica has been known for little more than ten years. Tremendous progress has been made with respect to precise control of the structure, texture, and chemical fimctionality of the surface of these materials. His lecture surveyed the synthesis of such materials, with a focus on organically ordered mesoporous materials. Quite a number of contributions dealt with amorphous fumed silica, its Physical-Chemical Features and Related Hazard Risk Assessment (M. Heinemann), the description of fractal aggregates (C. Batz-Sohn), and the Characterization of Size and Structure of Fumed Silica Particles in Suspension (F. Babick). E. Brendle reported on Adsorption of Water on Fumed Silica, and in a second paper he summarized research on Methylene Chloride Adsorption on Pyrogenic Silica Surfaces. 

Tombacz, E., Csanaky, C., and Illcs, E., Polydisperse fractal aggregate formation in clay mineral and iron oxide suspensions, pH and ionic strength dependence. Colloid Polym. Sci., 279, 484, 2001. 

The compressive yield properties are strongly dependent on the suspension structure. Mills et al. (186) showed that extensive preshearing of a flocculated suspension can result in a much denser floe morphology (in fractal terms), which was reflected by a decrease in the compressive yield stress by one order of magnitude. 

The assembly process of the nanoclusters is very sensitive to the temperature of the suspension. High-quality lattice arrangements were obtained between 20 and 30"C, and an HCl concentration between 0.2 and 0.3 M. At temperatures higher than 30"C, the nanoclusters form fractal patterns (Fig. 7), which results from the diffusion-limited aggregation (DLA) process of particles on the suspension surface... 

Figure 1.3.5 Electron micrograph of irreversible aggregate formed in suspension of spherical gold particles with diameter 15 nm. [Courtesy of Dr. David A. Weitz. From Weitz, D.A. Oliveria, M. 1984. Fractal structures formed by kinetic aggregation of aqueous gold colloids. Phys. Rev. Letters 52, 1433—1436. With permission.]...

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