Fractal dissolution

Polycondensation reactions (eqs. 3 and 4), continue to occur within the gel network as long as neighboring silanols are close enough to react. This increases the connectivity of the network and its fractal dimension. Syneresis is the spontaneous shrinkage of the gel and resulting expulsion of Hquid from the pores. Coarsening is the irreversible decrease in surface area through dissolution and reprecipitation processes. 

Emerald Tablet Modern Art Mandala Art Hermetic Art First Matter Art Fractal Art Calcination Art Lab Symbols Dissolution Art Flamel s Art Separation Art ... 

In situ SAXS investigations of a variety of sol-gel-derived silicates are consistent with the above predictions. For example, silicate species formed by hydrolysis of TEOS at pH 11.5 and H20/Si = 12, conditions in which we expect monomers to be continually produced by dissolution, are dense, uniform particles with well defined interfaces as determined in SAXS experiments by the Porod slope of -4 (non-fractal) (Brinker, C. J., Hurd, A. J. and Ward, K. D., in press). By comparison, silicate polymers formed by hydrolysis at pH 2 and H20/Si = 5, conditions in which we expect reaction-limited cluster-cluster aggregation with an absence of monomer due to the hydrolytic stability of siloxane bonds, are fractal structures characterized by D - 1.9 (Porod slope — -1.9) (29-30). 

The dissolution channels (wormholes), obtained under certain conditions of attack of carbonate rocks by hydrochloric acid, have been recently proven to have a fractal geometry. An equation was proposed, relating the increase of the equivalent wellbore radius (i.e. the decrease of the skin) to the amount of acid injected, in wellbore geometry and in undamaged primary porosity rocks. This equation is herein extended to damaged double porosity formations through minor modifications. 

Daccord G, Lenormand R (1987) Fractal patterns from chemical dissolution. Nature 325 41 3 Daccord G, Lietard O, Lenormand R (1993) Chemical dissolution of a porous medium by a reactive fluid, 2, Convection vs. reaction behavior diagram. Chem Eng Sci 48 179-186 Darmody RG, Thorn CE, Harder RL, Schlyter JPL, Dixon JC (2000) Weathering implications of water chemistry in an arctic-alpine environment, north Sweden. Geomorphology 34 89-100 Dijk P, Berkowitz B (1998) Precipitation and dissolution of reactive solutes in fractures. Water Resour Res 34 457-470... 

A reaction occurring at an interface of two phases. Some heterogeneous processes also display homogeneous aspects for example, a particular reaction may occur in only one of the system s phases (e.g., the rapid dissolution of a gas into a liquid followed by a particular reaction). See Fractal Reaction Kinetics... 

In conclusion, in most polar aprotic Li salt solutions, the morphology of Li electrodes upon charge-discharge cycling is very rough. The electrodes become covered with reactive dendrites that can be readily disconnected electrically from the bulk. Nonuniform Li dissolution further enhances the fractal structure of the electrode surface. These situations were recently rationalized and well explained by theoretical approaches and calculations [259,260],... 

Farm and Avnir [113] were the first to use fractal geometry to determine effects of surface morphology on drug dissolution. This was accomplished by the use of the concept of fractal reaction dimension dr [114], which is basically the effective fractal dimension of the solid particle toward a reaction (dissolution in this case). Thus, (5.7) and (5.8) were modified [113] to include surface roughness effects on the dissolution rate of drugs for the entire time course of dissolution... 

Dissolution in topologically constrained media gives rise to fractal fingering, Figure 6.8 B (cf. also figures in [201,204,205]). The tree-like structure shown here indicates the flow of liquid where dissolution takes place. 

According to van Damme [201], fractal fingering is in many respects a chaotic phenomenon because it exhibits a sensitive dependence on the initial conditions. Although this kind of performance for a dissolution system is currently unacceptable, it might mirror more realistically the erratic dissolution of drugs with very low extent of absorption. 

This form is very similar to the model often used when the molecules move across fractal media, e.g., the dissolution rate using a time-dependent coefficient given by (5.12) to describe phenomena that take place under dimensional constraints or understirred conditions [16]. The previous differential equation has the solution given by (9.9). 

Tromelin, A., Hautbout, G., and Pourcelot, Y., Application of fractal geometry to dissolution kinetic study of a sweetener excipient, International Journal of Pharmaceutics, Vol. 224, No. 1-2, 2001, pp. 131-140. 

Farin, D. and Avnir, D., Use of fractal geometry to determine effects of surface morphology on drug dissolution, Journal of Pharmaceutical Sciences, Vol. 81, No. 1, 1992, pp. 54—57. 

Valsami, G. and Macheras, P., Determination of fractal reaction dimension in dissolution studies, European Journal of Pharmaceutical Sciences, Vol. 3, No. 3, 1995, pp. 163-169. 

Daccord, G. and Lenormand, R., Fractal patterns from chemical dissolution, Nature, Vol. 325, 1987, pp. 41-43. 

Figure 76. Electrode tree (Wood s metal). Its impedance corresponds to its fractal geometry.282 (Reprinted from G. Daccord, R. Lenormand, Fractal patterns from chemical dissolution. , Nature, 325, 41-43. Copyright 1987 with permission from Nature Publishing Group.)...

Mass fractal dimension to describe dissolution behavior... 

Mass fractal dimension (Dm) was used to describe the pore structure and dissolution of pellets. However, measuring the mass fractal dimension prior to dissolution alone may not be sufficient. " As the dissolution... 

Bonny, J.D. Leuenberger, H. Determination of fractal dimensions of matrix type solid dosage forms and their relation with drug dissolution kinetics. Eur. J. Pharm. Bio-pharm. 1993, 39 (1), 31-37. 

Momonaga, M. Stavek, J. Ulrich, J. Interpretation of dissolution rates by the reaction fractal dimensions. J. Cryst. Growth 1996,166, 1053-1057. 

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