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Ind. Eng. Chem. Res. 2004, 43, 3750-3757
On the Origins of Paste Fracture Annette T. J. Domanti† and John Bridgwater* Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K.
Despite the use of paste extrusion to make a wide range of products, process design and operation can often be compromised by the occurrence of flow instabilities. These are manifest as surface fractures of a number of different types. Here, direct observations of a two-dimensional flow through transparent walls show, for the first time, that these fractures originate in the development of cracks first on one side and then on the other in the paste around the die exit. These fractures can occur in the region immediately prior to the exit, or they can arise directly at the exit. This behavior is consistent with numerical predictions of stresses at the exit, which reveal tension at the surface. Stress distribution, crack initiation, and crack growth to form surface fractures, together with the relationship of these factors to the paste formulation, raise important questions for the future. Introduction Pastes are common in the manufacture of a wide range of products, including foods, pharmaceuticals, fertilizers, traditional ceramic products such as bricks and tiles, and modern ceramics including catalyst particles. Materials that are regarded as pastes include mixtures of shear-thinning liquids and hard, often abrasive, particles; indeed, such mixtures form the basis of a wide range of catalytic substrates. The selection of a suitable liquid phase and its amount is thus a critical matter in the specification of the paste, and a method, part theoretical and part experimental, has been presented1 that provides a means of formulating the paste and designing equipment. However, physical questions are encountered because our knowledge is still rudimentary concerning many matters that influence paste flow and product quality. Three general difficulties are known to arise: (a) the migration of the liquid phase during processing, (b) the development of internal planes of structural anisotropy and weakness, termed laminations, and (c) the occurrence of flow instabilities called surface fractures that cause the surface of the product to be uneven. The latter can be so severe that an extrudate can be broken into separate pieces by the forces that operate. This work is concerned with the origins of the third of these issues. Despite the need to predict surface fracture during paste extrusion, very little has been written about the subject; this is in sharp contrast to the extensive literature on surface defects during polymer extrusion. Although the occurrence of surface fractures is wellknown to process designers and operators, the means of handling them is to resort to trial and error. Reports on such efforts are mainly sketchy, with material properties and processing conditions being incompletely given or partially analyzed. A useful small study was published by Harrison et al.,2 as well as a more extensive one by Benbow et al.3 In their work, paste is forced out of a cylindrical barrel through a circular hole
in its base into straight circular pipes, termed dielands, of various lengths. The physical form of the extrudate was observed for various materials as a function of the length of the dieland and the mean velocity within it. However this work, though substantially correct, contained errors and was superseded and significantly extended by studies4 of the same type. In the latter work, all of the prior experiments were repeated. For a number of pastes, it was found that an increase in the length of the dieland suppressed the formation of cracks or decreased the severity of cracks. Decreasing the die entry angle, defined as one-half of the included angle of a convergent channel at the entry to the dieland (with a flat base thus yielding an angle of π/2), also had a beneficial effect. In some pastes, increasing the extrusion velocity suppressed surface fracture, but in other cases, this was not found. The spacing of ridges on the surface was generally one-half of the diameter of the extrudate. Recently, reports5,6 on the extrusion of a material made from the mixing of a clay with oil have been published. These reports show that surface instabilities can be eliminated by the siting of a central rod into the flow, a practicable technique for the manufacture of hollow tubes. These reports also describe the detachment of flow in the dieland, which is linked with the occurrence of bubbles at the wall of the dieland. Whether such a phenomenon is possible with the more complex liquid-phase components (with a pronounced shear-thinning behavior needed for much practice) used here is not known. A recent, broad, and complete survey by Chandler et al.7 of the flow behavior of soft solids includes pastes. One effective and quite widely used way of describing the flow of a paste is available.1 In this approach, the material is characterized using a relationship for the extrusion pressure, P, for the flow of a paste from a barrel of diameter D0 into a dieland of diameter D and length L as follows
( )
P ) 2(σo + RV) ln * To whom correspondence should be addressed. Tel.: +(44) 1223 334798. Fax: +(44) 1223 334796. E-mail:
[email protected]. † Present address: The Australian Gas Light Company, Level 2, 33 Collins St., Melbourne, Australia.
D0 L + 4 (τ0 + βV) D D
(1)
The quantities σo, R, τ0, and β are termed extrusion parameters and have been shown to be properties of the paste. These parameters have become useful as stan-
10.1021/ie030666c CCC: $27.50 © 2004 American Chemical Society Published on Web 01/27/2004
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3751 Table 1. Recipes Used in Paste Batchesa paste
alumina glucose
