ARTICLE pubs.acs.org/IECR
Evaluation of Liquid Phase Migration in Pastes and Gels Martin A. Bardesley† and John Bridgwater*,† †
Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K. ABSTRACT: Mixing a frictional solid powder into a liquid to form a paste is a powerful way of forming a solid object. Products made in this way include bricks, tiles, fertilizers, foods, pharmaceuticals, and catalysts. Additives are included to give (i) green strength for processing after extrusion or molding, (ii) strength to the final fired product, and (iii) necessary final properties. The selection of a liquid phase, its amount, its suitability, and amount of additives then become critical issues. In particular the paste must be formulated so that problems do not arise due to liquid phase migration. A methodology has been developed to evaluate liquid phase migration. It is studied for a range of both ceramic pastes and gels typical of some seen in the manufacture of catalysts. A constant pressure is imposed on the material in a cylindrical ram, and the unsteady state drainage of liquid through a porous end plate is followed. This volume is proportional to the square root of time for most of the process, the constant of proportionality leading to a characterizing desorptivity. After a brief time lag, gels made by acidification of boehmite behaved similarly. Studies on model pastes made from alumina particles, water, Bentonite clay, plus a carbohydrate or starch revealed that liquid phase migration was enhanced by an order of magnitude if Bentonite clay were absent. It was significantly reduced if dextrin rather than glucose or lactose was an additive. The desorptivity permits ranking of the migration rates and shows when other work is needed to understand the origin of behavior.
’ INTRODUCTION The range of products using extrusion forming is broad and includes foods, fertilizers, bricks, pharmaceuticals, and a host of new materials and catalysts. Extrusion has been used for many years in the formation of products, but the items needed have evolved in complexity and particularly with a need to create special and complicated shapes. Pastes and gels occur widely in the processing industries. These are two classes of material of different physical character but can show similar behavior when undergoing extrusion. For example both pastes and gels can expel liquid in amounts that can have an adverse effect on process operation. The product is often of a poor quality, wet on the surface, deformed, or having a spatial variation of voidage. Pastes are often made from particles which, when hard and dry, can be abrasive. There is also a liquid phase to make extrusion possible. This liquid phase must be sufficient in amount and must have rheological properties so that the paste can be extruded readily. If the liquid content is too low, then the pressure drop is excessive, and rupture of equipment is possible particularly when enough liquid is expelled. If the liquid amount is too high, then the liquid drains too readily from the paste giving product of uneven quality or is soft, lacking structural integrity, making further processing impossible. Selection of the amount and composition of the liquid phase is thus a most important part of the design of the process and the design of the product. Gels are formed in a very different way, but similar issues due to phase migration arise in an extrusion step. Rheological parameters for use in the design of extrusion devices is dependent on the liquid content as explained by Benbow.1 During extrusion, a paste is subjected to a stress which is partly borne by the solid matrix and partly by the interstitial liquid. The pressure gradient in the latter causes liquid motion, and this in turn causes the solid matrix to consolidate. Even small changes in liquid content can cause unacceptable and rapid changes in extrusion pressure. r 2011 American Chemical Society
The movement of liquid during the processing of pastes and paste-like materials extends to many areas of technology. In catalyst manufacture, the extrusion of too much liquid can also adversely affect the strength of the green paste and can also cause shape changes and weakening of the pellet during firing. Uneven liquid distribution causes variability in the fired product. The phenomena are widespread. For example, Yaras2 reported that liquid phase migration was the cause of instabilities during the flow of two suspensions of 76.5 and 65.6 vol% solids. In the extrusion of icing sugar, Bayfield,3 difficulties due to the production of water droplets hampered production. Similar problems arise in the pharmaceuticals industry as in the extrusion of microcrystalline cellulose pastes.4,5 There are very significant issues in the manufacture of building materials. Bohnera7 reports on the issues faced in the injection of phosphate-based pastes, Perrot8 on the extrusion of cement-based mortars, Kuder9 on the extrudability of cements, Silva10 on mechanical strength, and Kaci11 on issues of flow and blockage. In all these studies the presence of liquid and the potential for liquid phase migration are of importance. Here the liquid phase motion is studied for a range of both ceramic pastes and gels used in the manufacture of catalysts. In the tests, the paste or gel is subjected to a constant pressure in a cylindrical ram extruder, and the unsteady state drainage out of the material through a porous end plate is followed as a function of time. The utility of this technique and the information gained to rationalize liquid phase migration is evaluated. Special Issue: Nigam Issue Received: May 18, 2011 Accepted: September 14, 2011 Revised: September 9, 2011 Published: September 14, 2011 1774
dx.doi.org/10.1021/ie201065c | Ind. Eng. Chem. Res. 2012, 51, 1774–1781
Industrial & Engineering Chemistry Research
ARTICLE
’ THEORY A review of the consolidation of a cylindrical packed bed of fine particles saturated with liquid, having a porous plate fitted at its base, is considered. The bed is subjected to the sudden imposition of a load to the top free surface. The total stress is the stress on a horizontal plane in the bed and is taken by the structure as a whole. The total stress is the sum of the effective stress, the normal force taken by the solid matrix divided by the total area of the bed, plus the pressure of the fluid in the porous structure. The following assumptions are made: (1) The coefficient of permeability is the same at every point in the consolidating layer and at every stage of consolidation. The implications are considered later. (2) The excess water drains out only in one dimension. (3) The time lag of the compression is caused exclusively by the flow of liquid in through the particle material. Follow now the formulation due to Smiles12who provided a one-dimensional consolidation model of dewatering during mud compaction. His model considers movement of both the solid matrix and the liquid, using continuity equations for each. Let the bed be of unit cross-section and let Fs(z,t), be the volumetric flux of solid at coordinate z, this being measured from the surface of the porous plate into the material. The flux of the solid is zero at the filter (z = 0) at all times t, and Fs(0,t) = 0, A material coordinate, m(z,t) is introduced that moves with the solid phase. Coupled mass balance equations then arise. The first expresses the movement of the solid phase and the second the change of m(z,t) with z in terms of ϕs, the volume fraction of solid phase at position z and time t: Then ∂m ¼ Fs ð1Þ ∂t z ∂m ¼ ϕs ∂z t It follows that Z z mðz, tÞ ¼ ϕs ðz, tÞdz
ð2Þ
ð3Þ
0
Introduce the moisture ratio θ which is the ratio of liquid volume to solid volume within an element of the bed. Then θ¼
1 1 ϕs
ð4Þ
A mass balance gives the volume V of liquid removed from the paste or gel, by time t. Using the material coordinates, this is expressed Z ∞ V ¼ ðθo θÞdm ð5Þ A 0 where A is the cross-sectional area of the sample, and θo is the initial liquid ratio of the paste or gel. Darcy’s law gives a relationship for m ∂θ ∂ ∂θ ¼ DðθÞ ð6Þ ∂t ∂m ∂m where a diffusivity D(θ) given by DðθÞ ¼
kðθÞ dP νð1 þ θÞ dθ
ð7Þ
Table 1. Formulation of the Standard α-Alumina Ceramic Paste - Mix 25 mean particle
amount in
size (μm)
batch (g)
α-alumina grade F1500 (Universal Abrasives, Stafford)
3.0
666
α-alumina grade F600
9.3
666
36
666
Bentonite clay (Steetley Minerals, Cleveland)
