Forces generated in solidifying liquid bridges between two small particles

m Powder Technolo~/87 (!996) 175-180

ELSEVI ER

Letter

Forces generated in solidifying liquid bridges between two small particles Gabriel I. Tardos, Rajan Gupta Department ~"Chemical Engineering. The City Collegeof the City Uniw~rity of New York, New York. NY 10031. USA Received24 July 1995;revised 26 October 1995

Abstract The formation of strong, solidified binder bridges is essential in powder granulation where small particles are held together and large permanent granules are formed during the process, Solid bridges can also be detrimental by binding particles into lamps during moistureinduced caking of an otherwise free flowiP,g powder. Two kinds of solidifying bridges, one due to drying of a concentrated polyrae~"seludon and the other due to crystalfizafion of a saturated salt solution, were studied experimentally in this work and some rather intriguing results are i~m,~ented here. It was found that large attractive forces, of the order of hundreds of times the weight of the polymeric bridge, develop in the solid neck during formation. Successive ruptures of polymer strands within the bridge occur during drying of the binder, thereby partially releasing some internal stres,~,The salt bridge, however, tends to push the particles apart with an ever increasing force that is not released in the dry bridge. The implication of these findings on granule formation during binder granulation and during powder caking are briefly discussed. Keywords: Solid bridges; Bridge stretlgth; lnte~anicle force.s;Yield slmngth

1. Introduction

Solid bonds or bridges between small powder particles occur during the production of ceramic parts from sintcred powders, the me,eafacture of tools from powdered metals and the production of tablets in the pharmaceutical industry. 'These solid bridges form by diffusion and mechanical defermotion and develop under the influence of high temperature and/or pressure. These processes have been studied extensively and a relatively large body of literature exists in the field [ I - 3 ] . There is, however, another class of processes during which solid bonds between small powder particles or granules form, usually during casual contact between particles. Here, the solid bond starts out as a liquid bridge which subsequently solidifies, crystallizes or reacts chemically with the solid. The precursor of the solid bond may be a local melt which cools, a solution which becomes more concentrated as the liquid evaporates or a slurry which becomes more viscous as fine powder particles are absorbed into the bridge. Good examples of such processes are granulation of fine powders and caking of boik powders during storage. In this letter, these second kind of bridges are studied and both the overall bridge strength aad the forces exerted on the two c o n n o t e d particles are measured. 0032-5910/96/$15.00 © 1996Elsevier Science S.A, All rights rust'awed SSD10032-591 O( 95 ) 021074- I

2. Background One of the important advaucas in the study o f powders was the development by Rumpf [4] of the concept that the strength of an agglomerate or a cake, % can be calculated from the strength of interparticle bonds, F, and some other powder characteristics through the now famous equation: 7= [(l -e)lel(FId~,)

(I)

where • is the porosity and dp is the initial particle size. Implicit in the Eumpf analysis is that all interpartk;lo bonds in the failure plane of the agglomerate rupture simultaneously. It is well known, however, that many brittle materials fail by propagation of cranks and flaws which act to concentrate stress and that it is only neeussary to break bonds immediately proceeding these crack tips. Rumpf's work was extended through the introduction ofmodere material science concepts of fracture mechanics by Johnson et al. [5] and Kendall [6,'/] who showed that the yiald sL,cngth can oe calculated from: 7 = 0.SKc/(C) °s = 15.5( 1 - •)*G/(Cdp) °s

(2)

Here. c is a measure of cracks or natural flaws in the material. K c is the fracture toughness which is a nteaanre of the necessary stress required to propagate flaws in the material and G is the adhesive, surface energy of the interpurticle

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G.L Tardo,v.R. Gupuz/Powder Technalogy 87 ~1996) 175-180

bonds. Despite some important differences in the approaches of Rumpf and Kendall it can be seen that, from both Eqs. ( 1) and (2), there is a proportional dependence of agglomerate strength on some measure of the strength of the interparticle bonds, whether it be the interpartielo force F, the bond energy G or the fracture toughness Kc. The fracture toughness and the bond energy inherently depend on the interparticle bond strength F, and h,:,nee a great deal of effort has been in';estcd in the literature ~o calculate and/or measure the i~terparticle force, F. A review of the field by Pietsch [ 8 ] revealed a large number of contributions studying interpartiele bonds generated by short range forces (van der Waals), the presence of liquids 19 I, magnetic and electric forces, etc. Solid bridges however, have not been studied extensively and in fact only two papers were reviewed [ 10,11 ] that showed that the force due to the solid bridge is proportional to the yield strength of the binding material, rn and hence the yield strength is given by the relation: ~-= [ M a p o / M o p n ] ( 1 - e) rn = t!tnerB

(3)

where Ma and Mp are the mass of the bridge and the parlicles, PB and Po are the density of the bridge and the particle and Wn is the degree of filling. It was also shown that the yield strength depends on the history or the evolution of the hridge and that this is a complex phenomenon which requires fa~ther study. During the present work, the strength of solidifying liquid bridges between two solid particles as well as the forces exerted by the bridge on the particles themselves were measured. The behavior was obsetwed for two different liquid bridges, one in which the bridge was a polymer solution which became more concentrated in time by solvent evaporation and a second one in which an inorganic salt crystallized in a saturated solution. Tile effect on strength due to different bridge shapes and volumes was also studied. It was observed that large tensile and compressive forces are developed in the bridge; these forces increase in time and reach a maximum within 50-90% of the total bridge drying (solidification) time.

3. Exper[menta! A schematic of the experimental apparatus is shown in Fig. 1, It is essentially a very sensitive force transducer of Prime Technologies design (FT5A: maximum load 5 g and sensitivity, ~ 2.5 rag), mounted on a 3-D positioning table (not shown) in the view of a Nikon 6C projection microscope. The two particles (in the shape of small cylindrical rinds, 5 mm in din'meier ) were glued to the arm of the force transducer and to a rod mounted on a second 3-D table. In additio0, the linear variable differential transformer (LVDT, position transducer, Fig. 1) enabled the measurement of the movement of the lower particle. During the present set of experiments, the lower particle was held in a fixed position and the

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Fig. I. Sehemaacof the experimentalset-up. LVDT (sensitivity, +..+10/~m) . was used to make sure that no movement occurred. The bridge is formed by placing the liquid material (binder) with the aid of a mierofiter syringe on the lower particle, by contacting it with the upper particle and then stretching the bridge as shown in the insert of Fig. 1. After stretching, the position of the lower surface is kept constant as explained above, and the bridge is left to dry. A minute displacement of the for,"~ transducer due to stresses exerted by the bridge causes ~,n imbalance in magnetic reluctance resulting in a pre-ealir'rated output voltage (2.775 V/g). Both the transducer force response and LVDT signal are amplified and filtered wit,~ a Validyne CDI9 carrier demodulator which gives up to 1.0 mV / volt sensitiuity. Data is then collected with a;~ IBM personal computer equipped with a data translation 2805 interface hoard and t~ c,~ versus time measurements are obtained. Two different liquid bridge materials we~:' tested during this experiment. An aqueous solution of carbc*wax-PEG 350 (28 wt.% concentration, /x=0.3906 kg/~n s, #=1032 kg/m 3) was used to simulate the properties t:fa typical binder used for industrial granulations and a sail :ated solution of sodium carbonate ( # = 1.221 kg/m 3) was used to elucidate the behavior of a typical crystalline powder duriag a caking process. In order to calculate the initial bridge weight, me, a magnified view (20 times ) of the drop lying on the lower particle was obtained by using the nficroseope operated in the shadow illumination mode. Subsequently, the height of the drop profile above the particle (cylinder) surface was me,.. ured. Since the diameter of tim cylinder is known, the volmae is calculated by assuming that the profile is circular (this assumption was found to give only a small error, less than 5-6% in most cases, by comparing the measured profile to the circular shape). The total weight of the bridge was used to render the measured forces dimensionless during kite experiments.

G.I. Tardos. R. Gupta I Pmvder Technology 87 ~1996) 175-180

4, ResuRs Fig. 2 shows a typical result of the force exerted by the earbowax solution on the upper particle while the lower !arrtitle is being held in a fixed position. The value of the force is made dimensionless with the initial weight of the bridge calculated as described above. The time of drying is uncontrolled in this experiment in that evaporation of the water solvent takes place naturally and is determined by the temperature and relative humidity in the chamber surrounding the microscope (20 °C and 55--60% RH). As seen in the figure, the particles are pulled together (positive force ) mdy by the surface tension of the liquid for about 20 rain, this is the fiat curve at the start of the process,

177

the force varies slight|yaround a va.~ueof 2-5 times the initial weight, me. A steep increase in the force is observed over the next hour or so while the force reaches a maximum value of about 250 tintes the initial weight of the bridge. This is a very large foree which causes, as can be seen at around 80 rain into the bridge strengthening time, rupture of the sofidified part of the bridge (this is associated with a steep decline in the measured fore,:). The maximum value measured at this point can be take~:, ~i:~a first approximation, to be the strength of the solid bridge. The bridge is seen to reform again, with the total force increasing, only to rupture again upon reaching a similar value at around 100 rain into the experiment. Fig. 3 shows a picture of the magnified microscope image of the solidifying bridge before and ~mmediately after it rup-

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Fig.3. Pictureof a semisolidcmbowaxbridge ( × 20; reducedin rept'oductionby 70%). (~) Sell,lyingbtidScwithFoIy.~.s:~ml;(b) bridgeafie~ru~m-e of sv~qd.

178

G.L Tardos. R Gtfpta / Powder Technology 87 (1996) 175-180

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Time (rain) Fig. 4. The influenceof bridge vo um~ on forces exerted on particles, a large bridge, n,,= 46 rag. h~.=0 23 cm; (b) small b=Sdge,m,,= 13.1 rag, h~= O.135 Cal. tured at around 80 min into the experiment described in Fig. 2. One can see the two solid particles, the outer solid (dark) regions of the bridge as well as the polymer strands in the solidifying inner core. The bright core is not a hole in the bridge but rather an arti fact of the back illumination and the curvature of the bridge surface as it is oriented towarO the light source. Several of these experiments were performed with different amounts of bridge material and with several values of the interparticle distance, he. The two parameters are not independent, however, in that larger bridge volumes require larger interparticle distances. Some measure of independence can be achieved by varying the initial shape of the bridge by

conoolling its "slenderness', but in all cases larger bridges men,at slightly different drying rates due to different surface area-to-volume ratios. Strengthaning of a large bridge (characteristics are shown on tile figure) is reprod~ced in Fig. 4(a). As seen, the material dries somewhat more slowly and attains smaller peaks of force before breaking; it was also found that the bridge ruptures more frequently within approximately the same time. The above results suggest that smaller bridges develop higher strength as the solvent evaporates and this was indeed d~monstrated with a small bridge; results are reproduced in 3ig. 4(b). While the bridge ruptured at the point when F = 200 me at about 40 rain into the formation of the bridge,

G.L Tardos,R Gupta/PowderTechnology87 (1996)175-180

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Fig. 5. Suenghlening~'t'¢ bridgeof sodiumcarbonatesolulion, me= 0.026 g, h. = 0+13cm. it continued to strengthen aud reached a peak value of 400 me. This force was subsequently released after several cracks formed upon further solidifieall.cn. It was observed, in general, that the final (residual) force after total solidification rarely exceeded about F = 50 me. Fig. 5 shows results obtained during drying and solidification of a saturated solution of sodium carbonate. The attractive force due to surface tension at short times can be observed until about 20 rain into the experiment. Once the bridge starts to solidify, however, the bridge dilates and pushes the panicles apart (negative force). The total force attains a more or less constant value after about 100 rain with a total value of the force at app~x,ximately F = 2 0 0 me. The bridge does not rupture in this ease and hence bridge strength cannot be evaluated from this experiment. In order to evaluate bridge strength, weights were applied to the lower particle ( see Fig. 1) after the bridge completely solidified. Unfortunately, the bridge did not rupture at this point but raffler detached itself from tile particle, the results of these measurements are not reported here.

bridges, which form more slowly and also dry more slowly, are lint ,,cry io~po~z.,'~t. Appropriate measures to generate s~nall bridges (by controlling spreading and surface adsorption of the liquid) and to control drying rates (by adjusting temperatures and gas flow rates) will thus have tremendous influence on the overall granulation process and will result in stronger granules produced during a shorter granulation. 2,'he existence of large internal forces during solidificafion and residual stresses which remain in the bridge after d'o'ing also explain a common observatinn in granules produced by binder granulation namely, internal cracks. Under extrenm conditions or if the binder is not selected properly, ',he liquid material is seen to peel off the solid surfaces after solidification resulting in weak agglomerates which easily break upon further handing. Fig. 6 repro&~,'es ascanning electron micrograph showing large (600/am) and small (eapproximalely 20 ~m) glass beads agglome~,ated with the polymeric binder used in the above experimenv; (PEG 350, 28 wt.% in waler).

g. Discussion These findings show that larger bridges made of a concentrated polymer solution of PEG-350 are weaker than smaller ones, This is mainly due to the fact :hat larger bridges contain more liquid and the distribution of solid and liquid material is less uniform. This causes more internal ruptures and heuc. smaller overall forces. The total drying time is also longer in this case compared to smaller bridges as is the distance between particles. These findings suggest that smaller bridges which form during granulation of a powder, for example, have an overwhelming influence on the process while large

Fig.6. SEMpictureof gr~lll¢ coml~od of largeand sm~ glassbeads in a PEG350 bhqd~ ( X2(]0;kedged in repnJductionby 71%).

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G.L Tardos. R. Gupta / Powder Technology 87 (1996) 175-180

One can see the small particles imbedded in the binder w h i l e the layer of small beads and binder is peeled off the larger particles. This is a cos e in which internal forces could move the smaller particles during solidification but break cff the material from the surface of the two larger particles wh;ch remain rigid. The instrument and procedure described here can easily be used for binder selection by using the actual solid particles in the experiment and attach them to the "arms' of the measuring device; granule strength can then be calculated by using the measured forces and, for example, Eq. ( l ). Caking of a powder stored in a hopper or a container may occur due to "bleeding' of a liquid species from the bulk powder and/or by adsorption of moisture from the surrounding atmosphere. This in turn causes the formation of liquid bridges at the particle-particle contact which arc, in effect, concentrated solutions of solubilized powder ingredients. Changes in temperature and/or relative humidity can result in solvent (water) evaporation and the formation of dr), bridges as shown. Compressive forces generated during the process will compact the material to the point of partic!e surface deformation and will result in the creation of large lumps. These findings support this view of caking even though other mechanisms are also possible.

6. Conclusions An instrument was developed to measure forozs between two solid particles connected by a solidifying liquid bridge. Measurements performed with a concentrated polymeric solution of PEG 350 in water showed that, as the solvent evaporates, solids strands form within the bridge. These

strands exert large attractive forces onto the two particles which reach two to four hundred times the weight of the bridge. Several ruptures occur during solidification so that the residual force in the solidified bridge rarely exceeds about fifty times the weight of the bridge. It was found that smaller bridges which have less volume become more homogeneous during solidification than larger bridges and generate larger forces. The saturated salt bridge of sodium carbonate also develops large forces (up to approximately two hundred limes the weight o f the bridge) but these tbrces were found to bc repulsive, i.e. tended to push the particles apart. Some implications of these findings to powder granulation and caking were discuss::d.

References [ I ] G.C. Kucrynski,Adv. Colloid hlterJace,'~cl., 3, ( 1972) 275. [ 2] W. Kloseand M. Lent. bael, 64 (1985) 193 [3] P, Compo. R. Pfeffer and G.I. Tardos, Potvder Technol., .51 (1987) 85. [4l H. Rumpf. Parlicte Tectmolo~y. Chapman and Hall. London. 1990. [51 K, Johnson. K. Kendall and A. V.obeUs.Prec. R. Soc. l,ondon. Ser. A: 324 (1971) 301. [6] K. Kendall. in BJ. Briscoe and M.J. Adams reds,). Tribol.gy in Particle Technology, Adam Hilger, Bristol. [987. [71 K, KendanPowderMetalL, 31 (1988) 28. [8] W Pieasch,Size Enlargement by Agglomeration, Wiley, New York. 1991. 19l B.J. Enais. R.H. Li. G.I. T:u'dt:sand R. Pfeflvr, Chem. Fag. Set.. 45 ([990) 3071. 110] W. Pielsch. Can. Z Chent. Ettg., 47 ( 1969~403. [ l I ] W. Pietsch. in M.E. Fayed and L. Onen (eds.L Hu:ldbook of Powder ,~cience and Technology. Van Nostrand Reinhold, New York. 1984. pp. 231-252