Tapped density is the term used to describe the bulk density of a powder (or granular solid) after consolidation/compression prescribed in terms of "tapping" the container of powder a measured number of times, usually from a predetermined height. The method of "tapping" is best described as "lifting and dropping". Tapping in this context is not to be confused with tamping, sideways hitting or vibration.
Tapped density is an important experimentally determined value in those industries producing and packaging powdered and granular materials such as beverages (dry form) & processed foods[1][2][3][4][5], and to those industries where powder packing is a critical process parameter, particularly pharmaceuticals[6][7], powder metallurgy[8][9] and industrial catalysis[10][11] (for example in the petrochemical industry).
Tapped density is variously reported in units such as g/cm3, g/cc, lb/cu.ft.
Powder bulk density edit
The bulk density of a powder simply expresses the amount, usually weight or mass, of a powder in a specified volume. However, since powders are composed of particles and voids, the volume occupied by a given number of particles depends on how closely they are packed. The packing of particles depends on their shape, cohesiveness, short-range motion and external forces. In practical terms, the bulk density of a powder tends to increase the more it is subjected to tapping, vibration and other mechanical action which causes particles to move relative to one another in a way that allows smaller particles to occupy the voids between larger particles.
Tapped density or tapped bulk density is one formal expression of bulk density obtained under specified conditions. The "end point" used for measurement of tapped volume and calculation of tapped density can be defined by total number of taps (either explicitly or the product of tapping rate and time or duration of tapping), or some defined amount of small change in tapped volume from time to time[12], since the theoretical final volume, at infinite time/taps is approached asymptotically in an approximately logarithmic manner[13].
Measuring tapped density edit
In general, any graduated container can serve as a means to determine tapped density. In practice, graduated glass measuring cylinders are most often used. In the standard methods below, the total capacity of the cylinder to be used, and the readability of its scale are stated. The cylinder can be tapped manually or by mechanical device.
Manual tapping edit
The raising and lowering of the cylinder by hand is done either (i) without reference to the height traversed and arbitrary acceleration in both upward and downward directions; the hand remaining in contact with the cylinder at all times (hand tapping), or (ii) by constraining the upwards distance traveled and allowing free-fall of the cylinder under gravity (drop box).In hand tapping the cylinder containing the powder is tapped by repeatedly striking its base down onto a hard surface[14][15][16][17]. A drop box has a hole in its lid, large enough for the body of the graduated cylinder to pass though it, but too small for the base of the cylinder. The distance between the bottom of the box and the underside of the lid defines the height through which the cylinder can be lifted and dropped.
Mechanical devices edit
Tap density analyzers (tap density testers) use an electric motor to turn a cam under a specially constructed cylinder holder. The holder secures the cylinder to a vertical shaft which runs in a low friction bearing. The tapping rate is normally expressed in taps per minute; the rate being typically a few hundred. The actual rate is determined by the rotational speed of the cam under the shaft/platform. Digital or electromechanical counters are usually incorporated in the device to automatically stop the cam rotation after a predetermined (yet adjustable) number of taps. The height through which the container falls is known as the drop height or stroke. It is set by the distance between the highest point on the cam and the striking surface. In the standard methods referred to below, the drop height is one of two values, 3mm (or 1/8") or 14mm, within tolerances specified therein. These values merely reflect drop heights in commercial equipment and have no special physical meaning otherwise.
Standard methods edit
The measurement of tapped (tap) density has been formalized in a number of standard methods particularly for metal powders[18][19], catalysts[20][21], pigments[22], dried food powders[23][24][25] and carbon[26].
Tapped density and powder flowability edit
The change in tapped powder volume has been related to flow properties of powders[27][28].
Carr's compressibility index and Hausner ratio edit
Tapped density is used in the calculation of Carr's Compressibility Index (Carr index), the percentage change in powder bulk volume (from its initial "loose" condition) upon tapping and of Hausner ratio, the fractional change in bulk volume from "loose" to tapped". Since any value of tapped bulk density strictly depends upon experimental details as drop height, number of taps, container geometry, sample mass etc, so must the "Carr" and "Hausner" values, notwithstanding any uncertainty in the starting "loose" or "freely settled" density value.
Descriptive equations edit
- Kawakita
Measuring the change in powder bed porosity as a function of the number of taps (N), Kawakita[29] described the compression of a powder as follows:
where C is equal to the Carr index (the percentage change in initial volume) and a and b are evaluated graphically by plotting N/C vs. N [30][31].
- Cooper-Eaton
The Cooper-Eaton model of compaction[32] was modified by Mohammadi and Harnby[33]
where Dt and Da are the theoretical tapped and aerated bulk densities respectively, DN is the observed bulk density after N taps. T is a so-called "compaction constant" and is inversely related to the rate of densification.
- Heckel
Heckel described the plastic compression of powder as a change in relative density, D, as a function of applied pressure[34][35]. A plot of the natural logarithm of the ratio (1/1-DN) vs. N, the number of taps (substituting for pressure), where DN is the relative powder density for a given number of taps, yields slope of value k which is related to the yield strength of the powder bed.
References edit
- ^ "Properties of Food Powders" by H. Hayashi in "Encyclopedia of agricultural, food, and biological engineering" (Dennis R. Heldman ed.) published by CRC Press, (2003)ISBN 0824709381
- ^ p 55 in "Physical Properties of Foods and Food Processing Systems" by M.J. Lewis, published by Woodhead Publishing, (1990)ISBN 1855732726
- ^ J.L. Willett, "Packing Characteristics of Starch Granules" Cereal Chemistry (2001) vol.78, pp 64-68.
- ^ R.A. Garcia, R.A. Flores and C.E. Mazenko "Factors contributing to the poor bulk behavior of meat and bone meal and methods for improving these behaviors" Bioresource Technol. vol. 98, (2007) pp 2852-2858.
- ^ G.V. Barbosa C. and H. Yan, p192 in "Characterization of Cereals and Flours: Properties, Analysis, and Applications" (eds.G. Kaletunc and K. Breslauer)CRC Press, 2003, ISBN 0824707346
- ^ T.P. Foster and M.W. Leatherman "Powder Characteristics of Proteins Spray-Dried from Different Spray-Dryers" J. Drug Dev. Ind. Pharm., vol. 21, (1995), pp 1705 - 1723.
- ^ L.X. Liu et al "Effect of particle properties on the flowability of ibuprofen powders" Int. J. Pharmaceutics, vol. 362, (2008), pp 109-117.
- ^ "Powder Metallurgy Technology" by G. S. Upadhyaya, published by Cambridge Int Science Publishing, (2002)ISBN 1898326401
- ^ P. Suri et al "Effect of mixing on the rheology and particle characteristics of tungsten-based powder injection molding feedstock" Mat. Sci. Eng. A, vol. 356, (2003) pp 337-344.
- ^ "Handbook of Heterogeneous Catalysis" by G. Ertl, H. Knözinger and J. Weitkamp, published by VCH, (1997)ISBN 3527292128
- ^ K. Al-Dalam and A. Stanislaus "Comparison between deactivation pattern of catalysts in fixed-bed and ebullating-bed residue hydroprocessing units" Chem. Eng. J., vol. 120, (2006), pp 33-42.
- ^ R. Nair R, et al (2004) "Investigation of Various Factors Affecting Encapsulation on the In-Cap Automatic Capsule-Filling Machine" AAPS PharmSciTech. Vol.5 (No.4): article 57.
- ^ p 454 in "Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales" by Andrea J. Liu and Sidney R. Nagel, CRC Press, 2001, ISBN 978-0748408795
- ^ p 446 in "Encapsulated and Powdered Foods" by Charles Onwulata, CRC Press, 2005, ISBN 978-0824753
- ^ p 160 in "Carbon Black: Science and Technology" by Jean-Baptiste Donnet, Roop Chand Bansal and Meng-Jiao Wang, CRC Press, 1993, ISBN 978-0824789756
- ^ Z. Chen and J.R. Dahn (2002) "Reducing Carbon in LiFePO4/C Composite Electrodes to Maximize Specific Energy, Volumetric Energy, and Tap Density" J. Electrochem. Soc., Vol. 149, pp A1184-A1189.
- ^ ISO 3953:1993 Metallic powders -- Determination of tap density
- ^ ASTM B527: Standard Test Method for Determination of Tap Density of Metallic Powders and Compounds
- ^ ISO 3953: Metallic powders -- Determination of tap density
- ^ ASTM D4164: Standard Test Method for Mechanically Tapped Packing Density of Formed Catalyst and Catalyst Carriers
- ^ ASTM D4781: Test Method for Mechanically Tapped Packing Density of Fine Catalyst Particles and Catalyst Carrier Particles
- ^ ISO 787-11: General methods of test for pigments and extenders - Part 11: Determination of tamped volume and apparent density after tamping
- ^ ISO 8967: Dried milk and dried milk products -- Determination of bulk density
- ^ ISO 8460: Instant coffee - Determination of free-flow and compacted bulk densities
- ^ ISO 6770: Instant tea - Determination of free-flow and compacted bulk densities
- ^ ISO 10236: Carbonaceous materials for the production of aluminium - Green coke and calcined coke for electrodes - Determination of bulk density (tapped)
- ^ H. Leuenberger and B.D. Roher (1986) "Fundamentals of Powder Compression. I. The Compactibility and Compressibility of Pharmaceutical Powders " Journal Pharmaceutical Research Vol.3, pp 12-22.
- ^ Q. Li, et al (2004) "Interparticle van der Waals force in powder flowability and compactibility" International Journal of Pharmaceutics, Vol.280, pp 77-93.
- ^ K.H. Ludde and K. Kawakita, (1966) Pharmazie Vol.21, pp393-403
- ^ p 62 in "Pharmaceutical Powder Compaction Technology" by G. Alderborn and C. Nyström, Informa Health Care, 1995, ISBN 978-0824793760
- ^ "Tablets & Capsules: Powder Density in Solid Dosage Forms" by M.A. Thomas (2005)available online
- ^ A.R. Cooper and L.E Eaton "Compaction behavior of several ceramic powders" J. Am. Ceram. Soc., vol.45 (1962), pp97-101.
- ^ M.S. Mohammadi and N. Harnby, "Bulk density modeling as a means of typifying the microstructure and flow characteristics of cohesive powders" Powder Technol. Vol.92 (1997) pp1-8
- ^ R.W. Heckel (1961) "Density pressure relationship in powder compaction" Trans Metall Soc AIME Vol.221(suppl a)pp 671-675
- ^ R.W. Heckel (1961) "An analysis of powder compaction phenomena" Trans Metall Soc AIMEVol.221(suppl b)pp 1001-1008.
External links edit
- ASTM International, formerly known as the American Society for Testing and Materials.
- MPIF: Metal Powder Industries Federation.
- USP: United States Pharmacopeia.
- ISO: International Organization for Standardization.