Properties Of Solids

Properties of Solids Among the properties of solids, the following are of particular significance in engineering operations: 1. Density, ρ - mass per unit volume - Units: g/cc, lb/ft3, kg/m3 2. Specific Gravity - ratio of the density of the material to the density of some reference material (ρ/ρ ref) - a dimensionless ratio whose numerical value may be the same as the density of the material 3. Bulk (or apparent density), ρb - total mass per unit of total volume - not an intrinsic characteristic of the material since it varies with the size distribution of the particles and their environment - influenced by porosity of the solid and the material with which the pores, or voids, are filled - for a single, nonporous particle the true density ρ equals the bulk density ρb 4. Hardness - resistance to indentation (for metals and plastics) - resistance to scratching (for minerals); usually expressed in terms of Mohs’ scale 5. Brittleness or friability - the ease with which a substance may be broken by impact - the hardness of a material is not a sure criterion of its brittleness - for example: horn, some plastics and gypsum are soft and tough and are not easily broken by impact; coal is soft and friable - friability is the opposite of toughness - toughness refers to the property of metals and alloys called impact resistance 6. Friction - resistance to sliding of one material against another material Particulate Solids Chemical engineers meet particulate solids in carrying out many unit operations like crushing, drying, filtering, crystallization, solid-fluid reacting, dust collecting as a part of many process that produces a solid product, and as catalysts in many industrially important chemical reactions. In chemical engineering, solid particles ranging in size between quarried rock and smoke are of interest. Typical size range: 105 to 1 microns (1 micron = 1/1000 mm). - the particles are larger than most individual molecules and larger than particles in colloids - particles are unaffected by Brownian-motion forces - particles are small enough that they are usually found in large numbers

***Description of properties of particulate solids uses summation arithmetic and statistical expressions. Two classes of properties of particulate solids: 1. Individual particle properties - size, shape, volume, surface area, mass - properties of the bulk solid material that are retained by small particles (thermal conductivity, solid density, specific heat, hardness, hygroscopic tendency) 2. Solids-voids phase properties - void fraction of the mass, effective density, surface area per cubic foot - effective thermal conductivity, permeability (a measure of the pressure drop due to fluid flow through the mass), angle of repose *** The properties of the solids-voids phase depend upon the properties of the particles, but the phase properties must be expressed so that the effect of all the particles present is considered. The separation of materials on the basis of size is frequently important as a means of preparing a product for sale or for a subsequent operation. It is also a widely used means of analysis, either to control or gage the effectiveness of another operation, such as crushing or grinding, or to determine the value of a product for some specific application. Methods of Particle-Size Measurement Various methods are used for measurements of particle size. These depend on the size range, the physical properties, and the conditions of dryness and wetness permissible. 1. Microscope - for very small sizes of the order of a few microns - a sample of the material is put under a microscope and each particle is measured by an optical micrometer or by a measurement of a photomicrograph of known magnification - this method is extremely laborious but can be used where other methods cannot - frequently employed to measure particles of dust from the atmosphere and to evaluate the effectiveness of air filters - other example: liquid droplets can be measured using this technique 2. Standard Sieve/Screening - most common method where the solid phase is placed on top of a series of screens - each screen has smaller openings than the one above, usually in 21/n series - as the sieves are shaken, the particles fall through them until a screen is reached in which the openings are to small for the particles to pass - the size of the particles found on any screen is expressed as an appropriate mean length between the openings in the screen above and that on which the particle rests (i.e. arithmetic average of the two screen openings) 3. Particle-settling velocity method

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the settling velocity is a function of both the particle and fluid densities and the particle projected area the dimension of the particle is given as the diameter of the sphere that would fall with a velocity equal to the observed falling velocity of the particle types: sedimentation, elutriation and centrifuging

Particle-Size Measurement by Screen Analysis/Screening Most particle-size determinations are made by screen analysis when the particles are within the size range that can be measured by screens. Screening - separation of a mixture of various sizes of particles into two or more portions, each of which is more uniform in size of particle than is the original mixture - accomplished by passing the material over a surface provided with openings of the desired size - the equipment may take the form of stationary or moving bars, punched metal plate, or woven wire mesh Two Types of Screening 1. Dry Screening - treatment of a material containing a natural amount of moisture or a material that has been dried before screening 2. Wet Screening - water is added to the material being treated for the purpose of washing the fine material through the screen Definition of Terms: Screen aperture – the clear space between the individual wires of the screen Mesh – number of apertures per linear inch; a nominal figure which does not permit accurate computation of the screen openings or aperture without knowledge of the wire sizes used Example: a 10-mesh screen will have 10 openings per inch, and the aperture will be 0.1 inch minus the diameter of the wire Screen interval – the relationship between the successive sizes of screen openings in a series. The standard screens employ a screen interval in which the factor is 2½ although 2 ¼ is also used. Oversize – the material that fails to pass through the screen; also known as plus material Undersize – the material that passes through the screen openings; also known as minus material Screen blinding – clogging of the screen openings with sample particles Screen Effectiveness – fractional recovery of desired material times the fractional removal of undesired material for either the oversize or undersize fraction When more than one screen is used and more than two sizes are produced, the various fractions may be designated according to the openings employed in making the separations. Three Methods of Indicating Size Fractions

I

II

Oversize ¼ in. Through ¼ in. on 1/8 in. Through 1/8 in. on 1/16 in. Undersize

+ ¼ in -1/4 + 1/8 in. -1/8 + 1/16 in. -1/16 in.

III + ¼ in 1/4 / 1/8 in. 1/8 / 1/16 in. 1/16 / 0 in.

Method of Reporting Screen Analyses Initially, results of screen analyses are presented in tabular form. Results of Typical Screen Analyses Tyler Screen Mesh -8 + 10 -10 + 14 -14 + 20 -20 + 28 -28 + 35 -35 + 48 -48 + 65 -65 + 100 -100 + 150 -150 + 200

Average Particle Diameter, Dave cm in 0.2007 0.0790 0.141 0.0555 0.1001 0.0394 0.0711 0.0280 0.0503 0.0198 0.0356 0.0140 0.0252 0.0099 0.0178 0.0070 0.0126 0.0050 0.0089 0.0035

Mass Fraction 0.03 0.14 0.25 0.2 0.14 0.09 0.06 0.04 0.03 0.02

Mass Fraction through each Screen 1 0.97 0.83 0.58 0.38 0.24 0.15 0.09 0.05 0.02

The designation -8 + 10 means particles smaller than 8 mesh but greater than 10 mesh. Alternate methods of designation would be 8/10 or “through 8 mesh, on 10 mesh.” Screen Effectiveness The effectiveness of screens is based upon both the recovery in the product of the desired material in the feed and the exclusion or rejection from the product of the undesired material in the feed. Effectiveness = recovery x rejection Recovery = Pxp/FxF where P, F xP, xF

= mass of product and feed, respectively, where either the oversize or undersize cut may be considered as product = mass fraction of desired-size-range material in feed and product, respectively

and rejection = 1 – recovery of undesired material = Capacities

Reading Assignment: Perry’s Chemical Engineer’s Handbook pp 19-18 to 19-23 (including 19-24 for Figures)