6 BASIC NOTATION c – cohesion [kPa]; d – particle diameter [m]; D – shear cell diameter [m]; E – modulus of elasticity [MPa]; ff – flow function; H – height [m]; i – flow index; k – pressure ratio; L – length [m]; ∆L – displacement [mm]; m – mass [kg]; N – normal force [N]; p – pressure [MPa]; Q – volume flow rate [m 3 h -1 ]; R – radius [mm]; R h – Hausner Ratio; t – t<strong>im</strong>e [s]; T – tangent force [N]; V – volume [m 3 ]; w – moisture content [%]; γ – bulk unit weight [kN m -3 ]; ε 1 , ε 2 , ε 3 – principal strains; ε v – volumetric strain; µ – friction coefficient; ν – Poisson’s ratio; φ – angle of internal friction [deg]; Φ – angle of repose [deg]; ρ – bulk density [kg m -3 ]; σ 1 , σ 2 , σ 3 – principal stresses [kPa]; σ c – unconfined yield strength [kPa]; σ r – consolidation reference stress [kPa]; τ – shear stress [kPa].
7 1. INTRODUCTION Granular materials are substances made up of many distinct solids (“grains”) that have been present in human activity since very early history in forms such as cereal grains or construction materials. Granular materials are <strong>im</strong>portant constituents in numerous industrial processes. Such industries as: chemicals, cosmetics, pharmaceuticals, biotechnology, ceramics, food, energy, paper/wood, metallurgy, cement, glass, minerals, consumer products, plastics strongly depend on granular materials. A single shift in conditions can drastically change performance of a process in those industries. Following growing industrial use of granular materials a number of branches of engineering evolved devoted to understanding how to deal with these materials, among them powder technology, soil mechanics, geotechnology, foundation engineering, earthquake engineering, erosion control and mining engineering. The most <strong>im</strong>portant technologies of process engineering involving granular materials as listed at ‘Powder, bulk solids’ portal are: pneumatic conveying, transport, size reduction, spheroidization, screening, coating, mixing (blending), segregation, product consistency, weighing, metering, packaging and bagging, storage, stratification, dust collection, instrumentation and control, feeding, quality control. Each of the above applies specific equipment. For example a group of particle enlargers and formers constitute of: briquetters, coaters, compactors, conditioners, dedusters, densifiers, disc pelletizers, drum flakers, drum pelletizers, encapsulators, extruders, flakers, fluid bed agglomerators, granulators, instantizers, kneaders, laboratory mixing agglomerators, pelletizers, pinmixers, powder coaters, powder presses, rewetting agglomerators, roller presses, rotary agglomerators, rotating pans, screens, spheroidizers, spray agglomerators, spray congealers, tablet coaters, tablet presses, vibratory agglomerators. As compared to liquid granular material reveal three distinct differences in mechanical behavior: Granular materials are characterized by higher than zero angle of internal friction that in the case of liquids is zero. As a result of that static pressure in liquids is not dependent on direction, while in granular material pressure may vary with direction of measurement. Static granular material may carry shear stress, while liquid cannot. Therefore the surface of static liquid is flat, while the free surface of static granular material has conical shape. In granular material tangent stress under condition of shear load does not depend on velocity of deformation, but depends on the mean stress. In liquid shear stress depends on velocity of deformation (as an effect of viscosity), but does not depend on pressure.
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116 Table 16.7. Mean values (±St.
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118 Table 16.9. Mean values (±St.
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