Size reduction forces involved

The breakage theory of spheres is a reasonable approximation of what may occur in the size reduction of particles, as most size-reduction processes involve roughly spherical particles. An equation for the force required to crush a single particle that is spherical near the contact regions is given by the equation of Hertz (Timoschenko and Goodier, Theory of... 

The top-down approach involves size reduction by the application of three main types of force — compression, impact and shear. In the case of colloids, the small entities produced are subsequently kinetically stabilized against coalescence with the assistance of ingredients such as emulsifiers and stabilizers (Dickinson, 2003a). In this approach the ultimate particle size is dependent on factors such as the number of passes through the device (microfluidization), the time of emulsification (ultrasonics), the energy dissipation rate (homogenization pressure or shear-rate), the type and pore size of any membranes, the concentrations of emulsifiers and stabilizers, the dispersed phase volume fraction, the charge on the particles, and so on. To date, the top-down approach is the one that has been mainly involved in commercial scale production of nanomaterials. For example, the approach has been used to produce submicron liposomes for the delivery of ferrous sulfate, ascorbic acid, and other poorly absorbed hydrophilic compounds (Vuillemard, 1991 ... 

Size reduction involves the decrease in size of a panicle or granule by fracturing the material using, generally, one of the four forces shear, compression, impact, and tension. Single or combination of forces being applied to the material affect the level of size reduction that will be achieved, but also the magnitude and duration of the applied force(s) will help determine the overall resultant panicle size distribution. 

This process involves the application of compression, tension and/or shear forces to break apart the plastics. It is a notable method for size reduction. Mechanical factors are not predominant during biodegradation process, but mechanical... 

The size reduction of a material — in the cement industry the materials concerned are minerals or mixtures of minerals — therefore involves overcoming specific resistances or forces. In the main these are crystal bonding forces and interfacial bonding forces. In crystalline materials, fracture is initiated at flaws which are always present in such materials and which constitute weak spots that impair the homogeneity of the crystals. When the material is subjected to load, these flaws act as notches where stress concentrations occur and where fracture will be initiated when the stresses exceed the local strength of the material. 

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