Particle shape cone-shaped

STM and AFM profiles distort the shape of a particle because the side of the tip rides up on the particle. This effect can be corrected for. Consider, say, a spherical gold particle on a smooth surface. The sphere may be truncated, that is, the center may be a distance q above the surface, where q < r, the radius of the sphere. Assume the tip to be a cone of cone angle a. The observed profile in the vertical plane containing the center of the sphere will be a rounded hump of base width 2d and height h. Calculate q and r for the case where a - 32° and d and h are 275 nm and 300 nm, respectively. Note Chapter XVI, Ref. 133a. Can you show how to obtain the relevent equation ... 

Kang, Fan and Kim(96) measured coefficients for heat transfer from a cone-shaped heater to beds of glass particles fluidised by water. They also found that the heat transfer coefficient passed through a maximum as the liquid velocity was increased. The heat transfer rate was strongly influenced by the axial dispersion coefficient for the particles, indicating the importance of convective heat transfer by the particles. The region adjacent to the surface of the heater was found to contribute the greater part of the resistance to heat transfer. 

Dust masks, or particulate filter respirators, protect the respiratory system against any kind of inhaled particles. The simplest type, in the form of a cone-shaped fibrous filter that fits over the nose and mouth, is held in place by an elastic band around the back of the head. It is disposable, relatively comfortable to wear, and is useful when the dust is neither excessive nor toxic. It becomes readily clogged and should be discarded and replaced whenever breathing becomes restricted. Its use should not be carried over from day to day. 

Bowen and Masliyah examined the axial resistance of cylinders with flat, hemispherical and conical ends, and of double-headed cones and cones with hemispherical caps, together with the established results for spheroids. Widely used shape factors (including sphericity) did not give good correlations, while Eqs. (4-26) and (4-27) were found to be inapplicable to particles other than cylinders and spheroids. The best correlation was provided by the perimeter-equivalent factor Yj defined in Chapter 2. With this parameter, the equivalent sphere has the same perimeter as the particle viewed normal to the axis. Based on their numerical results, Bowen and Masliyah obtained the correlation... 

The disk centrifuge is the type of centrifuge used most often for bioseparations. It has the advantage of continuous operation. It consists of a short, wide bowl 8 to 20 in. in diameter that turns on a vertical axis (Figure 10.2b). The closely spaced cone-shaped discs in the bowl decrease the distance that a suspended particle has to be moved to be captured on the surface and increases the collection efficiencies. In operation, feed liquid enters the bowl at the bottom, flows into the channels and upward past the disks. Solid particles are thrown outward and the clear liquid flows toward the center of the bowl and is discharged through an annular slit. The collected solids can be removed intermittently or continuously. 

The chamber shape is chosen to accommodate the type of atomizer used. Droplets are ejected in a narrow cone from a nozzle which therefore requires a tall tower to prevent particle contact with the walls before they are dry. 

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