Specific Surface from Mass Distribution Function; FPT Ch2 Q7

Описание: Worked solution for Question 7, Chapter 2 (available as free download at https://www.particles.org.uk/particle...) in Fundamentals of Particle Technology. The question asks for the Specific Surface Area per Unit Volume, of a distribution of particles given a continuous function (i.e. equation) for the cumulative mass undersize of the distribution. Differentiation is required to determine the relative mass per micron range equation, which is then used in the equation for Specific Surface Area per unit volume. Using a mass distribution only requires one integration to be performed to calculate the Specific Surface Area per unit Volume. The answer is then used to calculate the Sauter mean diameter (sometimes called the D3,2 or surface area to volume diameter). Don't forget, this equivalent spherical diameter is probably the most relevant diameter for use in design and control equations, much better at representing the behaviour of the particulate system than the median size known as the D50. However, the Sauter mean does need calculating whereas the D50 is often simply read off a graph. Modern instruments for particle sizing do routinely include the Sauter mean (D3,2) as well as the median size (D50), together with the graphs of amount of particles present against particle size: both in cumulative and differential form.