By Mark D. Ardema
Unlike different books in this topic, which are inclined to be aware of 2-D dynamics, this article makes a speciality of the appliance of Newton-Euler how to advanced, real-life 3D dynamics difficulties. it really is therefore perfect for optional classes in intermediate dynamics.
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Extra resources for Newton-Euler dynamics
The Deborah number, De, can be generally defined as the ratio of a characteristic relaxation time of the fluid (such as ) to a characteristic time of the flow. It thus indicates the relative importance of elastic phenomena. As defined it applies to transient flows; however, it is sometimes applied to steady shear flow by using the shear rate as characteristic time, or to oscillatory flow by using the peak shear rate ␥0 . Other authors characterize the elastic response in steady shear flow by means of the Weissenberg number, Wi, the product of a characteristic time of the fluid and the shear rate.
2 Colloidal stability Driven by Brownian motion, colloidal particles will come into contact at a rate that is governed by diffusion. Von Smoluchowski (1917; see framed story, Chapter 4) first calculated the resulting rate of flocculation, known as rapid Brownian 18 Introduction to colloid science and rheology flocculation, assuming that each binary collision would cause the two particles to stick together: J0 = 8kB T 2 3kB T n = 2 . 18) The rate of doublet formation is dependent on the rate of diffusion and is proportional to the square of the particle volume fraction.
19) 2a In the above, G(r) is a hydrodynamic function discussed in Chapter 2 that describes the resistance to motion as two particles move towards one another. 3) that provides significant stability by retarding the rate of Brownian flocculation. 25 e max /kB T −1 . 20) Note that W∞ is the rate of rapid Brownian flocculation or aggregation in the absence of any stabilizing forces. 20) shows how the stability ratio can increase substantially above that for rapid Brownian flocculation. Higher values could, for example, be achieved by an increase of the surface charge or a reduction in electrolyte concentration.
Newton-Euler dynamics by Mark D. Ardema