Bubble buoyancy for a wide range of Reynolds numbers and different

In the preceding sections the possibility of the strong influence of the fi-ee surface zone near the front stagnant point on the transport stage of microflotation was emphasised. Eq. (10.40) enables us to estimate the critical condition of the appearance of an f.s.f.z. The parameters v and Re relate to the bubble with a completely retarded surface and can be described by equations derived for solid spheres. 

In the range 2 Re 750 the empirical relation between Reynolds number and Froude numberreads (Peebles Garber 1953, Grassman 1961, Hosier 1964), 

The velocities of bubbles of diameters between 0.1 and 2 mm are of the same order as those obtained from Eq. (10.45). Measured velocities are also presented in the second column of Table 10.1, taken from Schulze (1992), from which the Reynolds numbers are calculated (third column). The substitution of Reynolds numbers into Eq. (10.45) yields theoretical velocity values (column 4). The comparison of values of the second and fourth columns confirms the usefulness of Eq. (10.45). 

The substitution of values for v and Re into Eq. (10.40) yields values for Ay = y - y which are given in the last column. 

The large scatter is caused by differences in place and time of the measurements. According to Fainerman (private communication) the initial value of the surface tension of bidistilled water is approximately 72.7 mN/m at 20°C. Its value decreases by 0.02 mN/m during 8 minutes. The initial value relates to a freshly formed water-air interface and can be characterised by y . Thus Ay = y, - y can be estimated to be 0.02 mN/m. For water from river Kalmius 

---

Bubble Buoyancy for a Wide Range of Reynolds Numbers and Different Degrees of Water Contamination, and the Free Surface Zone near the Front Stagnant Point... 

---