Drag coefficient Tomiyama

More recently, Tomiyama and co-workers [154, 155, 156, 157] performed detailed experiments investigating the drag coefficient of a single bubble in a stagnant liquid. They proposed a drag coefficient parameterization which is split in three categories. These are pure, gently-contaminated, and contaminated systems, respectively. 

The drag coefficient is frequently estimated using the relation suggested by Tomiyama et al [149], as described in sect 5.2.4. 

When these different drag coefficients are grouped together, they are often referred to as Tomiyama s drag law (Tomiyama, 2004). In summary, for clean systems the following expression is obtained ... 

Tomiyama, A., Kataoka, L, Zun, 1. Sakaguchi, T. 1998 Drag coefficient of single bubbles under normal and microgravity conditions. The J.S.M.E. International Journal 41, 472-479. 

The modified Mendelson s equation is a special form of the Fan-Tsuchiya equation where the viscous term, that is, the first term on the right side of Eq. (6), is omitted. Just as general as the Fan-Tsuchiya equation for bubbles in liquids, the correlation by Tomiyama et al. (1995) given in terms of drag coefficient. 

Tomiyama A, Kataoka I, Sakaguchi T. Drag coefficients of bubbles. 1. Drag coefficients of a single bubble in a stagnant liquid. Nippon Kikai Gakkai Ronbunshu B-hen 61 2357 2364, 1995. 

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