Bubbles in viscous liquids: shapes, wakes and velocities

Abstract

The shapes and terminal velocities of bubbles rising in viscous liquids have been determined. For Morton numbers (M) greater than 4 × 10−3 the drag coefficient and dimensionless bubble shape are functions only of Reynolds number (R). Shape regimes and terminal rise velocities have been correlated. The flow field around a rising bubble was visualized through the hydrogen bubble tracer technique. For M > 4 × 10−3 and R < 110 the bubbles trailed closed, laminar toroidal wakes. For R > 110 the wake was open and unsteady. Streamlines for the flow were obtained by raising a ciné camera at the same speed as the bubble and filming the H2 tracer bubbles. Results are presented for R < 150 and 7·4 × 10−4 < M < 850.

A bridge between projection methods and SIMPLE type methods for incompressible Navier–Stokes equations

“…We simulate the case of Mo = 1.31 and Eö = 161. Figure 4 shows that our computational interface shape is very consistent with the experimental result from Bhaga and Weber [38]. Figure 5 further shows that our computational shapes in a big region of Mo (from Mo = 9 × 10 −2 to Mo = 9 × 10 −5 ) and Eö (from Eö = 3.6 to Eö = 36).…”

“…Equations (38), (41) and (42) form the standard SIMPLE method [14,16]. For the SIMPLE method, the pressure correction from the Poisson equation (42) is utilized to correct the velocity by (41).…”

“…Employing an underrelaxation technique for the momentum equation of Equation (38) for the standard SIMPLE method, we have…”

“…The SIMPLE type methods can also be written as a four-step fractional step formula. For example, we can write the standard three-step SIMPLE method of (38), (41) and (42) …”

“…Following, we consider two iteration algorithms for the application of 1501 SIMPLE type methods to calculations of unsteady flows. Based on the standard SIMPLE method of Equations (38), (41) and (42) and using the first-order fully implicit technique to update the temporal term, we have SIMPLE-A algorithm as…”