Formation of a thin circulation layer in a two-fluid rotating flow

Recent numerical simulations predict the formation of a thin circulation layer (TCL) near the interface in a steady axisymmetric swirling flow of two immiscible fluids. This phenomenon, of fundamental and practical interest, has not been detected in prior experiments. The current experimental study reveals that the TCL does develop, but in a way which has not been predicted. The flow is driven by the rotating lid in a vertical cylindrical container—a model of a vortex bioreactor. The centrifugal force pushes the upper fluid from the axis to the sidewall near the lid and the fluid goes back to the axis near the interface. This centrifugal circulation (CC) drives the anticentrifugal circulation (AC) of the lower fluid at a slow rotation. As the rotation speeds up, a CC cell emerges below the interface-axis intersection. It expands downward and occupies almost the entire lower-fluid domain while the AC shrinks into a thin ring adjacent to the interface-sidewall intersection. As the interface starts to visibly rise near the axis, a new AC cell emerges below the interface-axis intersection. This cell and the AC ring merge and form the TCL, attached to the entire interface from below. The TCL is observed in a wide range of the lid angular velocity, until the flow becomes unsteady and three-dimensional. The resulting multicellular flow pattern is favorable for efficient mixing in bioreactors.

Figure 1

Problem schematic [22].

Figure 2

(a) Photo and (b) schematic of the experimental setup [22].

Figure 3

Photos of PIV images of the meridional motion and profiles of velocity along the axis at (a) $\mathrm{Re}=50$, (b) $\mathrm{Re}=100$, (c) $\mathrm{Re}=200$, and (d) $\mathrm{Re}=300$ [22].

Figure 4

(a) Schematic of meridional motion at $\mathrm{Re}=200$ and profiles of radial velocity near the interface in oil (open circles) and glycerin (solid circles) at (b) $\mathrm{Re}=50$, (c) $\mathrm{Re}=100$, (d) $\mathrm{Re}=200$, and (e) $\mathrm{Re}=300$.

Figure 5

Photos of flow patterns (left) and plots of velocity distribution at the axis (right).

Figure 6

Dependence on the Reynolds number of (a) the TCL thickness and (b) interface height $z_{\mathrm{i}}$ at the axis (squares) and at the sidewall (circles).

Figure 7

Photos of vortex breakdown bubble in the oil flow and plots of velocity distribution at the axis.

Figure 8

Photos of the bell-shape interface and plots of velocity distribution at the axis.

Figure 9

Photos (left) and PIV images of the meridional flow (right).

Figure 10

Photos (left) and PIV images of the meridional flow (right) near the interface with a better resolution than that in Fig. 9.

Figure 11

Schematic of changes in the flow topology as TCL develops: (a) $\mathrm{Re}=300$, (b) $\mathrm{Re}=400$, (c) $\mathrm{Re}=650$, and (d) $\mathrm{Re}=700$.