The 7th Asian Symposium on Computational Heat Transfer and Fluid Flow, Tokyo, Sep. 3-7, 2019

ASCHT2019-179

Thermal and Flow Characteristics of Marangoni Convection
Near a Micro Bubble Attached to the Channel Wall
Takaya Atsumia, Kazuya Tatsumia*, Kyoko Namurab,
Reiko Kuriyamaa, Motofumi Suzukib, and Kazuyoshi NakabeaaDepartment of Mechanical Engineering and Science, Kyoto Universityb
Department of Micro Engineering, Kyoto University
Kyoto-Daigaku-Katura , Nishikyo-ku, Kyoto 615-8540, Japan* Corresponding author, E-mail: tatsumi@me.kyoto-u.ac.jp
Abstract

In this study, the Marangoni convection generated by locally heating the wall near a micro-bubble which is attached tothe channel wall is investigated using numerical solution. When the position of the hot spot deviated from the center ofthe bubble, a pair of vortices closely located to the bubble was formed. The position of the hot spot affected the flow
structure significantly: namely the height position of the high temperature area at the bubble surface changes, and thedistance to the top and bottom walls of the hot spot defines the vortex size and direction.
Keywords : Micro-Bubble, Marangoni Convection, Numerical Analysis, Hot Spot, Vortices

1. Introduction
Marangoni flow around a bubble provides various types of aspects in relation to the properties of the bubble andtemperature distribution. One interesting phenomenon is the Marangoni convection around the bubble attached to the wallof a microchannel, the wall of which is locally heated near the bubble. In this case, a pair of strong vortices with thevorticity direction perpendicular to the wall is generated (see Fig.1) [1]. These flows can be applied to microfluidic devices
for fluid mixing, driving flow, concentrating and dispersing particles. However, the three-dimensional flow structure, thecause of the flow, and the effects of the hot spot conditions are not understood yet. In this study, we will numericalinvestigate the heat and flow characteristics of this Marangoni flow, and evaluate the effects of the hot spot location andthe size on the flow structure.

2. Numerical method
The governing equations solved in the present computation are the continuity, Navier -Stokes, and energy conservation
equations. The equations are discretized using Finite Volume method. Immersed boundary (IB) method was used tomodel the interface between the fluid and bubble. Marangoni effect was considered by inserting the modified velocity
derived from Eq. (1) to the grid to which the IB method was applied.
𝜕𝑢𝑠
1 𝜕𝜎 𝜕𝑇=−(1)𝜕𝑛𝜇 𝜕𝑇 𝜕𝑠

𝜇 is viscosity, 𝜎 is surface tension. 𝑠 and 𝑛 are the tangential and the normal directions to the interface, respectively. The
fluid properties of water at 20°C was used in the computation as the effects of property variation as the temperature effectwas not large. Figure 2 shows the computational domain of the sphere bubble attached to the bottom wall. The radius ofthe bubble is R = 25m, and the distance between the bubble center and channel wall is 24.5m. A hot spot of circularshape of radius 5m is applied to the bottom wall at location of (0,l,0). The temperature of the hot spot is uniform, andis 80°C, while other boundaries were set as 20°C. No-slip condition is applied to the top and bottom boundaries of thedomain, and symmetric condition is applied to the side boundaries for temperature and velocity fields.

Figure 1: Top view of a pair of vortices
generated around the micro bubble [1].

(a) top view(b) side view
Figure 2: Computational domain of the sphere (bubble)
attached to the bottom wall of parallel plate channel.

The 7th Asian Symposium on Computational Heat Transfer and Fluid Flow, Tokyo, Sep. 3-7, 2019

3. Results and Discussion
Figure 3 shows the streamlines and temperature of the bubble surface, Tsurf, for the case of the hot spot located at thebubble center (l=0). Tsurf shows an axisymmetric distribution about the z – axis, and a vortex ring is generated around thebubble due to the Marangoni effect.
Figure 4 shows the case of the hot spot location deviated from the bubble center (l/R=2.0). In this case, high Tsurf area atthe bubble surface is located at the side of the bubble surface. The fluid flows from this area to the low temperature area
along the surface due to the Marangoni effect. The flow, then, reaches the top and bottom walls and flow in the x directions
along the wall. The flow partially separates from the bubble and wall, and a portion of the fluid flow back and generatevortices as shown in Fig. 4(a) as fluid should be supplied to the high Tsurf area.
Figure 5 shows the result of the case when the hot spot is located closer to the bubble center within R as l/R=0.4. Tf shownin the figure is the temperature of the fluid at y - z section (x=0). Area of high Tf and Tsurf is formed in adjacent to thebottom wall. Due to the tangential direction of the high Tsurf area, Marangoni convection in x and y positive directions isgenerated significantly. To conserve the mass, part of the flow forms vortices near the wall and returns to the high Tsurfarea. On the other hand, Marangoni convection and vortices decreases near the top wall. The effect of the area size of thehot spot is also discussed in our presentation.

4. Conclusions
We investigated the mechanism of the Marangoni flow and a pair of vortices generated around the micro-bubble attachedon the channel wall. As the hot spot is located far from the bubble, high temperature area is formed at the side of thebubble and a large scale vortices is generated in the height direction of channel. When hot spot is located very close tothe bubble, strong vortices is generated locally which was attributed to the direction of the Marangoni flow and flow
separation. Thus we can control the vortex structure by changing the position (and size) of the heating area.

Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 17H01050.

References[1] K. Namura et al., Applied Physics Letters, 106, 043101 (2015).
[2] Y. Zheng et al., Lab. Chip, 11, 3816 (2011).

Figure 3: Streamlines and surface temperature
distribution for the case of heating the bubble's center.

(a) top view(b) bird-eye view
Figure 4: Streamlines and temperature distribution of
bubble surface and fluid for the case of l=50m.

(a) top view(b) side view(c)bird-eye view
Figure 5: Streamlines and temperature distributions of bubble surface and fluid for the case of l=10m.