# Numerical Investigation on the Symmetric Breakup of Bubble within a Heated Microfluidic Y-Junction

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}at the maximum mass flux. The studies from Qiu et al. [25], Yuan et al. [26], and Yin et al. [27] also indicated the merits of configuring micro-pinfin structure for two-phase flow. Apart from the application of pinfin, the open microchannel structure could also produce better heat transfer [28,29]. Vontas et al. [30] numerically evaluated the effect of wettability on boiling heat transfer. The heat transfer mechanism was found to vary with wettability. Generally, the hydrophilic surface could lead to a larger CHF owing to the efficient liquid supply, while the hydrophobic surface could produce a larger heat transfer coefficient due to easier nucleation [31]. Based on this point, some studies focused on the surface with heterogeneous wettability [32,33], which was the combination between the hydrophilic and hydrophobic surfaces. The kind of working fluid also significantly influenced the phase-change process [34]. Compared with the single kind of working fluid, the mixture working fluid may be beneficial to heat transfer [35]. It is well-known that instability of heat transfer is harmful in engineering applications [36], and many works are devoted to the suppression of instability. Lu et al. [37] conducted experiments on flow instability under boiling conditions. Instability was prone to emerge at annular flow mode. A prediction model was developed to predict the instability behavior. By performing detailed analyses, Alugoju et al. [38] revealed that the instability can be mitigated by employing the diverging microchannel.

## 2. Problem Description and Mathematical Model

#### 2.1. Problem Description

^{2}to 12,000 W/m

^{2}. The saturated HFE-7100 liquid entered the microfluidic Y-junction through the inlet, with the Reynolds number (Re, U·W/υ) varying from 180 to 420. The properties of HFE-7100 are gathered in Table 1 [39]. To efficiently facilitate the heat transfer performance, the seed bubble strategy was adopted [40], where the bubble diameter was fixed at 0.8 W. Before placing the seed bubble, the single-phase case was run until the velocity and temperature fields became steady. In the simulation, the contact angle for all the walls was set as 0°.

#### 2.2. Mathematical Model

_{S}:

## 3. Verification of the Numerical Model

^{2}. The initial bubble length was 3 W. Figure 2c,d, respectively, show the bubble nose location and the distribution of local heat transfer, which were consistent with the simulation from Magnini et al. [47]. In brief, the established numerical model was capable of simulating the two-phase flow and phase change accurately.

## 4. Results and Discussion

#### 4.1. Bubble Behaviors and Flow Characteristics

^{2}to 16,000 W/m

^{2}. The bubble was pushed forward by the fluid and symmetrically broke within divergence region, with continuous growth. By changing the heating intensity, two various breakup modes can be seen: (1) “Breakup with tunnel” emerging at low q (see Figure 3b). Under this mode, the bubble volume was still small when arriving at divergence, and thus the channel cannot be fully blocked. The liquid can easily bypass the bubble and flow to the downstream. It is worth noting that the bubble breakup was closely related to the generated shearing force [48]; (2) “Breakup with obstruction” emerging at high q. Under this mode, the significant bubble growth occurred, and the channel was fully blocked by the bubble. The liquid cannot easily bypass the bubble, and only the accumulated pressure drove the breakup process. The velocity field was significantly affected by the bubble growth characteristics, and one of the most notable features was the significant acceleration of downstream liquid at smaller Re and higher q.

_{in}·t/W. During the breakup process, the bubble neck thickness monotonically declined, where the declining rate experienced large variations. For the earlier squeezing stage, the declining rate of neck was relatively small and uniform. It was found that this stage took up the majority of breakup process. As the time elapsed, the bubble broke more rapidly, indicating the appearance of pinch-off stage. The breakup was governed by surface tension and could not halt in this stage [10]. In other words, if the upstream liquid supply was removed, the bubble could still break into two daughter bubbles. The duration time of the pinch-off stage was much shorter than that of the squeezing stage. As a special case, in the case of q = 2000 W/m

^{2}(with Re = 300), the bubble cannot touch the windward wall in the initial stage, which attenuates the breakup rate. This stage was named as ‘pre-breakup’ stage. Along with the increase in Re, the breakup rate increased, and the critical neck thickness for the breakup stage transition tended to decrease. Generally, the effect of q on the breakup rate was weak.

_{0}). The bubble volume increased due to evaporation, with increasing growth rate. In the later stage, the bubble evaporation area increased. The evaporation strengthened because of the low flow velocity and accumulation of sensible heat for branching channel. The fluctuations of bubble volume emerged at larger Re. The terminal bubble volume was decreased by 66.2% as Re varied from 180 to 420. The terminal bubble volume at q = 16,000 W/m

^{2}was 7.42 times larger than that at q = 2000 W/m

^{2}.

#### 4.2. Two-Phase Heat Transfer Performance

#### 4.2.1. Transient Heat Transfer

_{l}represented the coefficient of heat conductivity for liquid. Under the single-phase case, the Nu of BC-W wall was the largest, which was found to drastically decrease along the downstream direction. The Nu of BC-L wall was always the smallest, which was relatively smooth. Interestingly, the Nu of BC-T wall increased first and then decreased.

^{2}became notable, while it was still inconspicuous for the case of q = 2000 W/m

^{2}. The Nu at Re = 180 was larger than that at Re = 300, which was caused by the thinner liquid film thickness emerging at lower flow velocity. When the bubble nose located at downstream 7 W (see Figure 8j–l), both the affecting region and intensity of heat transfer enhancement drastically increased. At q = 2000 W/m

^{2}, the Nu in film region for BC-L wall was far larger than that for BC-W and BC-T walls. The difference in Nu in film region for different walls became tiny at q = 8000 W/m

^{2}.

#### 4.2.2. Time Variation of Heat Transfer

^{2}and 4000 W/m

^{2}, it was seen that the slight negative enhancement of heat transfer existed in the BC-T wall.

#### 4.2.3. Heat Transfer Enhancement

_{tp}/Nu

_{sp}) was conducted to directly show the evaporating heat transfer characteristics. The definition of time-averaged Nusselt number for the main channel was:

_{1}and t

_{2}respectively indicated the instants that the bubble nose just touching the heated main channel and touching the heated branching channel. The definition of the time-averaged Nusselt number for the branching channel was:

_{3}indicated the instant that the bubble nose just left the heated part. The heat transfer enhancement for the overall microchannel was acquired by averaging the treatment for the heat transfer enhancement of different walls.

^{2}to 16,000 W/m

^{2}. Interestingly, the heat transfer of BC-L wall showed a declining trend as q exceeded 8000 W/m

^{2}. This was because the bubble breakup mode had converted to “breakup with obstruction”. The contact degree between the bubble and BC-L wall during breakup process was weakened under this mode.

## 5. Conclusions

- Bubble breakup behaviors were significantly affected by evaporation. The “breakup with tunnel” and “breakup with obstruction” modes respectively occurred at low and high q. The bubble successively experienced long-period squeezing stage and short-period pinch-off stage during the breakup process, where the breakup rate under pin-off stage was much larger. Along with increase in Re, the bubble broke more rapidly, and the critical neck thickness tended to decrease. The influence of heat flux on the breakup was weak. The downstream fluid accelerated more obviously at smaller Re and higher q. The bubble annihilated the vortices existing within the divergence region and made the fluid flow more uniform.
- The evaporating heat transfer was affected by bubble behaviors. Compared to the single-phase case, the heat transfer was drastically improved due to the evaporation under two-phase case. The most significant enhancement occurred at the leeward wall. The increase in Re promoted single-phase convective heat transfer while hindering the two-phase heat transfer. Slight negative enhancement of heat transfer existed at lower q. In addition, the phenomenon of heat transfer deterioration was observed at higher q. Generally, the heat transfer was enhanced as q was increased.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Time variation of the local Nusselt number. (

**a**–

**c**) show the bubble profiles. (

**d**–

**f**), (

**g**–

**i**), and (

**j**–

**l**) respectively correspond to the instants of bubble nose locating at 1 W, 3 W, and 7 W.

**Figure 9.**Time variation of the averaged Nusselt number for different walls. (

**a**–

**d**), (

**e**–

**h**) respectively show the effects of Re and q on the averaged Nusselt number.

**Figure 10.**Time-averaged heat transfer enhancement for the microfluidic Y-junction versus Re (

**a**) and q (

**b**).

**Table 1.**Physical properties of HFE-7100 medium [39].

Properties | Liquid | Vapor |
---|---|---|

ρ (kg/m^{3}) | 1425 | 5.15 |

μ (Pa·s) | 3.56 × 10^{−4} | 1.11 × 10^{−5} |

σ (N/m) | 0.0136 | 0.0136 |

c_{p} (kJ/(kg·K)) | 1.430 | 0.900 |

λ (W/(m·K)) | 0.0618 | 0.0103 |

h_{fg} (kJ/kg) | 117.8 | 117.8 |

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**MDPI and ACS Style**

Chen, J.; Du, W.; Kong, B.; Wang, Z.; Cao, J.; Wang, W.; Yan, Z.
Numerical Investigation on the Symmetric Breakup of Bubble within a Heated Microfluidic Y-Junction. *Symmetry* **2022**, *14*, 1661.
https://doi.org/10.3390/sym14081661

**AMA Style**

Chen J, Du W, Kong B, Wang Z, Cao J, Wang W, Yan Z.
Numerical Investigation on the Symmetric Breakup of Bubble within a Heated Microfluidic Y-Junction. *Symmetry*. 2022; 14(8):1661.
https://doi.org/10.3390/sym14081661

**Chicago/Turabian Style**

Chen, Jingbo, Wen Du, Bo Kong, Zhiguo Wang, Jun Cao, Weiran Wang, and Zhe Yan.
2022. "Numerical Investigation on the Symmetric Breakup of Bubble within a Heated Microfluidic Y-Junction" *Symmetry* 14, no. 8: 1661.
https://doi.org/10.3390/sym14081661