## 4 Conclusions  
In this paper, the physical fields of oil-water two-phase flow and oil-phase solute convection and diffusion in water are successfully coupled. Toluene is used as the contaminant dissolved in the oil phase and the chemoattractant of chemotactic bacteria. Based on the control equation of phase field model and the convection-diffusion equation of chemoattractant, the oil-water two-phase transfer field is simulated. Based on the convection-diffusion equation of bacteria and the chemotaxis velocity equation, the migration of chemotactic bacteria in the oil-water two-phase transfer field is simulated and the following conclusions are drawn:  
1. For the distribution of residual oil volume, under all of the simulation conditions, the residual oil volume in the high permeable area is significantly lower than that in the low permeable area, and residual oil droplets are easy to form in the small throat, high permeable area, and a residual oil belt is formed in the area connected with the low permeable area in the large throat, high permeable area. It is difficult for the water phase to invade the large-size, low-permeable zone, and the corresponding water phase begins to invade the small-size low-permeable zone after 1 min;
2. With the increase of the hydrophilic degree of the wetting wall, the overall residual oil is less, and the wall hydrophilicity promotes the oil phase to be displaced from the low permeable area. However, even when the wall wetting angle is \(\pi/6\) rad, there is still a large quantity of residual oil in the low permeable area;  
Figure 11: Average concentration of chemotactic bacteria with time at different flow rates.  
3. The higher the inlet flow rate is, the shorter the time is that is required to form the dominant channel in the high permeable area, and the relationship between the residual oil in the high permeable area and the flow rate is not significant. However, when the water phase drives the oil phase at a low flow rate (1.13 or 2.26 m/d), the water phase in 1 min tends to invade the low permeable area; 4. For the density distribution of chemotactic bacteria, from the beginning to the end, the chemotactic bacteria are largely gathered at the oil-water interface, and the number is more than that in the water phase. Therefore, chemotactic bacteria can react to the concentration gradient of the chemoattractant toluene formed by the oil-water two-phase transfer field, and enrich near the pollutants; 5. The lower the inlet velocity, the higher the average density of chemotactic bacteria in the chip at quasi-steady state. This is because when the inlet velocity is high, the chemotactic bacteria are washed away by water, which is not conducive to enrichment in the pollutant transition zone.  
Conceptualization, methodology, numerical simulation, L.H., T.H. and Z.D.; formal analysis, L.H.; writing--original draft preparation, L.H.; writing--review and editing, X.W., L.F. and T.L.; supervision, X.W. and L.F.; funding acquisition, C.Y. and X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Opening Fund of Shandong Key Laboratory of Oil-field Chemistry and the Fundamental Research Funds for the Central Universities, grant number 19 CX05006A, Shandong Provincial Natural Science Foundation, grant number ZR2021 ME108, and the National Natural Science Foundation of China, grant number 51874330 and 51974341.  
Not applicable.  
The authors sincerely acknowledge the assistance in microfluidic experiments from [PERSON] and [PERSON], and access to relative facilities and discussion from [PERSON], [PERSON], and [PERSON].  
The authors declare no conflict of interest.