Micro circular pipe flow in micron-sized soft particle solution considering the effect of spatial configuration force
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摘要: 針對微米級軟顆粒溶液在微小孔道流動不符合泊肅葉流動規律問題，考慮受固體管壁影響軟顆粒形變產生的空間位形力作用，基于Navier-Stokes理論，推導軟顆粒溶液在圓管中的流速分布及流量表達式，引入顆粒形變因子以表征空間位形力作用的影響；建立考慮空間位形力作用的圓管流動數學模型.由微尺度流動特征實驗，得到軟顆粒溶液微圓管流動規律，與泊肅葉流動對比，結果顯示當管徑小于顆粒直徑時，相同壓力梯度下考慮空間位形力作用的流速比泊肅葉流動擬合結果更接近于實驗數據.通過數值計算分析發現，與泊肅葉流動下的速度分布和平均流量相比，當微圓管尺寸減小時，空間位形力作用隨之增大，其更大程度上影響流體在微圓管內的流動規律；當顆粒呈非球形且最小投影面積相同時，偏離球形顆粒程度越大，空間位形力作用越大，因此空間位形力作用在微小孔道流動中不可忽略.Abstract: With the development of liquid production and molecular synthesis technology, the application of soft particle solutions has become increasingly widespread. Soft particle solutions are also used in oil exploitation technology. The soft particles can be elastically deformed through the pores, and the whole process produces a resistance effect on flow. After breaking through the tunnel, the original shape is restored and continuously moved to the deep part of the oil layer. The soft particles do not only block the porous medium but also increase flow resistance. Moreover, they can generate deformation and break through the pores under a certain pressure to reach the depth of the reservoir. The microscopic forces mainly include Van der Waals force, electrostatic force, spatial configuration force, and surface tension. The effect of the spatial configuration force caused by the deformation of the soft particles affected by the tube wall action is considered to address the problem that micron-sized soft particle solutions in microtube deviate from the Poiseuille law. On the basis of Navier-Stokes theory, the flow velocity distribution and flow expression of the polymer solution in the tube were derived. A particle deformation factor was introduced to characterize the effect of the spatial configuration force. A mathematical model of microtube flow was established by considering the spatial configuration force. From the micro-scale flow characteristics experiment, the microtube flow in micron-sized soft particle solution was obtained. As evidenced by the results, when the tube diameter is smaller than the particle diameter, the flow velocity considering the spatial configuration force is closer to the experimental data than the Poiseuille flow under the same pressure gradient. Through the analysis of influencing factors, the spatial configuration force cannot be neglected in the microtube flow. Compared with the Poiseuille flow, the spatial configuration force increases and affects the microtube flow when the microtube size decreases. When the particles are non-spherical and the minimum projected area is the same, the greater the degree of deviation from the spherical particles and the greater the effect of the spatial configuration force.
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圖 1 球形顆粒通過圓柱形孔道示意圖.(a)顆粒未進入孔道；(b)顆粒完全進入孔道
Figure 1. Schematic diagram of spherical particles passing through a cylindrical tunnel: (a) outside the tunnel; (b) in the tunnel
圖 2 圓柱形顆粒通過圓柱形孔道示意圖.(a)顆粒未進入孔道；(b)顆粒完全進入孔道
Figure 2. Schematic diagram of cylindrical particles passing through a cylindrical bore: (a) outside the tunnel; (b) in the tunnel
圖 3 不同形狀顆粒和不同管徑比的形變因子分布
Figure 3. Distribution of deformation factors of particles with different shape particles and tube diameter ratios
圖 4 水平放置的微圓管流體流動示意圖
Figure 4. Scheme of fluid in the horizontal placement of microtube
圖 6 泊肅葉流動、考慮空間位形力流動和實驗流速與壓力梯度的關系.(a)15 μm；(b)10 μm
Figure 6. Relationship between Poiseuille flow, considering spatial configuration force flow, experimental flow velocity and pressure gradient: (a)15 μm; (b)10 μm
圖 7 空間位形力作用下不同圓管半徑的速度分布.(a)5 μm；(b)10 μm；(c)15 μm；(d)20 μm
Figure 7. Velocity distribution under different diameters considering spatial configuration force: (a)5 μm; (b)10 μm; (c)15 μm; (d)20 μm
圖 8 空間位形力作用下不同圓管半徑的平均流量變化曲線.(a)1~5 μm；(b)5~10 μm；(c)10~15 μm；(d)15~20 μm
Figure 8. Average flow curve under different diameters considering spatial configuration force: (a)1~5 μm; (b)5~10 μm; (c)10~15 μm; (d)15~20 μm
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