Micro circular pipe flow in micron-sized soft particle solution considering the effect of spatial configuration force

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.