# Asymmetric Magnetohydrodynamic Propulsion for Oil-Water Core Annular Flow Through Elbow
## 2 Magnetohydrodynamic Principles  
Magnetohydrodynamics (MHD) is the study of electrically conducting fluids, and the conductive medium is usually plasma or liquid metal, in which the magnetic field plays a dynamical role [35]. At present, the main research fields of MHD are astrophysics [36; 37; 38], micro- and nano-robot drive [39; 40; 41; 42; 43], accelerators [44; 45; 46; 47; 48], and so on [49; 50; 51]. Magnetohydrodynamics is based on the basic principle that through the interaction between the magnetic field generated by the electromagnetic coil and the electric field generated between the electrode plates, charged particles are subjected to the Lorentz force in the space between the electric and magnetic fields, resulting in definite acceleration [52; 53; 54]. The specific operating principle is shown in Figure 1. As can be seen from the diagram, the charged particle is accelerated in the direction of the force by the Lorentz force generated by the interaction of an applied static magnetic field with a constant voltage. Therefore, the principles of MHD can be used to accelerate or decelerate the electrolyte solution and to change the direction of fluid flow [55]. Depending on the type of electrical current applied, magnetic fluids are subdivided into DC (Direct Current) and AC (Alternating Current) magneto-fluid accelerators [56; 57; 58]. As heavy oil is constantly moving in the pipeline, and the AC-type magneto-fluid accelerator is unsuitable for scenarios where the conductor is continuously moving, the DC-type magneto-fluid accelerator was chosen for this design.  
In the process of oil and water two-phase flow through the elbow, due to the centrifugal force at the bend, gravity, and other factors, the center of the pipeline oil phase will have an impact on the water phase of the package, resulting in the rupture of the oil-water ring. The oil-water circulation conveying process is realized by the water ring wrapping the oil ring. When the oil-water ring flows through the elbow, due to centrifugal force, oil-water density difference, and other factors, the outer water ring is thrown to the outside of the pipe, and the thickness of the water ring becomes insufficient to support the oil ring, which destroys the original annular structure, thus leading to the rupture phenomenon. After the rupture of the oil-water annulus, the oil phase wrapped in the annulus due to the density difference will naturally float and may come into contact with the pipe wall to affect the movement of the outer water ring, accelerating the separation of the oil-water phase stratified flow. At the same time, the high viscosity of heavy oil will cause it to adhere to the pipe wall and form scaling, which will block the pipeline over time and cause a series of effects on heavy oil transportation. The differential MHD heavy oil flow stabilization accelerator in this design relies on the DC-type magneto-fluid accelerator design principle. By adding a set of electromagnetic devices at the elbow, the differential drive of the oil and water phases is achieved, so the oil-water ring can maintain a stable oil-water annular flow pattern through the elbow pipe section. When the oil-water ring passes through the elbow, the device outside the pipe will provide external force to the flowing water phase to ensure that the water phase will not break. The device will also act on the oil phase to prevent the oil phase from floating upwards, realizing the repair of the soon-to-be-damaged oil-water ring and ensuring that the oil-water ring passes through the transportation process smoothly in the elbow.