Analysis Of Incompressible Viscous Non-Newtonian Fluid Of Single Screw Extruder

Over the past few decades, the single screw extruder is widely used in areas such as pharmaceuticals, food production, continuous feed processing and polymer processing, it played an important role. Due to the complexity of its own geometry and the motion for fluids, although over the several decades, there are many scholars have done some research on the theory of solid and melt conveying, as well as to the numerical of mixing characteristics in screw channel and simplify physical models, a number of relevant literature and monograph published by them, but the mathematical theoretical is still very backward, so far, there is not a complete model which establish from conveying, melting to extruding, the most of the relevant mathematical model from analysis to calculate all focused on the metering section.In Eulerian coordinate system, this article studied the inflow-outflow boundary value problem for three-dimensional viscous incompressible shear-thinning non-Newtonian rotating flow through the metering section of a single-screw extruder. In the rotating coordinate system, for the partial differe-ntial equations of motion for incompressible shear-thinning non-newtonian fluid Through Coordinate transformation, the inner rigid rotation is converted into rotation of boundary, the fixed point theorem method and the energy estimate are used to prove the existence of the weak solutions, meanwhile, we have proved the uniqueness result which is in the case of the initial conditions and the angular velocity of the rigid are small enough. In above of partial differential equations, p is pressure, u=(u1,u2,u3)T is velocity, τ(Du) is partial stress tensor,▽=((?),(?),(?))T is the velocity gradient and is divergence operator, S0be the subdomain of the metering section of the cylindrical screw extruder occupied by the screw at the initial time,Γharrel denotes the surface of the barrel, and inflow-outflow boundary condition along the axial direction y3, say Γin and Γout, satisfy the Bird-Carreau constitutive equations τ(Du)=[μx+(μ0＋μ∞)(1＋λ2Du:Du)2]Du. where μ0is the viscosity at zero shear rate,μ∞is the viscosity at infinite shear rate,μ0>μ∞>0. λ>0is the consistency of the fluid,-1≤<γ<0is the power index. In addition, this paper also simple analysed and calculated some special circumstances,(such as the isothermal stationary slow flow in the metering section of the single screw extruder), under a rectangular geometry model of screw channels which be unwrapped and completely ignored the convective term, the pressure gradient is known, calculation of the velocity field by a standard method of separation of variables, although the convective term is not ignored, also through the Galerkin method construct a weak solution, It provided further theoretical guarantee for approximate calculation.