Mr Edward Bihari

Honours thesis

The flapping paddle mixer

It can be desirable in some fields of chemistry, medicine and biology to be able to mix fluids in a vat. These applications can involve the need for efficient mixing of chemical reactants. One method of accomplishing this mixing is in the use of turbulent flow, where high fluid velocities and energy are used. This paper considers a more gentle way of mixing without resorting to turbulent flows and the extent to which this is possible. In this paper, the mixing of an incompressible viscous fluid in a rectangular vat drawn in Figure 1 is considered. The vat is considered to be entirely two-dimensional and horizontal so that no body forces such as gravity are present. The fluid inside the vat is mixed using a paddle that fiaps backwards and forwards periodically. In this paper, the vat considered is exactly twice as long as it is wide, and the paddle's position as a function of time if prescibed by a simple cosine function, the amplitude of which is one fifth of the length. In the second section, the equations that govern the flow velocity in the Flapping Paddle Mixer will be presented. These equations are the incompressible Navier-Stokes equation and the continuity equation. These equations will be reformulated in terms of quantities called streamfunction and vorticity into a form that is more suitable for solution. The boundary conditions will be investigated so that the problem is specified completely. The method of solution of the problem presented in this section is discussed. This solution involves the finite difference method. In the third section, it is shown how the flow velocity solved for in the first section can be used to trace the particles around the mixer in order to infer how well the mixing is achieved. The Matlab code used for this process is first validated by tracing the particles through a point vortex and next through the more complicated flow of a Rotlet in order to replicate the results given by Cox and Finn fifi. In the fourth section, the results of applying the Matlab codes developed in the second and third sections are presented, including plots of the velocity field in the Flapping Paddle Mixer, of the advection of particles in the mixer, and of the vorticity in the mixer, where vorticity will be defined in the second section.