Migration in slow slurry flow including the effect due to Brownian Motion

• Main Author: Ibrahim, Mohammad
• Published: University of Surrey 2012
• Subjects: 540.475
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604351

When a dense particle-fluid mixture is made to flow in a conduit, experiments show that the particles tend to move to the centre where the shear rate is smallest. The effect vanishes when the particles are sufficiently small for thermal agitation by Brownian motion to dominate. While various theories have been put forward in the fluid mechanics literature to attempt to explain these phenomena, for further theory development it would be good to have microscopic data. As it is very difficult to obtain such data by experimental methods, simulation is the way forward. An existing Discrete Element code, initially developed for direct shear, has been modified for this purpose. For dense slurries the forces between particle-pairs are dominated by the lubrication limit, which holds when the gap width between particles, h, is much smaller than t heir mean diameter. The interaction needs to be modified to take account of the roughness of the particle surfaces (no matter how small this may be) to avoid a singularity at h = O. The interaction needs further augmentation to indicate what happens at h = 0 and for this eventuality a simple collision rheology is introduced. Brownian motion is implemented through a time-dependent, fluctuating force on the particles. This force is applied at each time step and for consistency the magnitude of the force must therefore be time-step-dependent. In the thesis, a methodology is outlined to characterise this. Starting from dilute aggregates, a fluctuating force spectrum is derived, which embodies the properties of the fluid and which can be carried over to the dense slurry case. The fluid is represented via. the interaction and the Brownian force spectrum and does not need to be modelled in any other way. Thus the particle motion is all that is required for this type of flow, which makes the process ideal for the Discrete Element Method. By adding fluctuations the aggregate increases its energy, which has to be conducted away through the walls. This can be done by giving the walls a fixed temperature and in the thesis a method is described of how this may be done in a physically realistic manner. A number of simulation runs are presented, both with and without Brownian motion. It is shown that the simulation captures the migration effect very well and shows that when the Brownian forces are increased (quantified by the Pclet number) the migration effect fades. Statistics of microscopic data, such as the particulate fluctuation energy arc also presented