The Interaction Between Particles With An Interstitial Fluid & The Application In DEM

In this article a theoretical study of interactions between two particles with an interstitial fluid in an immersed system has been proceeded. GranUlar materials with such a fluid, which is widely applied in the areas of food, detergent, fertilizer etc, are frequently processed in industries in order to promote their handleability and flowability. Agglomeration is often useful and has advantage over a discrete system whereas exhibits some disadvantages in some cases, therefore it is necessary to discover its microscopic behaviors with some appropriate manner, eg numerical simulation with the Distinct Element Method. Based on Reynolds?lubrication theory, an approximate pressure equation for the tangential interaction between two arbitrary rigid spheres with an interstitial power-law fluid has been derived. In solving the equation, singularity appeared at the central line of the contact area has been successfully avoided with a technique, which is capable of transiting the initial condition into a boundary condition elsewhere, then a numerical solution to the pressure distribution can be obtained. Afterwards the integral expression of both the viscous force and the viscous moment is given. Comparison between the numerical solution and the asymptotic solution by Goldman et al is also presented, which indicates the proposed numerical results are reasonable much better than that asymptotic solution. In order to incorporate the algorithm into simulation with the Distinct Element Method, a technique of regression is utilized, and as a result, a set of regression formulas is obtained. Comparison on the tangential force and the moment between the numerical results and those with regression formulas shows that the later is in good coincidence with the numerical ones with a deviation less than 2%. Although in the derivation an approximation is taken, which needs to be proved afterwards, however, at least it could reduce to the solution that Goldman had reported for Newtonian case when the power index equals 1. In order to simplif~r the computation comparison for the magnitude between the normal and the tangential forces is made when the both interactions exist, from which it is observed that there is some relation between the both. Because the normal solution is more accurate than the tangential one, therefore the tangential force or moment can be obtained utilizing this relation from the normal solution, which had been analyzed previously. Consequently a regression procedure is used and a common formula is inferred. Comparison between the numerical and the regressed results shows a good agreement with an error of less than 2%. Finally, numerical simulation of the Distinct Element Method has been done for two simple examples, one is a periodic cell considering of two-dimensional arranged regular spheres under some applied condition, the other is a oblique collision between two spherical agglomerates. Visualized effects and behaviors for the interactions, including energy consumption and damage feature of liquid bridge, are briefly presented.