The presence of a wall near a rigid sphere is known to disturb the particle fore and aft flow field and thereby affect particle drag and lift. This effect has wide ranging implications in particulate flows such as the dynamics of blood cells in microvessels or the transport of particulates in channel and pipe flows. In this study, an Immersed Boundary Direct Numerical Simulation (IB-DNS) is used to predict the dynamics of a rigid spherical body in the presence of a wall at laminar flows. The wall effect is shown to be significant when the dimensionless ratio (L/D) of the particle diameter (D) to the wall distance (L) is less than 3, and when particle Reynolds number is less than 10. Based on the IB-DNS results, a correlation for the wall effect on drag coefficient is derived that can be used to predict the actual drag coefficient for rigid spheres under the influence of a wall for L/D between 0.75 and 3 and Reynolds number between 0.18 and 10. The data underlying the correlation developed herein is validated by comparison to published experimental, numerical, and analytical correlations. The application of the IB-DNS method to study the wall effect is both novel and significant. It is novel in that such an application is not yet demonstrated. It is significant in that it; (1) utilizes a uniform Cartesian fluid mesh and (2) requires no sub domains of higher grid resolution in the wall gap.

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