Drag laws for fluid-particle flows with particle size distribution Project Goal: Develop a constitutive model for the fluid-particle drag force for suspensions of binary mixtures of particles and generalize to Multicomponent systems Sundaresan: ACS-PRF: 43901-AC9

Drag laws: Low Reynolds number Flows Prior work: Van der Hoef et al., JFM (2005): Fluid flow past stationary bidisperse particle assemblies Drag correlation in terms of gas velocity Image taken from this source. Many recent studies on fluid-particle drag in such suspensions [van der Hoef et al. (2005), Beestra et al. (2007)] consider the special case of a fixed bed, where there is clearly no mean relative motion between the two solid phases. However, the inter-penetrating continua models for flowing binary suspensions require more general drag force models, where different types of particles can have different local averaged velocities relative to the interstitial gas. We are using a direct numerical simulation method to study this problem. Question that we address: Drag law in dynamically evolving binary suspensions where two types of particles have different local average velocities relative to the fluid phase.

Drag law for low Reynolds number flows of binary mixtures equally sized particles Fluid-particle force per unit volume of suspension: Results obtained in this study , , The drag force expressed in the volume-specific form. u denote local average velocity. Subscripts 1 and 2 denote the two types of particles. P is the pressure in the fluid phase. b denotes the volume-specific friction coefficient for a random array of stationary particles, already available in the literature. f denotes volume fraction.