This study introduces a new point-particle force model that attempts to account for the hydrodynamic influence of the neighbouring particles in an Eulerian–Lagrangian simulation. In previous point-particle models the force on a particle depends only on Reynolds number and mean volume fraction. Thus, as long as the mean local volume fraction is the same, the force on different particles will be estimated to be the same, even though the precise arrangement of neighbours can be vastly different. From direct numerical simulation (DNS) it has been observed that in a random arrangement of spheres that were distributed with uniform probability, the particle-to-particle variation in force can be as large as the mean drag. Since the Reynolds number and mean volume fraction of all the particles within the array are the same, the standard models fail to account for the significant particle-to-particle force variation within the random array. Here, we develop a model which can compute the drag and lateral forces on each particle by accounting for the precise location of a few surrounding neighbours. A pairwise interaction is assumed where the perturbation flow induced by each neighbour is considered separately, then the effects of all neighbours are linearly superposed to obtain the total perturbation. Faxén correction is used to quantify the force perturbation due to the presence of the neighbours. The single neighbour perturbations are mapped in the vicinity of a reference sphere and stored as libraries. We test the pairwise interaction extended point-particle (PIEP) model for random arrays at two different volume fractions of $\unicode[STIX]{x1D719}=0.1$ and 0.21 and Reynolds numbers in the range $16.5\leqslant Re\leqslant 170$ . The PIEP model predictions are compared against drag and lift forces obtained from the fully resolved DNS simulations performed using the immersed boundary method. Although not perfect, we observe the PIEP model prediction to correlate much better with the DNS results than the classical mean drag model prediction.

Recent research (Zeng, PhD thesis, 2007; Zeng et al., Phys. Fluids, vol. 21, 2009, art. no. 033302) has shown that both the shear- and wall-induced lift contributions on a particle sharply increase as the gap between the wall and the particle is decreased. Explicit expressions that are valid over a range of finite Re were obtained for the drag and lift forces in the limiting cases of a stationary particle in wall-bounded linear flow and of a particle translating parallel to a wall in a quiescent ambient. Here we consider the more general case of a translating and rotating particle in a wall-bounded linear shear flow where shear, translational and rotational effects superpose. We have considered a modest Reynolds number range of 1–100. Direct numerical simulations using immersed boundary method were performed to systematically figure out the characteristics of hydrodynamic forces on a finite-sized particle moving while almost in contact with a wall. We present composite correlation for the hydrodynamic forces which are in agreement with all the available low-Reynolds-number theories.

Linearized viscous compressible Navier–Stokes equations are solved for the transient force on a spherical particle undergoing unsteady motion in an inhomogeneous unsteady ambient flow. The problem is formulated in a reference frame attached to the particle and the force contributions from the undisturbed ambient flow and the perturbation flow are separated. Using a density-weighted velocity transformation and reciprocal relation, the total force is first obtained in the Laplace domain and then transformed to the time domain. The total force is separated into the quasi-steady, inviscid unsteady, and viscous unsteady contributions. The above rigorously derived particle equation of motion can be considered as the compressible extension of the Maxey–Riley–Gatignol equation of motion and it incorporates interesting physics that arises from the combined effects of inhomogeneity and compressibility.