Nano- and micrometer particles tend to stick together to form agglomerates in the presence of attractions. An accurate calculation of the drag and lift forces on an agglomerate is a key step for predicting the sedimentation rate, the coagulation rate, the diffusion coefficient, and the mobility of the agglomerate. In this work, particle-resolved direct numerical simulation is used to calculate the drag and lift forces acting on linear and irregular agglomerates formed by spherical particles. For linear agglomerates, the drag coefficient CD follows the sine squared function of the incident angle. The ratio between CD of a linear agglomerate and that for a sphere increases with the agglomerate size, and the increasing rate is a function of the Reynolds number and the incident angle. Based on this observation, explicit expressions are proposed for CD of linear agglomerates at two reference incident angles, 60° and 90°, from which CD at any incident angle can be predicted. A new correlation is also proposed to predict the lift coefficient CL for linear agglomerates. The relative errors for the drag and lift correlations are ∼2.3% and ∼4.3%, respectively. The drag coefficient for irregular agglomerates of arbitrary shape is then formulated based on the sphericity and the crosswise sphericity of agglomerates with a relative error of ∼4.0%. Finally, the distribution of the lift coefficient for irregular agglomerates is presented, which is non-Gaussian and strongly depends on the structure. The mean values and the standard deviations of CL can be well correlated with the Reynolds number.
When sedimenting in a viscous fluid under gravity, a cloud of particles undergoes a complex shape evolution due to the hydrodynamic interactions. In this work, Lagrange particle dynamic simulation, which combines the Oseen solution for flow around a particle and a Gauss–Seidel iterative procedure, is adopted to investigate the effects of the particle inertia and the hydrodynamic interactions on the cloud's sedimentation behavior. It is found that, with a small Stokes number (St), the cloud evolves into a torus and then breaks up into secondary clouds. In contrast, the cloud with a finite Stokes number becomes compact in the horizontal direction and is elongated along the vertical direction. The critical St value that separates the breakup mode and the vertical elongation mode is around 0.2. The cloud response time (t̂r) and the maximum settling velocity (V̂max) are measured at different Stokes numbers, particle Reynolds numbers, and particle volume fractions. A linear relationship, t̂r=aSt, is found between t̂r and the Stokes number and the correlation between V̂max and St can be well described by an exponential function V̂max=b1exp−b2St+b3. At last, the chaotic dynamics of the sedimentation system are discussed. A small difference between the initial configurations diverges exponentially. The sedimentation system containing particles with larger inertia has a lower divergence rate.
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