Drag and lift forces acting on linear and irregular agglomerates formed by spherical particles

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.