The solid–liquid two-phase flow with coarse particles is ubiquitous in natural phenomena and engineering practice, which is characterized by coarse particles, high particle concentration, and large particle size distribution. In this work, the numerical models describing two-phase flows are reviewed, which given that the Eulerian–Lagrangian method is applicable in this work. Then, some modified models are proposed for the situation where the conventional Eulerian–Lagrangian method is not applicable to deal with coarse particles. The continuous phase equations of liquid are solved based on the finite volume method. The pressure implicit with splitting of operators algorithm for solving the Navier–Stokes (N–S) equations of the pseudo-single-phase flow, considering phase fraction and momentum exchange source term, is proposed. The discrete coarse particle is tracked in the Lagrangian method. A virtual mass distribution function is proposed for calculating coarse particle volume fraction. A weighted function method relating to the particle size is given for the interpolation between the Eulerian and Lagrangian fields. The barycentric coordinates are introduced into the particle localization. All the modified models are algorithmically implanted in the open-source field operation and manipulation (OpenFOAM) as a new solver named coarse discrete particle method FOAM (CoarseDPMFoam). Subsequently, the applicability of the numerical simulation method is verified by some typical test cases. The proposed numerical simulation method provides new ideas and methods for the mechanism investigation and engineering application of the two-phase flow with coarse particles.

Solid–liquid two-phase flow with dense coarse particles in the pipeline exists widely in energy and resources engineering, especially in the prospective hydraulic lifting scenario of deep-sea mining. In this paper, the coarse particles' transportation behavior in a vertical pipe is investigated based on an optimized Eulerian–Lagrangian method proposed in our previous work. The coarse particle transportation in the vertical pipe is characterized as multi-processes and multi-physical effects and is not fully captured due to the limitations on experimental apparatus, experimental measurement techniques, and numerical simulation techniques. Little research has been done on the local characteristics of the flow and their effect on the hydraulic lifting performance. The characteristics of the internal flow field, particle retention, and hydraulic lifting efficiency are disturbed under the condition of the continuous supply with the constant inlet two-phase concentration and velocity. The simulation results illustrate that particle transportation process can be roughly divided into three stages, single phase flow stage, mixing stage, and stable transportation stage, and shows a dilute-dense non-continuous flow pattern due to particle retention. Based on parametric studies, the retention phenomenon is alleviated by the increase in the water inlet velocity and almost disappears at approximately 12 000 of the Reynolds number, where the flow pattern transition occurs. Finally, the hydraulic lifting performance, such as a critical lifting condition and the friction loss, is analyzed and the transition of flow pattern is discussed.

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell–substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction–diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin–ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.