Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For monodispersed suspension and transport in porous media with distributed pore sizes, the microstochastic model allows for upscaling and the exact solution is derived for the obtained macroscale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores.

The fundamental aspects of the Taylor-series expansion method of moment (TEMOM) model proposed to model the aerosol population balance equation due to Brownian coagulation in the continuum regime is shown in this study, such as the choice of the expansion point u, the relationship between asymptotic behavior and analytical solution, and the error of the high-order moment equations. All these analyses will contribute to the buildup of the theoretical system of the TEMOM model.

Manipulation and sorting of particles utilizing microfluidic phenomena have been a hot spot in recent years. Here, we present numerical investigations on particle trapping techniques by using intrinsic hydrodynamic effects in an expansion-contraction microfluidic device. One emphasis is on the underlying fluid dynamical mechanisms causing cross-streamlines migration of the particles in shear and vortical flows. The results show us that the expansion-contraction geometric structure is beneficial to particle trapping according to its size. Particle Reynolds number and aspect ratio of the channel will influence the trapping efficiency greatly because the force balance between inertial lift and vortex drag forces is the intrinsic reason. Especially, obvious inline particles contribution presented when the particle Reynolds number being unit. In addition, we selected three particle sizes (2, 7, and 15 μm) to examine the trapping efficiency.

A coupled system model of partial differential equations is presented in this paper, which concerns the variation of the pressure and temperature, velocity, and density at different times and depths in high temperature-high pressure (HTHP) gas-liquid two-phase flow wells. A new dimensional splitting technique with Eulerian generalized riemann problem (GRP) scheme is applied to solve this set of conservation equations, where Riemann invariants are introduced as the main ingredient to resolve the generalized Riemann problem. The basic data of “X well” (HTHP well), 7100 m deep, located in Southwest China, is used for the case history calculations. Curve graphs of pressures and temperatures along the depth of the well are plotted at different times. The comparison with the results of Lax Friedrichs (LxF) method shows that the calculating results are more fitting to the values of real measurement and the new method is of high accuracy.

The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for $m_0$ and 4% for $m_2$. The detailed distribution of each submodal could also be investigated through current model.

Collision between 2D circular particles suspension in Couette flow is simulated by using multiple-relaxation-time based lattice Boltzmann and direct forcing/fictitious domain method in this paper. The patterns of particle collisions are simulated and analyzed in detail by changing the velocity of top and bottom walls in the Couette flow. It can be seen from the simulation results that, while the velocity is large enough, the number of collisions between particles will change little as this velocity varies.

Porous asphalt is a standard asphalt built on aggregate storage bed which allows water to drain through it and reduces stormwater runoff. However, porosity of the porous asphalt and the storage bed may be effectively reduced due to trapping suspended solids from the water or from the asphalt damage. In this paper, we present mathematical modeling and numerical simulation of flow and damage of porous asphalt-paved roads. A mathematical model to describe the fine-particles transport carried by a two-phase flow in a porous medium is presented. The buoyancy, capillarity, and mixed relative permeabilities correlations to fit with the mixed-wet system are considered. Throughout this investigation, we monitor the changing of the fluids properties such as water saturation and solid properties such as porosity and permeability due to trapping the fine-particles.

This paper presents a modeling and computational study on particle erosion in curved ducts. It is found that the average erosion rates per impact range from $4.2\times {10}^{-7}$ to $9.5\times {10}^{-3}$ mm³/g under current conditions. For each doubled inlet velocity, the increases of erosion rates per impact are 2–14 times. The erosion rate per impact varies with particle diameter with “√” shape through bends, which is similar to the particle deposition behavior in duct flows. The erosion rate curves per injected particle show the shapes of a 90-degree anticlockwise rotated “S” and a wide open “V,” respectively, for three larger and smaller inlet velocities. The average erosion rates per injected particle are 1.4–18.9 times those rates per impact due to huge amounts of impacting, especially for those depositing particles. It is obvious that the erosion rate distribution per impact is similar to a “fingerprint” with five clear stripes and a lower “cloud” along the bend deflection angle for the three largest particles; yet, for other smaller particles, the erosion rate distributions are much like an entire “cloud.”

The concentration and orientation of suspended fibers in a mixing layer are investigated numerically. Two cases (diffusive and nondiffusive) are investigated for the fiber concentration distribution. The fine structures of the instantaneous distributions under these two cases are very different due to molecular diffusion. Sharp front of concentration is observed in the nondiffusive case. However, there is no obvious difference in the mean concentration between the two cases. With regard to the orientation, a fiber may rotate periodically or approach an asymptotic orientation, which is determined by a determinant defined with the stain rate. The symmetric part of the strain rate tends to make a fiber align to an asymptotic orientation, while the antisymmetric part drives a fiber to rotate. When a fluid parcel passes through a region with relatively high shear rate, fibers carried by the fluid parcel are most likely to rotate incessantly. On the other hand, in the region of relatively high extension rate, fibers tend to align to some asymptotic orientation. Generally, fibers tend to align with the shear plane. This fact has significant implications in predicting the rheological properties of fiber suspension flows.

Numerical simulations were conducted to study the melt flow under the influence of control devices in a T-type two-strand bloom caster tundish via the open source Computational Fluid Dynamics software OpenFOAM. Three different cases were studied: a bare tundish, a tundish with two pairs of baffles, and a tundish equipped with a turbulence inhibitor and a pair of baffles. Turbulence inhibitor and baffles arrangement showed an improvement of the fluid flow characteristics, yielding lower values of dead volume and higher values of plug flow. With a turbulence inhibitor, the velocity of metal which flows directly toward the tundish floor is smaller and the turbulence kinetic energy of the melt top surface is lower than the other two arrangements.

The fluid-driven efficiency of the micropump based on induced charge electroosmotic was studied by numerical simulation method. In this paper, we propose to make some improvement against the T-shaped piping design of micropump, and we embed a janus cylinder in the junction of the T-shaped pipe for the micropump design. We offer different voltage to the inlet of the pipe and carry out the numerical study of the fluid field induced by the cylinder, and the comparison of the velocity and flux of the outlet in different voltage as carried out. It is found that there are two symmetrical circulations around the polarizable side of the cylinder. And the comparison results show that the flow and the velocity of the outlet were increased with the increasing voltage of the entrance.

We introduced a direct and effective approach to obtain the exact analytical solution for the nanoparticles-water flow over an isothermal stretching sheet with the effect of the slip model. In particular, we examined and compared the effect of the existence of five metallic and nonmetallic nanoparticles, namely, Silver, Copper, Alumina, Titania, and Silicon Dioxide, in a base of water. The most interesting physical parameters were then discussed in the presence of no-slip model, first order slip, and second order slip parameters. It is found that, with no-slip effect, the present exact solutions are in a very good agreement with the previous published results. On the other hand, with the effect of the slip model, increase in the nanoparticle volume friction decreases the velocity for the high density of nanoparticles, increases it for the low density of them, and increases the temperature for all investigated nanoparticles. Further, increase in the wall mass decreases the velocity and temperature; however, it increases the local skin friction. Furthermore, increase in the slips slows down the velocity, increases the temperature with an impressive effect in the injection case, and decreases the local skin friction and the reduced Nusselt number. It was also demonstrated that, as the nanoparticle becomes heavier, this results in increase and decrease in reduced skin friction coefficient and reduced Nusselt number, respectively, with significant effect in the presence of the second slip. Finally, Silver is the suitable nanoparticle if slowing down the velocity and increasing the temperature are needed; Silicon Dioxide is the appropriate nanoparticle if different behavior is to be considered.

The boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective boundary condition is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the local Nusselt number and the local Sherwood number as well as the temperature and concentration profiles for some values of the convective parameter, stretching/shrinking parameter, Brownian motion parameter, and thermophoresis parameter. The results indicate that the local Nusselt number is consistently higher for higher values of the convective parameter. However, the local Nusselt number decreases with increasing values of the Brownian motion parameter as well as the thermophoresis parameter. In addition, the local Sherwood number increases with increasing Brownian motion parameter and decreases with increasing convective parameter and thermophoresis parameter.

The method of moments is employed to predict the evolution of aerosol particles in the rainfall process. To describe the dynamic properties of particle size distribution, the population balance equation is converted to moment equations by the method of moments and the converted equations are solved numerically. The variations of particle number concentration, geometric mean diameter, and geometric standard deviation are given in the cases that the Brownian diffusion and inertial impaction of particles dominate, respectively. The effects of raindrop size distribution on particle size distribution are analyzed in nine cases. The results show that the particle number concentration decreases as time goes by, and particles dominated by Brownian diffusion are removed more significantly. The particle number concentration decreases much more rapidly when particle geometric mean diameter is smaller, and the particle size distribution tends to be monodisperse. For the same water content, the raindrops with small geometric mean diameters can remove particles with much higher efficiency than those with large geometric mean diameters. Particles in the “Greenfield gap” are relatively difficult to scavenge, and a new method is needed to remove it from the air.