Search Results (26)

The quasi-steady low-Reynolds-number flow induced by a linear chain of multiple slip spheres translating along their common axis in a Newtonian fluid is investigated. The particles are allowed to differ in radius, Navier slip coefficient, migration velocity, and interparticle spacing. A semi-analytical solution of the governing Stokes equation is obtained using a boundary collocation method. Hydrodynamic interactions among the particles are shown to be significant under appropriate geometric and surface conditions. For the two-sphere configuration, the computed hydrodynamic forces agree closely with previously published asymptotic solutions derived via the twin multipole expansion method. In the three-sphere case, the presence of a third particle substantially modifies the forces acting on the other two, demonstrating non-negligible many-body interaction effects. The interaction strength is found to be more pronounced for smaller particles or those with lower slip coefficients. Calculations for longer particle chains further reveal a clear hydrodynamic shielding effect within the assembly. Full article

An analysis is presented for the steady thermophoresis and photophoresis of a homogeneous dispersion of identical aerosol spheres of typical physical properties and surface characteristics. The analysis assumes a moderately small Knudsen number (less than about 0.1), such that the gas motion lies within the slip-flow regime, including thermal creep, temperature jump, thermal stress slip, and frictional slip at the particle surfaces. Under conditions of low Peclet and Reynolds numbers, the coupled momentum and energy equations are analytically solved using a unit cell approach that explicitly incorporates interparticle interactions. Closed-form expressions are derived for the mean particle migration velocities in both thermophoresis driven by a uniform temperature gradient and photophoresis induced by an incident radiation field. The results reveal that the normalized particle velocities, referenced to those of an isolated particle, generally decrease with increasing particle volume fraction, though exceptions occur for thermophoresis. While thermal stress slip and thermal creep exert no influence on the normalized thermophoretic velocity, they markedly affect the normalized photophoretic velocity, which rises with the thermal stress slip to the thermal creep coefficient ratio. For both phenomena, the normalized migration velocities increase monotonically with the particle-to-fluid thermal conductivity ratio. Full article

This paper focuses on mixed seeds of Vicia villosa and Avena sativa, with their discrete element model and contact parameters being systematically calibrated and validated to provide reliable theoretical support for the structural design and parameter optimization of the air-assisted seed delivery system. The physical properties of both seed types, including triaxial dimensions, density, moisture content, Poisson’s ratio, and shear modulus, were first measured. The Hertz–Mindlin (no slip) contact model and the multi-sphere aggregation method were employed to construct the discrete element models of Vicia villosa and Avena sativa, with preliminary calibration of the intrinsic model parameters. Poisson’s ratio, elastic modulus, collision restitution coefficient, static friction coefficient, and rolling friction coefficient between the seeds and PLA plastic plate were determined through uniaxial compression, free fall, inclined sliding, and inclined rolling tests. Each test was repeated five times, and the calibration criterion for contact parameters was based on minimizing the relative error between simulation and experimental results. Based on this, experiments on the packing angle of mixed seeds, steepest slope, and a three-factor quadratic rotational orthogonal combination were conducted. The inter-seed collision restitution coefficient, static friction coefficient, and rolling friction coefficient were set as the experimental factors. A total of 23 treatments were designed with repetitions at the center point, and a regression model was established for the relative error of the packing angle with respect to each factor. Based on the measured packing angle of 28.01° for the mixed seeds, the optimal contact parameter combination for the mixed seed pile was determined to be: inter-seed collision restitution coefficient of 0.312, static friction coefficient of 0.328, and rolling friction coefficient of 0.032. The relative error between the simulated packing angle and the measured value was 1.32%. The calibrated inter-seed contact parameters were further coupled into the EDEM–Fluent gas–solid two-phase flow model. Simulations and bench verification tests were carried out under nine treatment combinations, corresponding to three fan speeds (20, 25, and 30 m·s⁻¹) and three total transport efficiencies (12.5, 17.5, and 22.5 g·s⁻¹), with the consistency coefficient of seed distribution in each row being the main evaluation variable. The results showed that the deviation in the consistency coefficient of seed distribution between the simulation and experimental measurements ranged from 1.24% to 3.94%. This indicates that the calibrated discrete element model for mixed seeds and the EDEM–Fluent coupled simulation can effectively reproduce the air-assisted seed delivery process under the conditions of Vicia villosa and Avena sativa mixed sowing, providing reliable parameters and methodological support for the structural design of seeders and DEM-CFD coupled simulations in legume–grass mixed sowing systems. Full article

The quasi-steady creeping flow of a viscous fluid around a slip sphere translating perpendicular to one or two large slip planar walls at arbitrary relative positions is analyzed. To solve the axisymmetric Stokes equation for the fluid flow, we construct a general solution using fundamental solutions in spherical and cylindrical coordinate systems. Boundary conditions are first applied to the planar walls using the Hankel transform and then to the particle surface using a collocation method. Numerical results of the drag force exerted by the fluid on the particle are obtained for different values of the relevant stickiness/slip and configuration parameters. Our force results agree well with existing solutions for the motion of a slip sphere perpendicular to one or two nonslip planar walls. The hydrodynamic drag force acting on the particle is a monotonic increasing function of the stickiness of the planar walls and the ratio of its radius to distance from each planar wall. With other parameters remaining constant, this drag force generally increases with increasing stickiness of the particle surface. The influence of the slip planar walls on the axisymmetric translation of a slip sphere is significantly stronger than its axisymmetric rotation. Full article

Porous media have great application prospects, such as transpiration cooling for the aerospace industry. The main challenge for the prediction of gas permeability includes the geometrical complexity and high Knudsen number of gas flow at the nano-scale to micro-scale, leading to failure of the conventional Darcy’s law. To address these issues, the Quartet Structure Generation Set (QSGS) method is improved to construct anisotropic and heterogeneous three-dimensional porous media, and the lattice Boltzmann method (LBM) with the multiple relaxation time (MRT) collision operator is adopted. Using MRT-LBM, the pressure boundary conditions at the inlet and outlet are firstly dealt with using the moment-based boundary conditions, demonstrating good agreement with the analytical solutions in two benchmark tests of three-dimensional Poiseuille flow and flow through a body-centered cubic array of spheres. Combined with the Bosanquet-type effective viscosity model and Maxwellian diffuse reflection boundary condition, the gas flow at high Knudsen (Kn) numbers in three-dimensional porous media is simulated to study the relationship between pore-scale anisotropy, heterogeneity and Kn, and permeability and micro-scale slip effects in porous media. The slip factor is positively correlated with the anisotropic factor, which means that the high Kn effect is stronger in anisotropic structures. There is no obvious correlation between the slip factor and heterogeneity factor. Full article

This study investigates the consistent and uniform movement of two spherical particles within an infinite porous medium saturated with a couple stress fluid, with a particular focus on the effects of surface slippage. The research reveals that surface slippage significantly reduces the drag force experienced by the particles, thereby influencing their hydrodynamic interactions. Conversely, increases in permeability and particle size similarity tend to enhance both the drag force and the inter-particle interaction forces, affecting the overall dynamics of particle motion. The analysis is conducted within the low-Reynolds-number regime, characteristic of laminar flow dominated by viscous forces, and employs boundary collocation methodologies to derive semi-analytical solutions to the governing differential equations. This approach enables a detailed characterization of the flow behavior and inter-particle forces in intricate fluid environments, including those with porous matrices and complex rheological properties. The findings from this investigation are consistent with prior numerical analyses, notably those conducted by Alotaibi and El-Sapa (2025), and corroborate earlier studies by Shehadeh and Ashmawy (2019), which examined cases of no slippage and permeability effects. Additionally, the results align with earlier research by Shreen et al. (2018) concerning viscous fluids, thereby reinforcing the validity of the conclusions. Overall, the study enhances the understanding of particle-fluid interactions in porous, couple stress-rich media, providing valuable insights into the roles of surface slippage, permeability, and particle size in determining hydrodynamic forces. Full article

This research investigates the impact of second-order slip conditions, Stefan flow, and convective boundary constraints on the stagnation-point flow of couple stress nanofluids over a solid sphere. The nanofluid density is expressed as a nonlinear function of temperature, while the diffusion-thermo effect, chemical reaction, and thermal radiation are incorporated through linear models. The governing equations are transformed using appropriate non-similar transformations and solved numerically via the finite difference method (FDM). Key physical parameters, including the heat transfer rate, are analyzed in relation to the Dufour number, velocity, and slip parameters using an artificial neural network (ANN) framework. Furthermore, response surface methodology (RSM) is employed to optimize skin friction, heat transfer, and mass transfer by considering the influence of radiation, thermal slip, and chemical reaction rate. Results indicate that velocity slip enhances flow behavior while reducing temperature and concentration distributions. Additionally, an increase in the Dufour number leads to higher temperature profiles, ultimately lowering the overall heat transfer rate. The ANN-based predictive model exhibits high accuracy with minimal errors, offering a robust tool for analyzing and optimizing the thermal and transport characteristics of couple stress nanofluids. Full article

This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart, the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings. A purely viscous medium and no-slip conditions are used to validate the numerical approach and results. Full article

In this article, we address resistance forces and torques acting onto a body with arbitrary shape moving in an unsteady Stokes flow. We start analyzing the functional form of the expressions for forces and torques, which depend on the frequency parameter and on the position of the body in the domain of the fluid, and determining the asymptotic limits for high and low frequencies. In this regard, we show that, for high frequencies (hence short times), forces and torques are obtained by the associated hydrodynamic problems considering ideal potential flows, independently of the geometry of the problem. Afterwards, with the aim of obtaining expressions for forces and torques valid in the entire range of frequencies, we extend to the unsteady case the reflection method, largely employed in the theory of the steady Stokes flows. In this way, general expressions are provided in terms of the Faxén operators of the body and the Green function associated with the geometry of the confinement, that are valid, to the leading order, at any frequency, independently of the geometry of the problem. Finally, as the application of the general expressions, explicit relations for the resistance forces acting onto a spherical body with no-slip boundary conditions near a plane wall with full-slip boundary conditions are obtained, valid over the entire frequency range, provided that the distance between the plane and the sphere is larger than one sphere radius. Full article

This work focuses on the effects of ultrasonic shot peening (USP) on grain refinement and orientation behavior in the surface region of GH4151 superalloy. The microstructure evolution of the alloy under USP durations were studied. The effects of USP-induced grain refinement, orientation, and dislocation motion behavior were analyzed. The results indicated that during the USP process, the plastic deformation of the surface layer of superalloys is accompanied by changes in grain size and orientation. The random impact of the spheres on the surface area promotes grain refinement and grain rotation, enhancing the randomness of grain orientations and reducing the texture strength and the proportion of “soft” orientation distribution. Over a long period of treatment, a large number of spheres cause the slip planes and slip directions of each grain to rotate due to the additional shear stress from the impact, resulting in relatively consistent plastic deformation on the surface and the enhanced randomness of grain orientations, thus reducing the high texture strength introduced by previous machining processes. The understanding of dislocation pile-up behavior and the relationship between externally applied shear stress, pile-up characteristics, and grain refinement is essential for optimizing the USP process and achieving the desired material properties. Full article

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived. Full article

To provide the necessary theoretical models of sphere–soil interaction for the structural design, motion control, and simulation of spherical robots, this paper derives analytical expressions for traction force and driving torque when spherical robots slide and sink into sandy terrain, based on terramechanics and multibody dynamics. Furthermore, orthogonal experimental analysis identifies the load, joint angular acceleration, and maximum joint angular velocity of spherical robots as influencing factors, highlighting that the load significantly affects their longitudinal motion performance. Experimental results indicate that rolling friction and additional resistance on sandy terrain cannot be ignored. The corrected theoretical model effectively replicates the temporal variation of driving torque exerted by spherical robots on sandy terrain. Numerical computations and experimental analyses demonstrate that increasing the radius of the sphere shell, the load, and the slip ratio all lead to increased traction force and driving torque. However, traction force and driving torque begin to decrease once the slip ratio reaches approximately 0.5. Therefore, in the design of spherical robot structures and control laws, appropriate parameters such as load and slip ratio should be chosen based on the established sphere–soil interaction theoretical model to achieve high-quality longitudinal motion performance on sandy terrain. Full article

As computer capabilities improve, Molecular Dynamics simulations are becoming more important for solving various flow problems. In this study, Couette and Poiseuille flows at different wall temperatures were investigated using a hard-sphere Molecular Dynamics simulation approach. Although a low spacing ratio was used in the simulations, the results are valid for rarefied gas flows when proper scaling based on the Knudsen number was used because only binary collisions with a hard-sphere model were considered. The main focus of this study was the examination of the effects of various wall speeds, pressure gradients, and wall temperatures. A pressure gradient was generated by developing a modified selective periodicity condition in the flow direction. With the combined effect of the pressure gradient and the wall velocities, subsonic, transonic, and supersonic speeds in nanochannels were examined. With the combination of different parameters, 1260 simulation cases were conducted. The results showed that there are temperature and velocity slips that are dependent on not only the temperature and velocity values but also on the magnitudes of a pressure gradient. The pressure gradient also caused nonlinearities in temperature and velocity profiles. Full article

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation. Full article

The flow field around a straight chain of multiple slip spherical particles rotating steadily in an incompressible Newtonian fluid about their line of centers is analyzed at low Reynolds numbers. The particles may vary in radius, slip coefficient, and angular velocity, and they are permitted to be unevenly spaced. Through the use of a boundary collocation method, the Stokes equation governing the fluid flow is solved semi-analytically. The interaction effects among the particles are found to be noteworthy under appropriate conditions. For the rotation of two spheres, our collocation results for their hydrodynamic torques are in good agreement with the analytical asymptotic solution in the literature obtained by using a method of twin multipole expansions. For the rotation of three spheres, the particle interaction effect indicates that the existence of the third particle can influence the torques exerted on the other two particles noticeably. The interaction effect is stronger on the smaller or less slippery particles than on the larger or more slippery ones. Torque results for the rotation of chains of many particles visibly show the shielding effect among the particles. Full article