Papers by Keyword: Sphere

Abstract: The research presented in this scientific paper focuses on modeling the dynamics of multicomponent systems with particles of different geometries using the GROMACS software package. Three main types of particles were analyzed in the study: spheres, ellipsoids, and plates, each of which has its own unique geometric characteristics that affect their behavior in the environment. The modeling allowed us to investigate the influence of particle shape on their diffusion, self-organization, and interaction between particles of different shapes. In particular, spherical particles, having an isotropic geometry, show the highest diffusion coefficient, since their symmetrical structure minimizes the resistance of the environment. This, in turn, makes them ideal for modeling simple interactions in liquids or colloids. Ellipsoidal particles, due to their anisotropy, have a slightly reduced diffusion coefficient, since their orientation in space affects the motion. Plates, which have a significant surface area relative to the volume, demonstrate the lowest diffusion rate, which is associated with a large interaction with the environment and the resistance created by their geometry. The results of the study also showed that the diffusion coefficient decreases with increasing particle size for all types. At the same time, spheres demonstrated the highest diffusion coefficient at the same size compared to other geometries, while plates have the lowest values ​​of this indicator. Analysis of the trajectories of particle motion in space using the GROMACS software allowed us to assess the influence of geometry on particle mobility. It was found that spheres exhibit the largest displacement amplitude, which indicates their high mobility and chaotic nature of the motion. Ellipsoids have a more stable motion with smaller displacements, which is associated with their geometric anisotropy. Plates, due to the large resistance of the environment, have the smallest displacements, which indicates limited mobility. It should be noted that the obtained research results open up opportunities for a deeper understanding of interactions in complex multicomponent systems and can be useful for further research in various fields. It is also worth noting that the comparison of different types of particles with different geometries and their influence on diffusion processes allowed us to obtain valuable information for improving models and practical applications in relevant fields of science and technology.

Abstract: The article discusses the application of the discrete element method (DEM) for modeling the behavior of spherical particles in granular media. Key aspects of particle contact interactions, including frictional forces, elasticity, coordination number, and the shape factor of spherical particles, are analyzed and investigated. It is worth noting that the proposed methodology enables the study of the mechanical properties of systems with particles of various sizes and compositions, as well as the modeling of their behavior in confined spaces and under dynamic influences. The modeling results demonstrate the high accuracy and versatility of the DEM for analyzing processes in bulk materials, particularly transportation, mixing, and granulation. The findings underscore the effectiveness of using DEM to solve complex problems and highlight prospects for its further improvement.

Abstract: In an open or unbounded system, when a solid sphere freely falls into a liquid, it accelerates until it reaches a terminal velocity. At this point, the gravitational force, buoyant force, and viscous drag acting on the sphere are balanced. Stokes' law describes that in a laminar flow state, the viscous drag on the sphere is proportional to its radius, velocity, and viscosity coefficient. In this paper, an experimental system was constructed and the vertical and horizontal positions of spheres were measured with different sizes and densities in liquids of different diameters and viscosities, and the vertical and horizontal positions, velocities, and accelerations of spheres were analyzed. The data analysis shows that the sphere is not only subjected to the viscous drag and but also the boundary forces from the system. This work will have a significance in modeling and computer simulation of accurate measurement of liquid viscosity.

Abstract: The article presents modelling of spherical elements based on the developed computer model. We recorded the main combinations of spherical particles during filling, which are formed in the hopper. It was found that the most likely combination that occurs when modelling spherical elements consists of three balls. It should be noted that in the cross-section of such a combination passing through the center of the balls, an equilateral triangle is formed. And in the cross-section of the structure, which consists of four spherical balls, a rhombus is formed, if you connect the centers of these spherical elements. It is worth noting that from this formed combination of spherical elements, it can be seen that the rhombus forms two smaller equilateral triangles that fix the process of pushing the spherical balls apart. In turn, the process of pushing spherical elements apart made it possible to fix the contact between spherical elements, as well as to state the stable position of each (individual) particle. This paper also presents the main fragments of encoding the source text of a 3D computer model for modelling spherical elements, which made it possible to optimize the model parameters. It was found that from the obtained data on the distribution of coordination numbers for different volume fillings of spherical elements, it follows that the largest filling was 72 %, which corresponds to the state when 112 lobules have an average coordination number of 3,92.

Abstract: The motion of a rigid sphere located at tissue-mimicking material interface in response to a dynamic force of short duration for the purpose of the determination of material viscoelastic properties was investigated in this study. The experiments were performed using a rigid sphere located at tissue-like material (gelatin phantom) interfaces. An electromagnet was used to apply the desired dynamic force to the sphere and a high-speed camera was used to track the movement of the sphere. Using the experimentally measured response of the sphere and the dynamic response of the sphere predicted by a sophisticated analytical model of the sphere located at a medium interface, the shear modulus, density and damping of the tissue-mimicking material were determined. The procedure followed in this study successfully produced the shear modulus, density and viscous damping ratio of the 20% (and 30%) gelation phantom as 1320 Pa, 1040 kg/m³ and 0.12 (and 2580 Pa, 1180 kg/m³ and 0.2), respectively. As the sophisticated theoretical model that is valid for small and large sphere displacements includes many parameters for the system such as the mass and size of the sphere, the inertia force of the medium involved in motion and the radiation damping due to shear waves and the experimental setup is very straightforward, it is believed that the procedure proposed in this study can be widely exploited to identify accurate material viscoelastic properties in practice.

Abstract: The investigation on mixed convection boundary layer of a viscoelastic fluid over a sphere which is embedded in porous medium under convective boundary condition is carried out in this paper. The boundary layer equations of viscoelastic fluid are an order higher than Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Hence, the augmentation on extra boundary conditions is needed in order to solve this problem. The governing partial differential equations are first transformed into non-dimensional forms and then solved numerically using the Keller-box method by augmenting extra boundary conditions at infinity. The numerical results obtained for limiting case are comparing with related outcomes in order to validate the present results. Results on the effects of the viscoelastic parameter in the presence of porosity and mixed convection on the skin friction and heat transfer as well as velocity and temperature profile have been discussed.

Abstract: In this work, consideration is given to the problem of dissolution of a buried solid sphere in the liquid flowing uniformly through the packed bed around it. The differential equations describing fluid flow and mass transfer by advection and diffusion in the interstices of the bed are presented and the method for obtaining their numerical solution is indicated.From the surface concentration fields, given by the numerical solution, the concentration boundary layer thickness as a function of the relevant parameters were undertaken. Mathematical expressions that relate the dependence with the Peclet number and d/d₁ ratio of an immersed active sphere are proposed to describe the approximate size of the concentration boundary layer thickness.

Abstract: The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.

Abstract: The transport phenomenon of mass transfers between a moving fluid and a reacting sphere buried in a packed bed, with “uniform velocity”, was analysed numerically, for solute transport by both advection and diffusion to obtain the concentration field and, from it, the dimensionless concentration boundary layer thickness, , for , and . The bed of inert particles is taken to have uniform voidage. For this purpose, numerical solutions of the partial differential equations describing mass concentration of the solute were undertaken to obtain the concentration boundary layer thickness as a function of the relevant parameters. Finally, mathematical expressions that relate the dependence with the Peclet number and inert particle diameter are proposed to describe the approximate size of the concentration boundary layer thickness.

Abstract: This work demonstrated an approach of oil/water (O/W) microemulsion on preparation of hollow spheres with mesopores in the shell, in which a cationic surfactant was used as structural directing agent, alkane molecule as mesopore-swelling agent and oil droplets. The morphology and pore architecture of the obtained hollow spheres were characterized by SEM, XRD, TEM and N₂ adsorption/desorption isotherms. Cubic (Ia3d) mesopores are present in the shell and provide open channels for mass transport in between the hollow core and outer environment. The obtained hollow spheres with cubic mesoporous shell possess the potential of being used as nanoreactor and nanocontainer in the fields of catalysis and drug delivery.