Effects of friction ratio of granular material on convection in two dimensional under vertical vibration

Abstract

Effective mixing and precise separation of granular materials are essential for many industries that use granular materials as raw materials in production, such as pharmaceuticals, food processing, and construction [1]. These granular materials are typically subjected to internal changes due to vibration during transportation, which directly impacts the quality and uniformity of the product. One of the key mechanisms that affects the separation and mixing phenomena is convection. Friction between particles and wall friction are important factors for convection [2-5]. However, previous studies have not been clear about the effects of friction on convection under different amplitudes. Therefore, this study investigated the influence of wall friction, particle friction, and vibration amplitude on the convection phenomena in granular materials under vertical vibration. The research aimed to numerically and experimentally investigate the influence of the particle frictions on the convection in 2D granular materials composed of disk particles under vertical vibrations. These numerical and experimental results were then compared to each other. The present study began with the implementation of 2D simulations by using the Non-smooth Contact Dynamics (NSCD) method. The granular sample used in this study consists of 4000 disk particles with an average diameter D = 10 mm. The diameters were uniformly distributed within the range of 9 mm to 11 mm, resulting in a creation of a monodisperse granular sample. The interparticle friction coefficient (μp) and wall-particle friction coefficient (μw) were systematically changed within the range of 0.1 to 1.0. The particles were contained within a container subjected to the vertical vibration, characterized by a constant dimensionless acceleration of Γ = 5. The vibration frequency was adjusted to corresponding to the different vibration amplitudes of 0.35D, 0.5D, and 1.0D. Next, 4000 Polymethyl Methacrylate (PMMA) particles were used in the experiment to prepare the granular sample. These particles were categorized into five different sizes: 9 mm, 9.5 mm, 10 mm, 10.5 mm, and 11 mm. The wall-particle friction coefficients (μw) were specifically varied by 0.15, 0.26, 0.36, 0.46, 0.61, 0.81, and 0.95, with the selection of different wall materials, including polytetrafluoroethylene (PTFE) tape, polyethylene (PE) tape, masking tape, sandpaper No. 10000, sandpaper No.5000, and polyurethane (PU) tape. On the other hand, the interparticle friction coefficient (μp) remained constant at a value of 0.5. The granular sample was subjected to the vertical vibration with the same conditions as done in the simulations. The vibrational amplitudes were adjusted to 0.5D and 1.0D. High-speed cameras were employed to capture the particle positions at various time steps. These capture positions were then used to calculate the particle velocities. The index associated with the convection of particles in the granular material can be subsequently determined. This index, a dimensionless angular velocity W, was introduced and developed to describe the occurrence, intensity, as well as the direction of convection. In comparison, the results obtained from both simulations and experiments showed a similar trend. It was observed that convection remained absent when the friction coefficient μw ≤ 0.2 or μp ≤ 0.1 (the value of W approached to zero or was less than 5 × 10–4) for all vibrational amplitudes. The onset of convection appeared when μw ≥ 0.4 and μp ≥ 0.2. This phenomenon is caused by the wall friction force, inducing particles to climb on nearby ones while moving downward. At the same time, the interparticle friction plays a role in preventing slippage during this climb. The intensity of convection, denoted by the value of W, increases with μp, reaching a maximum when μw = μp. Subsequently, the intensity of convection was relatively constant when μp > μw. This is due to the fact that the wall friction force cannot overcome interparticle friction force. Additional observations from the experimental and simulation results revealed that all convections observed were the normal convections (W > 0). This provides particles at the wall move downward while those in the center region of the container migrate upward. The vibrational amplitude significantly affects the convection in the granular samples with the higher interparticle and wall-particle friction coefficients, i.e. μp and μw ≥ 0.6. In this case, the higher friction force results in a loose-packed structure, thus leading to particles moving downward freely through such voids. As a consequence, the dimensionless angular velocity increases rapidly. Additionally, the dimensionless angular velocity obtained from the experiments and the simulations yield similar results, but that obtained from the experiments were slightly higher than that obtained from the simulations. This can be explained by the front and back cover plates of the container used in the experiments provided the friction forces driving the particles downward faster.