Dynamics Of Segregation Behaviors In Bi-disperse Granular Mixtures

A great of substantial interests have been concentrated on the segregation behavior of granular materials for recent 30 years,due to its ubiquitous presence in our daily lives and in many industrial precesses.However,no general understandings of this intriguing phenomenon has been achieved.Most of the researchers agree that a variety of mechanisms compete together to account for the segregation behavior,while one or several of them play the dominant role for different segregation patterns.A small change of the system conditions could lead to completely different segregation phenomenon,which cannot be explained by the existing mechanisms,and thus a new kind of mechanism is urgent.The profiles of the spatial structure and kinetic energy of granular system are of great inhomogeneity,which makes the numerical simulations of granular segregation behavior very difficult to proceed.Previous works on the segregation phenomenon are mostly qualitative descriptions based on experimental observations,focusing on the effects of intrinsic properties of granular materials and of the conditions of the system,while very few attentions are paid to the dynamics of the separation process.Actually,a systematical analysis of the evolution of the granular segregation can help construct the complete picture of the segregation issue,and also could provide a great amount of quantitatively experimental data which are indispensable for the success of numerical simulations and theoretical models.Therefore,a detailed investigation of the dynamics of granular segregation process is not only an essential aspect of the segregation research,but also could be a breakthrough of the granular segregation issue.This paper aims to get some quantitative results of the granular segregation process by analyzing the state evolution of the granular mixtures,to explore the underlying physics of each stage contributing to the segregation behavior,and then to propose corresponding theoretical models based on the quantitative relations gained from the experimenal measurements.We focused on a new kind of segregation behavior,namely the periodic segregation(PS),of which the segregation status varies with time with good periodic characteristics.The symmetry of the segregation can be modulated by controlling the interstitial air pressure of the mixtures and the vibration strength.We defined an order parameter to quantitatively distinguish the segregation state,and the corresponding relations between the order parameter and the experimental observations are built.Both of the experimental observations and the order parameter imply that the segregation process consists of two stages,that is the percolation process of the small particles through the permeable layer of big particles and the arching process of the bottom layer including the arching of the flat interface and the eruption of the arching heap due to its instability.These two stages periodically occur which results in the periodic characteristics of the segregation behaviors of the bi-dispersed granular mixtures.The periodic time of the two stages are extracted from the order parameter and then are plotted as a function of the vibration strength.We introduced a classical volcano model to analyze the eruption process,and a good match of the evolution of heaping profile of the upper surface with the volcano model is achieved.We then discussed the similarities and the differences of these two eruption processes.Next we focused on the heaping instabilities of the bottom layer and a phenomenological model is built by introducing the continuum equations,aiming to understand the two instabilities of the layered mixtures,that is,the instability of the flat interface of the bottom layer and the instability of the arching heap.When excited by external vibration,together with the suppression of upper layer,the flat interface of the bottom layer becomes unstable and begins to arch,and thus there exists a critical heaping vibration strength and a critical volume ratio of upper copper particles.We measured the critical vibration accelerations at fixed volume ratios,which can be the demonstration of the model.The heaping angle is predicted by the model when there is a jump of heaping angle from zero to a specific value after the arching happened,and we got a good match with the experimental measurements.As the vibration strength increases,the arching heap keeps growing and would eventually breaks the suppression of the upper layer,bursting into the top surface.The model predicts the second kind of critical vibration acceleration,which fits the experimental data well.The percolation of small particles through the layer of big particles is one of the most important mechanisms for granular segregation,and also a very complicated dynamical process.We found that the permeable layer of big particles would contineously change their spatial positions,as well as the spatial structures and the profile of the kinetic energy of the particles assembly as the percolation proceeds in the bi-dispersed granular system.Thus we simplified the process by setting up just one single layer of permeable particles.The experimental measurements show a non-monotonic dependence of the percolation flux on the vibration strength.By observing the motion of granuar particles,we found that the assembly of small particles periodically detaches the bottom,flying into the air,which results a discontinue percolation mass flow of the process.Hence we divided the percolation process into two stages: the flight stage,which makes no contribution to the mass flow;the adhesive stage,where the percolation flow happens.After removing the flight time from the whole process,we recalculated the adhesion flux,and the results show a nearly linear increase of the adhesion flux with the increasing vibration strength.The adhesion flux is determined by the vibration velocity,and has no dependence on the vibration frequency and acceleration.So far,we obtained a great quantity of quantitative experimental data,including the quantitative description of the segregation state,the dependence of the percolation flux of the mass flow on the vibration strength,and a phenomenological model about the heaping instabilities.These quantitative results not only can be of great help to the final understanding the granular segregation issue,but also could assistant to guide some industrial production processes proceeding with granular materials,improving the production efficiency.