Tightening (Compaction) of Bi-Component Micromechanical (Granular) System





granular screen technologies, granular bi-component mixture, Kirkwood-Buff theory, packaging, compaction, Carnahan-Starling model, liquid mixtures, excess properties of mixtures


Introduction. One of the traditionally relevant problems of the theoretical framework for production and technology is the description, parameterization, and prediction of the properties of the mix depending on the parameters of the mix components. One of the most significant problems that hinder the effective use of granular
materials, for example, in the construction industry, is the difficulty of ensuring their maximum compaction to increase the efficiency of their practical application.
Problem Statement. The understanding of the principles due to which the basic parameters of such systems are formed is based on theoretical models that allow the parameterization of the measurement data in terms of parameters that characterize the individual pure components (reference data). The construction of such models is a very difficult task that requires phenomenological information from alternative sources.
Purpose. Based on the Kirkwood-Buff theory and the data of analysis of experimental data on the study of macroscopic parameters of bi-dispersed granular mix we have developed a theoretical algorithm for describing and parameterizing its physical and mechanical characteristics in terms of its macroscopic and partial properties.
Materials and Methods. The methods of theoretical statistical physics for bi-component model systems, in particular the Kirkwood-Buff theory, the model equation of the state (the Carnahan-Starling equation), and phenomenological information on the dynamics of compaction of binary granular mixes have been used in the research.
Results. Using the Kirkwood-Buff and Carnahan-Starling theories and phenomenological data, we have developed a continuous description of the macroscopic properties of binary granular systems, which operates on the partial parameters of its components.
Conclusions. The obtained data have confirmed the influence of multi-dispersion on the dynamics of compaction, i.e. the mix ability to change its local structure of packing under external impact.


Uchida, T., Kawahara, Y., Hayashi, Y., Tateishi, A. (2020). Eulerian Deposition Model for Sediment Mixture in GravelBed Rivers with Broad Particle Size Distributions. Journal of Hydraulic Engineering, 146(10), 04020071. doi: 10.1061/ (ASCE)HY.1943-7900.0001783.

Knott, J. F. (1978). Fundamentals of fracture mechanics. Moscow: Metallurgiya [in Russian].

Gerasymov, O. I., Khudyntsev, M. M., Andrianova, I. S., Spivak, A. Ya. (2016, November). Granular materials in utilization technologies of radiation-harmful substations. Proceedings of the National Forum: ”Problems, perspectives and strategy of waste utilization in Ukraine” (22—23 Nov 2016, Kyiv), 40—42. Kyiv [in Ukrainian].

Gerasymov, O. I., Somov, M. M. (2015). Statistical description of excess properties of many-particle binary systems.

Ukrainian Journal of Physics, 60(4), 324—327. doi: 10.15407/ujpe60.04.0324.

Gerasymov, O. I., Zagorodny, A. G., Somov, M. M. (2013). Toward the analysis of the structure of granular materials. Ukrainian Journal of Physics, 58(1), 32—39. doi: 10.15407/ujpe58.01.0032.

Pillitteri, S., Lumay, G., Opsomer, E., Vandewalle, N. (2019). From jamming to fast compaction dynamics in granular

binary mixtures. Scientific Reports, 9(1), 7281. doi: 10.1038/s41598-019-43519-6.

Jaeger, H. M., Nagel, S. R. (1992). Physics of the granular state. Science, 255(5051), 1523—1531. doi: 10.1126/science.255.5051.1523.

Aste, T., Weaire, D. (2000). The Pursuit of Perfect Packing. Bristol. doi: 10.1887/0750306483.

Weitz, D. A. (2004). Packing in the spheres. Science, 303(5660), 968—969. doi: 10.1126/science.1094581.

Torquato, S. (2018). Perspective: Basic understanding of condensed phases of matter via packing models. The Journal of chemical physics, 149(2), 020901. doi: 10.1063/1.5036657.

Torquato, S., Stillinger, F. H. (2010). Jammed hard-particle packings: From Kepler to Bernal and beyond. Reviews of modern physics, 82(3), 2633—2672. doi:10.1103/RevModPhys.82.2633.

Berryman, J. G. (1983). Random close packing of hard spheres and disks. Physical Review A, 27(2), 1053—1061. doi: 10.1103/PhysRevA.27.1053.

Onoda, G. Y., Liniger, E. G. (1990). Random loose packings of uniform spheres and the dilatancy onset. Physical review letters, 64(22), 2727—2730. doi: 10.1103/PhysRevLett.64.2727.

Song, C., Wang, P., Makse, H. A. (2008). A phase diagram for jammed matter. Nature, 453(7195), 629—632. doi: 10.1038/nature06981.

Noirhomme, M., Ludewig, F., Vandewalle, N., Opsomer, E. (2017). Cluster growth in driven granular gases. Physical Review E, 95(2), 022905 doi: 10.1103/PhysRevE.95.022905.

Lumay, G., Vandewalle, N. (2005). Experimental study of granular compaction dynamics at different scales: grain mobility, hexagonal domains, and packing fraction. Physical review letters, 95(2), 028002. doi: 10.1103/PhysRevLett.95.028002.

Carvente, O., Ruiz-Suarez, J. (2005). Crystallization of confined non-brownian spheres by vibrational annealing. Physical review letters, 95(1), 018001. doi: 10.1103/PhysRevLett.95.018001.

Panaitescu, A., Reddy, K. A., Kudrolli, A. (2012). Nucleation and crystal growth in sheared granular sphere packings. Physical review letters, 108(10), 108001. doi: 10.1103/PhysRevLett.108.108001.

Knight, J. B., Fandrich, C. G., Lau, C. N., Jaeger, H. M., Nagel, S. R. (1995). Density relaxation in a vibrated granular

material. Physical Review E, 51(5), 3957—3963. doi:10.1103/PhysRevE.51.3957.

de Richter, S. K., Hanotin, C., Marchal, P., Leclerc, S., Demeurie, F., Louvet, N. (2015). Vibration-induced compaction of granular suspensions. The European Physical Journal E, 38(7), 74. doi: 10.1140/epje/i2015-15074-7.

Nicolas, M., Duru, P., Pouliquen, O. (2000). Compaction of a granular material under cyclic shear. The European Physical Journal E, 3(4), 309—314. doi:10.1007/s101890070001.

Roquier, G. (2016). The 4-parameter compressible packing model (cpm) including a new theory about wall effect and loosening effect for spheres. Powder Technology, 302, 247—253. doi: 10.1016/j.powtec.2016.08.031.

Farr, R. S., Groot, R. D. (2009). Close packing density of polydisperse hard spheres. The Journal of chemical physics, 131(24), 244104. doi: 10.1063/1.3276799.

Danisch, M., Jin, Y., Makse, H. A. (2010). Model of random packings of different size balls. Physical Review E, 81(5),


Chen, D., Torquato, S. (2015). Confined disordered strictly jammed binary sphere packings. Physical Review E, 92(6), 062207. doi:10.1103/PhysRevE.92.062207.

Hopkins, A. B., Jiao, Y., Stillinger, F. H., Torquato, S. (2011). Phase diagram and structural diversity of the densest binary sphere packings. Physical Review Letters, 107(12), 125501. doi:10.1103/PhysRevLett.107.125501.

Behringer, R. P., Chakraborty, B. (2018). The physics of jamming for granular materials: a review. Reports on Progress in Physics, 82(1), 012601. doi: 10.1088/1361-6633/aadc3c.

Boutreux, T., de Gennes, P. G. (1997). Compaction of granular mixtures: a free volume model. Physica A, 244(1—4), 59—67. doi: 10.1016/S0378-4371(97)00236-7.

Gerasymov, O. I., Khudyntsev, N. N., Klymenkov, O. A., Spivak, A. Y. (2005). The kinetics of processes occurring in

granular materials in the field of vibroaccelerations. Ukrainian Journal of Physics, 50(6), 623—631.

Gerasymov, O. I., Vandewalle, N., Spivak, A. Ya., Khudyntsev, N. N., Lumay, G., Dorbolo, S., Klymenkov, O. A. (2008).

Stationary states in a 1D system of inelastic particles. Ukrainian Journal of Physics, 53(11), 1128—1135.

Kirkwood, J. G., Buff, F. P. (1951). The statistical mechanical theory of solutions. I. The Journal of chemical physics, 19(6), 774—777. doi:10.1063/1.1748352.

Carnahan, N. F., Starling, K. E. (1969). Equation of state for nonattracting rigid spheres. The Journal of chemical physics, 51(2), 635—636. doi:10.1063/1.1672048.

Mansoori, G. A., Carnahan, N. F., Starling K.E., Leland Jr., T. W. (1971). Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres. The Journal of Chemical Physics, 54(4), 1523—1525. doi:10.1063/1.1675048.

Pillitteri, S., Opsomer, E., Lumay, G., Vandewalle, N. (2020). How size ratio and segregation affect the packing of binary granular mixtures. Soft Matter, 16(39), 9094-9100. doi: 10.1039/D0SM00939C.

Vandewalle, N., Lumay, G., Gerasimov, O., Ludewig, F. (2007). The influence of grain shape, friction and cohesion on granular compaction dynamics. The European Physical Journal E, 22(3), 241—248. doi:10.1140/epje/e2007-00031-0.

Aliotta, F., Gapiński, J., Pochylski, M., Ponterio, R. C., Saija, F., Salvato, G. (2007). Excess compressibility in binary liquid mixtures. The Journal of chemical physics, 126(22), 224508. doi:10.1063/1.2745292.




How to Cite

Gerasymov О., Andrianova . І. ., Spivak А., Sidletska . Л. ., Kuryatnikov В. ., & Kilian . А. . (2021). Tightening (Compaction) of Bi-Component Micromechanical (Granular) System. Science and Innovation, 17(4), 79–88. https://doi.org/10.15407/scine17.04.079



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