Effect of particle morphologies on the percolation of particulate porous media: A study of superballs

Theoretical Research on Diffusion Radius of Cement-Based Materials Considering the Pore Characteristics of Porous Media

In engineering, loose sandy (gravelly) strata are often filled with cement-based grout to form a mixed material with a certain strength and impermeability, so as to improve the mechanical properties of sandy (gravelly) strata. The tortuosity effect of sandy (gravelly) strata and the time-varying viscosity of slurry play a key role in penetration grouting projects. In order to better understand the influence of the above factors on the penetration and diffusion mechanism of power-law slurry, based on the capillary laminar flow model, this research obtained the seepage motion equation of power-law slurry, the time-varying constitutive equations of tortuosity and power-law fluid viscosity were introduced, and the spherical diffusion equation of penetration grouting considering both the tortuosity of porous media and time-varying slurry viscosity was established, which had already been verified by existing experiments. In addition, the time-varying factors of grouting pressure, the physical parameters of the injected soil layer, and slurry viscosity on penetration grouting diffusion law and the influencing factors were analyzed. The results show that considering the tortuosity of sandy (gravelly) strata and the time-varying of slurry viscosity at the same time, the error is smaller than the existing theoretical error, only 13~19%. The diffusion range of penetration grouting in the sandy (gravelly) strata is controlled by the tortuosity of sandy (gravelly) strata, the water-cement ratio of slurry, and grouting pressure. The tortuosity of sandy (gravelly) strata is inversely proportional to the diffusion radius of the slurry, and the water-cement ratio of slurry and grouting pressure are positively correlated with the diffusion radius. In sandy (gravelly) strata with a smaller particle size, the tortuosity effect of porous media dominates the slurry pressure attenuation. When the particle size is larger, the primary controlling factor of slurry pressure attenuation is the tortuosity effect of porous media in the initial stage and the time-varying viscosity of slurry in the later stage. The research results are of great significance to guide the penetration grouting of sandy (gravelly) strata.

A Universal Method for Modeling and Characterizing Non-Circular Packing Systems Based on n-Point Correlation Functions

A universal method for modeling and characterizing non-circular particles is developed. The n-point correlation functions (n = 1, 2 and 3) are efficiently computed with a GPU parallel computing procedure. An algorithm for dynamic packing of impenetrable non-circular particles is developed based on the fast estimation of overlap information using a one-point correlation function. The packing algorithm is independent of particle shape and proved to be reliable by examples of polygons and super-ellipses. In addition, penetrable packings are generated in an efficient and precise way. Using a two-point correlation function, these non-circular packs are accurately characterized and compared in terms of features such as penetrable and impenetrable, packing fraction and particle shape. In addition, three-point correlation functions are also illustrated and discussed.

Continuum percolation-based tortuosity and thermal conductivity of soft superball systems: shape dependence from octahedra via spheres to cubes

Understanding the effect of particle shape on the percolation threshold, tortuosity and thermal conductivity of soft (geometrical overlapping) particle systems is very crucial for the design and optimization of such materials, including colloids, polymers, and porous and fracture media. In this work, we first combine the excluded-volume theory with the Monte Carlo simulations to determine the percolation threshold for a family of soft superballs, the shape of which interpolates between octahedra and cubes via spheres. Then, we propose two continuum percolation-based models to respectively obtain the tortuosity and effective thermal conductivity of soft superball systems considering their percolation behavior, where monodisperse overlapping superballs are uniformly distributed in a homogeneous solid matrix. Specifically, both models cover the whole feasible range of superball volume fractions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of precisely predicting the percolation threshold, tortuosity and thermal conductivity of such systems. Furthermore, we apply the proposed models to probe the influence of particle shape on these important parameters. Our results show that the decreasing percolation threshold and tortuosity as soft particles become more anisotropic is consistent with increasing conductivity. It suggests that the anisotropic-shaped inclusion phase is more conducting than the spherical inclusion phase. The present theoretical strategies and conclusions may provide sound guidance for the synthesis of colloidal and polymer superballs.

Geometrical percolation threshold of congruent cuboidlike particles in overlapping particle systems

With the advances in artificial particle synthesis, it is possible to create particles with unique shapes. Particle shape becomes a feasible parameter for tuning the percolation behavior. How to accurately predict the percolation threshold by particle characteristics for arbitrary particles has aroused great interest. Towards this end, a versatile family of cuboidlike particles and a numerical contact detection algorithm for these particles are presented here. Then, combining with percolation theory, the continuum percolation of randomly distributed overlapping cuboidlike particles is studied. The global percolation threshold ϕ_{c} of overlapping particles with broad ranges of the shape parameter m in [1.0,+∞) and aspect ratio a/b in [0.1, 10.0] is computed via a finite-size scaling technique. Using the generalized excluded-volume approximation, an analytical formula is proposed to quantify the dependence of ϕ_{c} on the parameters m and a/b, and its reliability is verified. The results reveal that the percolation threshold ϕ_{c} of overlapping cuboidlike particles is heavily dependent on the shapes of particles, and much more sensitive to a/b than m. As the cuboidlike particles become spherical (i.e., m=1.0 and a/b=1.0), the maximum threshold ϕ_{c,max} can be obtained.