Transition Behavior in Silicone-coated Sand Mixtures

Marie Tani , Honoka Fujio, and Rei Kurita

This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the article, journal citation, and DOI.

Sand sometimes shows fluid and solid like behaviors; it can be seen to flow in an hourglass; but the same grains may also be rigid with forming arches inside sand hoppers or dense sand may even be too rigid to dig. Thus, understanding their behaviors is of great interest for both fundamental science and industrial contexts such as in agriculture, mining, construction and pharmaceuticals.^1–5) Despite each grain being bound by classical equations of motion, the macroscopic behavior of granular media is not yet fully understood. Most studies have focused on dry grains to understand features such as packing states and jamming.^6–9) It is also known that forces inside a granular packing do not propagate homogeneously, but like a series of “chains”.¹⁰⁾ The strong localization of forces prevents spatial averaging, making the application of statistical physics challenging.

Granular materials in nature may include some amount of liquid. Adding some liquid to a granular system is known to make the system much stiffer compared to dry one due to microscopic capillary bridges between grains.^11–13) Recently, another type of interacting sand where grains are coated by silicone-oil is produced as a toy for kids. The silicone coating realizes a strong adhesive interaction between coated grains where stable capillary bridges are formed. As a result, the sand shows some characteristic behaviors although the macroscopic physical properties are not yet understood.

In this work, we studied the macroscopic features of composite sand systems where the silicone-coated sand is mixed to dry one. The mixture is characterized by the weight fraction α of the coated sand to the total grains as shown in Fig. 1. We performed three independent experiments; we screened the sand, measured the fractions of random close packed (RCP) and random loose packed (RLP) sand and the angle of repose of a sand pile. As a result, we found a transition of mechanical properties at \(\alpha\simeq 0.2\). Then we discussed that connectivity percolation or gelation might be a possible origin of this transition. Our results suggest that the macroscopic mechanical properties can be controlled by changing the fraction of coated sand.

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Figure 1. (Color online) (a) Pictures of grains (a1–a4) and sand piles (aI–aIV) with different fractions of coated sand α. Scale bars in (a1–a4) and (aI–aIV) are 1 mm and 1 cm, respectively. (b) Magnified pictures of sand just after silicone-coated grains are detached (b1) and silicone-coated and uncoated grains are detached (b2), respectively. Some liquid threads formed between grains are observed in (b1), but hardly seen in (b2). The times indicated in each picture in (b) are that since the grains were detached.

We used the mixture of two types of sands: normal sand and silicone-coated one. The normal (uncoated) sand is No. 5 from Tohoku Keisa with a density 2.62 g/cm³ (Tohoku-Keisa, Japan). The grain size is measured from magnified pictures as 0.08–0.35 and 0.23–0.55 mm long in their shorter and longer axes, respectively. As the coated sand, we mainly used a silicone-coated sand marketed as a children's toy (Dancing Sand, BorneLund, Japan). The density and grain size are 2.85 g/cm³, and 0.31–0.59 mm and 0.43–1.06 mm in their shorter and longer axes, respectively. Some part of experiment was performed using another series of sand mixtures where another commercial silicone-coated sand (Kinetic sand,¹⁴⁾ Rangs Japan) are used in order to see generality of the features. The density and grain size are 2.26 g/cm³, and 0.09–0.29 mm and 0.16–0.41 mm in their shorter and longer axes, respectively.

We then mixed coated sand and uncoated one to make the composite granular system of weight fraction α of coated sand compared to the total mass. We spread a certain amount of sand thinly in a large metallic tray, and mixed them well by hand until almost homogeneous sand mixtures seem to be obtained as shown in Fig. 1(a).

The silicone-coated grains adhere strongly to each other. We observed the microscopic properties of the sand and liquid threads formed between grains using a stereomicroscope (MVX10, OLYMPUS, Japan). When an aggregation of coated sand is separated, thick and strong threads of silicone-oil are formed between grains as shown in Fig. 1(b1). In contrast, the threads are hardly observed or they are quite thinner and less stable when the coated and uncoated grains are separated [Fig. 1(b2)]. We note that here we used a larger grain of garnet sand (Total-kikaku, Japan) to take the pictures in (b2) for easier handling and easier discrimination of grains. We emphasize that what we observed here is not different from what we confirmed for the mixture where coated sand are mixed with the uncoated sand from Tohoku Keisa, even after plenty times of our experiments. These results lead us to conclude that the adhesive interaction is significant only between coated grains and that the liquid seems to be not transported from coated grains to uncoated ones. Thus, we can investigate the physical properties of a partially interacting granular system by changing the weight fraction α [Fig. 1(a)].

We carried out a screening test as the first experiment of the three. Firstly, we put 200 g of sand in a sieve and measured the mass \(M_{0}\) of sand remaining on the mesh of the sieve. Figure 2(a) shows \(M_{0}\) for different α by using two sieves; the finer sieve (S or blue diamonds) is 13.5 cm in diameter with a \(0.767\pm 0.113\) mm mesh size; the coarser one (L or red circles) is 15.0 cm in diameter with a \(1.628\pm 0.204\) mm mesh size. As shown in Fig. 2(a), the sand spontaneously falls through the mesh when \(\alpha < 0.2\). With increasing proportions of coated sand (\(\alpha\geq 0.2\)), some sand stays on the sieve; \(M_{0}\) is not zero. This implies that some sand form arches between the sieve meshes in this region similarly to what is observed when granular media plug a hopper. Thus, we shook the sieve horizontally for \(\alpha\geq 0.2\) after measuring \(M_{0}\). The shaking amplitude and frequency are about 15 cm and 3 Hz, respectively. We continued the shaking until the weight M became 0 or the shaking number n became 100. Figure 2(b) shows the mass M remaining on the mesh of the sieve S as a function of shaking number n. The mass exponentially decreases with increasing n in the initial regime where the data points are indicated by full symbols. Each solid lines are fitting ones by a formula \(M=M_{0}\exp(-n/\nu)\) where ν is a fitting parameter. Then we found that ν depends strongly on the fraction α as shown in Fig. 2(c). We also note that M saturates for the intermediate α as shown in Fig. 2(b). In these cases, only spherical rigid clusters composed of coated and uncoated grains are observed after 100-time shaking of the sieve as shown in Fig. 2(d1). For much larger α, however, some sand is not in a spherical cluster even after 100-time shaking although it is connected each other [Fig. 2(d2)].

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Figure 2. (Color online) (a) Mass \(M_{0}\) remaining on the mesh of the sieve as a function of α. Blue diamonds and red circles correspond to smaller (S) and larger (L) mesh sizes, respectively. Green squares indicated as “L-k” is the result using the larger mesh size and Kinetic sand as coated sand. (b) Mass M as a function of shaking number n for the sieve S. Different symbols and colors correspond to different values of α indicated in the figure. Full symbols are the points in the initial regime where the mass exponentially decreases as indicated with the solid fitting lines: \(M=M_{0}\exp(-n/\nu)\) where ν is a fitting parameter. (c) Fitting parameter ν as a function of α. Error bars in (a–c) are standard deviations for 5 independent experiments. (d) Pictures of the sand in the sieve after a 100-time shaking: (d1) \(\alpha=0.5\) and (d2) \(\alpha = 1.0\). (e) The critical hole size \(D_{c}\) where the hole starts to plug as a function of α.

Furthermore, we carried out the similar experiment with another series of sand mixtures where Kinetic sand were used as coated sand. As shown in Figs. 2(a) and 2(c), the similar features are observed. Thus, the features are independent of the sand type and general for the interacting composite granular systems although the transition points are slightly different.

In order to see the origin of the difference in the transition points when the mesh size is different, we carried out another experiment; we put about 3 cm height sand mixture on a circular hole of diameter D and determined the critical value \(D_{c}\) below which the hole plugs [Fig. 2(e)]. The hole is made in a 2-mm-thick acrylic plate. Figure 2(e) shows that \(D_{c}\) increases significantly as α increases. \(D_{c}\) seems to be related to the cluster size of each sand. Thus, the result implies that the cluster size increases dramatically with increasing of α.

We then measured the packing fraction ϕ for both RLP and RCP states. We limit our experiments to \(\alpha\leq 0.5\) in order to avoid having clusters as shown in Fig. 2(d) which can significantly decrease the experimental accuracy. RLP states are generated by pouring mixtures into a container of 67.8 mm width and 42.5 mm depth from the top of the container. The flow rate of the sand poring is about 10 g/s. RCP states are generated by compacting mixtures down by external pressure (\({\simeq}5\times 10^{4}\) Pa) using a plate whose area is almost the same as the inner one of the container after pouring the sand in the container, and repeating the process for about 25 times until the container is full. We find the packing fraction ϕ by calculating from the measured mass of the sand in the container, the volume of the container, α, and the densities of the coated and uncoated sands. Figure 3(a) shows the packing fraction ϕ of RCP and RLP as functions of α. The packing fraction of RCP seems constant at around 0.6, which is close to the value 0.58 for RCP of dry sharp sand reported by Brown et al.³⁾ This is reasonable since the key factor governing packing fraction in RCP is only the hard-core interaction. On the contrary, the packing fraction of RLP strongly depends on α; \(\phi\simeq 0.47\) for small α is similar to the value 0.48 for RLP sharp sand.³⁾ However, at around \(\alpha = 0.2\), we see that ϕ suddenly decreases. Actually, some voids are observed in the picture of the sand in RLP state for \(\alpha=0.5\) as shown in Fig. 3(c) but not in that for \(\alpha=0.2\) as shown in (b). These results seem to mean that the adhesive interaction of grains of \(\alpha\geq 0.2\) can support their self-weight even when the packing fraction ϕ is low.

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Figure 3. (Color online) (a) Packing fraction ϕ of random close packed (RCP; blue diamonds) and random loose packed (RLP; red circles) gains, as functions of α. Error bars indicate the maximum and minimum values in three independent measurements. (b) and (c) Pictures of the sand loosely packed in the container: (b) \(\alpha=0.2\) and (c) \(\alpha=0.5\).

We also measured the angle of repose of sand piles. Similarly to the packing fraction measurement, we limit our experiments to \(\alpha\leq 0.5\) to avoid decreasing of the experimental accuracy. We poured the sand gently close to a transparent wall for easier observation of the angle. The height of pouring the sand is about 10 cm and the flow rate is about 0.5–5 g/s. The surface of the pile oscillates locally and temporally as the sand falls, and a relaxed sand pile is obtained after a while. We measured the global angle of the relaxed sand pile. We also confirmed that the static global angle does not depend on the pouring flow rate. We carried out the measurement for 7 independent sand piles for each value of α to find the average and standard deviation. As shown in Fig. 4, the angle θ remains approximately constant for small α but increases at \(\alpha\simeq 0.2\), where a transition behavior is observed also in the sieving test and the measurement of packing fraction.

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Figure 4. (Color online) Angle of repose θ as a function of α. The angles are globally measured after the sand pile relaxed. Error bars are standard deviations from seven independent measurements.

From the three independent experiments, we find a characteristic fraction of coated sand α where the macroscopic physical properties change. Some amount of sand stays on the mesh for about \(\alpha > 0.2\) [Fig. 2(a)], and the packing fraction of RLP (Fig. 3) and the angle of repose (Fig. 4) change in behavior at \(\alpha\simeq 0.2\). These measurements seem to be determined by a balance between the weight of the grains and the adhesive interaction in the sand mixture. Thus, one possible explanation of the transition at \(\alpha\simeq 0.2\) seems to be connectivity percolation, which is known to be seen at around 0.22–0.27, for example as reported by Phelps and Flynn; electric current passes in the container when metal spheres are packed with insulating ones with the ratio α of metal sphere to the whole and some voltage is applied between the ends of the container.¹⁵⁾ We furthermore note that the cluster size of the sand significantly increases with increases of α as shown in Fig. 2(e). However, some direct observations of the internal structure of the system is necessary in order to be concluded. In addition, more systematic experiments with slightly changing the fraction α to find a critical transition point and comparing it with that obtained from percolation theory are required. Those might be realized in the near future.

Furthermore, one may found that another transitive point seems to be exist at around \(\alpha = 0.4{\text{–}}0.6\) in Fig. 2(c). Around the point, some rigid clusters composed of coated and uncoated grains are also observed as shown in Fig. 2(d1), which is the reason why the second and the third experiments are limited for \(\alpha\leq 0.5\). We need more work to see what happens upper the point, which also might appear in the near future.

We then discuss the possibility of the composite sand system as a new type of granular medium. As seen in our three independent experiments, the macroscopic mechanical properties of the system can be easily controlled by changing the fraction of coated sand. We furthermore note that our system might have some similarity to gel where a polymer network takes an important role to determine ones macroscopic physical properties. The development and progress of gel are remarkable, for example, topological gel,¹⁶⁾ tetra-hydro gel,¹⁷⁾ and so on. Thus, the study of interacting granular systems and application might develop widely by following the knowledge of gel. We believe that other mechanical properties, e.g., rheology of the system also can be interesting and the understandings of such properties may follow.

To summarize, we observed a wide range of static behavior for mixtures of silicone-coated sand and uncoated sand. Capillary bridges formed by the coating liquid cause strong connectivity between coated grains. By increasing the fraction α of coated sand to total sand, we observed a transition at \(\alpha\simeq 0.2\). Our system may thus be valuable not only for the study of interacting granular systems but also for understanding, e.g., soft jamming and gelation in soft systems. We emphasize that our method making interacting granular systems by mixing coated and uncoated sand allows uniquely facile control over connectivity and also may improve the conventional methods for industrial applications.

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