Experimental study on dynamic angle of repose formation: Effect of granular type and water content

The experiment of granular in rotating cylinder is a common experiment to study granular material behaviour. In this study, we investigate the effect of granular type and water content on the dynamic angle of repose in a rotating cylinder. Rice seed, mung bean, and sand are used as samples. Experimental results show each sample has a different dynamic angle of repose that is related to the shape of the sample. We also study the effect of the water content on the sand sample. The addition of water content has no significant effect on the dynamic angle of repose. This occurs because the water content used has passed the critical point.


Introduction
The research into granular materials has advanced significantly due to their widespread applications in construction, manufacturing, pharmaceuticals, and agriculture.Industries dealing with grains often face challenges in their management, storage, and processing [1].It's essential to comprehend the properties of these granular materials to develop effective industrial equipment, guarantee dependable processing, and evaluate the primary material's quality.One crucial aspect of these materials is their flow properties [2], which dictate their discharge from storage structures like silos, transportation methods, mixing, compacting, and packaging procedures.Among the many factors affecting the flowability of granules, the angle of repose stands out as a key parameter [3].
In our research, we primarily focus on examining how different types of granules affect the dynamic angle of repose within a rotating cylinder.Prior studies suggest that the formation of these angles is largely determined by the granular material's shape [4].For instance, granules with more spherical shapes typically produce smaller angles inside the rotating cylinder [5].This observation aligns with the results from both experimental and simulation-based research utilizing the discrete element method [6].
Furthermore, we delve into the role of moisture content on angle formation within the cylinder.In some studies, the angle of repose increased as moisture content increased, indicating a positive correlation [7] [8][9].However, other studies have shown that the relationship between the angle of repose and moisture content can vary depending on the type of material being studied [10].For example, in the study by Visvanathan et al., the angle of repose for different grains increased linearly with moisture content.On the other hand, a linear relationship between the angle of repose and moisture content is not always observed.

Key parameters
When considering the dynamic angle of repose in a rotating cylinder, several key parameters play a significant role in influencing its value.One of the characteristic quantities in granular experiments within a rotating cylinder is the filling degree, which is the comparison of granular volume to the cylinder volume: Additionally, another characteristic quantity in granular experiments within a rotating cylinder is the Froude number Fr, which is the comparison between centrifugal force and gravity [11]: When examining the samples, various properties emerge.The concept of "sphericity" is used to gauge how closely an object resembles a sphere.Its formula is [12]: Here, S denotes sphericity, V represents the volume of an individual grain, and A stands for the grain's surface area.An ideal sphere would have a sphericity value of one.Furthermore, "circularity" is another parameter that determines the resemblance of an object's cross-section to a circle.It's represented as: In this case, C is the circularity, while P signifies the cross-section's perimeter.Additionally, the volume of an ellipsoidal object is derived from the formula: Where a is the ellipsoid's major axis length and b and c denote the lengths of its minor axes.
Widartiningsih et al., (2022) also mention that one would use equation to compute the surface area of the ellipsoid is The value of  ≈ 8 5 = 1.6 is optimal for nearly spherical ellipsoids, with a relative error of at most 1.178 %.Thus, in general area of the ellipsoid is defined as This structured breakdown offers a clear understanding of the parameters involved in granular experiments within rotating cylinders.

Experimental setup
The experimental setup is illustrated in Figure 1.We used a cylinder with an inner diameter of 39 cm and a thickness of 3 cm.The cylinder has serrations on the edge with a width of about 2.5 cm.The cylinder was rotated with a constant angular velocity of 6 rpm.Froude number in this experiment was   = 0.016.The recording was done using a smartphone camera with a 12-megapixel resolution and a frame rate of 30 FPS.The distance from the camera to the rotating cylinder was approximately 100 cm.The dynamic angles formed were measured using the tracking method by utilizing the Web Plot Digitizer application.

Effect of granular type
There were three types of non-spherical samples of granular used: Rice seed, mung bean, and sand.The physical properties of those samples are listed in Table 1.For each sample, we used volumes of 200 ml, 400 ml, 600 ml, 800 ml, and 1000 ml.Each volume associated with filling degree 0.06; 0.12; 0.18; 0.24; 0.30.The schematic representation at the initial condition for each sample at 0.30 is displayed in Figure 2. Figure 3 shows static and dynamic regions in the granular flow.In the static region, the granules did not move at all.Meanwhile, in the dynamic region, granular flow created three types of dynamic angles of repose: Upper angle of repose (UAR), Middle angle of repose (MAR), and Lower angle of repose (LAR).In this study, we measured UAR, MAR, and LAR for each sample with various filling degree.

Effect of water content
In this study, we also explored the effect of water content on sand.The sample is preheated in an oven at a temperature of 100 o C. The water content used ranges from 0 to 400 ml.The sand and water were mixed by stirring for about one minute.Details of the experiments are presented in Table 2.We defined water content on the mixture as:   For rice seed and sand sample, the increase of filling degree tends to be accompanied by an increase in UAR.Meanwhile, the increase of filling degree tends not to significantly change the UAR for mung bean sample.MAR tends to decrease for rice seed and mung bean sample but not for sand sample.For each sample, LAR tends to decrease by the increase of filling degree for each sample.Figure 6 shows comparison of UAR, MAR, and LAR for each sample.The sand sample has the largest UAR for each filling degree variation while mung bean has the smallest UAR.MAR for rice seed and mung bean tends to decrease but not for sand sample.LAR tends to decrease for each sample by the increase of filling degree.To discuss the characteristics of UAR, Figure 7 plots the relationship between UAR and sphericity parameter of the sample.We found that smaller UAR corresponds to bigger sphericity.Our result agreed with previous study [5], where particles that were more similar to a spherical would have a smaller UAR.This is because particles that were more similar to a spherical were easier to roll.Meanwhile, particles with smaller sphericity were better able to form higher formation and the angle formed will be larger.

Effect of water content
Figure 8 shows representative images of sand flow in a rotating cylinder for water content 0%, 14.28%, 25%, 33.33%, and 40%.The images were taken at 0.1, 0.6, 1.1, 1.6, and 2.1 where  represents the rotational period.In dry sample, the sand flow pattern tends to remain unchanged as shown in Figure 8(a).The addition of water influenced the sand flow pattern in a rotating cylinder.The pattern of the sand flow tends to be changed as shown in Figure 8(b)-(e) and AOR could only be observed at the initial time.We observed the avalanche phenomenon as a result of water bridge formation.Hamilton et al [13] and Herminghaus [14] found that cohesive nature of water bridge influenced single particles so that particles did not flow independently and caused avalanche phenomenon.
We also observed the formation of sand clumps in wet samples.Those sand clumps separated from the flow and sometimes did not fall to the bottom of the rotating cylinder.In wet sample with water content of 40%, we could not observe the AOR because the sample had turned into clumps as shown in Figure 8(e).Figure 9 shows AOR as a function of water content.The addition of water content did not have a significant influence on UAR.Prior study found that the addition of water content would result in bigger UAR and then UAR would stable after reached the critical point [15].The addition of water content would increase cohesive forces because more water bridges were formed.In our experiment, the UAR tends to remain unchanged because the water content used had already passed the critical point.As future plan, we are going to use water content within the range 0%-10% and various samples.

Conclusions
In this study, the influence of granular type and water content on the dynamic angle of repose in a rotating cylinder had been evaluated.It was observed for each sample i.e., rice seed, mung bean, and sand had different dynamic angle of repose (UAR, MAR, and LAR).We found that the value of LAR < MAR < UAR for each sample.It was interesting to see that particles that were more similar to a spherical would have a smaller UAR.We also found that the addition of water on sand sample influenced the sand flow pattern and dynamic angle of repose could only be observed at the initial time.The addition of water content did not influence UAR because the water content used had passed the critical point.

Figure 2 .
Figure 2. Schematic representation at the initial condition for (a) Rice seed, (b) Mung bean, and (c) Sand.

Figure 3 .
Figure 3. Granular flow in a rotating cylinder.

Figure 4 .
Figure 4. Representative of granular in a rotating cylinder at different filling degree.

Figure 5
Figure 5 shows the relationship between angle of repose and filling degree for each sample.There was observed that the value of LAR < MAR < UAR for each sample.The UAR for rice seed, mung bean, and sand respectively within the range [45 o -66 o ], [38 o -45 o ], and [63 o -79 o ].The MAR for each sample is respectively within the range [39 o -47 o ], [26 o -38 o ], and [36 o -51 o ] and LAR respectively within the range [22 o -36 o ], [12 o -30 o ], and [7 o -31 o ].For rice seed and sand sample, the increase of filling degree tends to be accompanied by an increase in UAR.Meanwhile, the increase of filling degree tends not to significantly change the UAR for mung bean sample.MAR tends to decrease for rice seed and mung bean sample but not for sand sample.For each sample, LAR tends to decrease by the increase of filling degree for each sample.

Figure 9 .
Figure 9. AOR for various water contents

Table 1 .
Properties of rice seed, mung bean, and sand

Table 2 .
Experimental variations effect of water on sand sample.
4.1.Effect of granular typeFigure4shows representative of granular in a rotating cylinder at different filling degree for each sample.At filling degree  = 0.06, only UAR and LAR were observed.For a bigger filling degree, MAR was observed between UAR and LAR section.