A new column collapse apparatus for the characterisation of the flowability of granular materials
Graphical abstract
Introduction
A wide range of powders and grains are handled in the packaging industry using bulk solids handling equipment, among which bag filling systems are of our interest. The performance of bagging machinery and the packaging quality rely on the first unit operation of dosing of the granular materials [1]. Dosing is carried out by gain-in-weight batching systems, consisting of a volumetric feeder that regulates the flow of bulk solids out of a supply hopper and into a weighing hopper [2]. Based on the applied material conveying techniques, a variety of feeder types exist [3]: free discharge by gravity feeders and rotary valves; positive displacement by belt, screw, and vibratory tray feeders; and pneumatic transport by fluidisation chambers. The operating efficiency of the feeders is critically affected by the flowability of the granular materials [4]. Nevertheless, it is still a common practice in the industry to base the feeder selection and design strategies solely on a qualitative assessment of flowability, the unreliability of which entails financial and environmental costs throughout the life cycle of the equipment. Therefore, the lack of a standard protocol for characterising granular flow phenomena remains a challenging issue in practical handling [5]. This motivates the development of experimental methodologies that can be equally applied to the diversity of powders and grains on the market. Then, robust classification strategies can be designed, relying on redundant material databases of the extracted parameters, combined with the engineering know-how and the mechanical behaviour modelling from experimental observations.
Flowability of granular materials involves complex mechanical behaviour issues, such as particle size segregation, affecting the homogeneity of free-flowing material batches [6], and jamming processes [7], which lead to the formation of stable arch and rathole structures [8,9]. The constitutive behaviour of bulk solids is otherwise affected by environmental conditions such as the ambient temperature and the relative humidity, the latter affecting the amount of stored water in hygroscopic materials [10]. In turn, the exposure to environmental conditions alters flowability by controlling slip-stick and caking processes [11,12]. The effect on flowability of the material properties of powders and grains produced by the food and agri-food, construction and mining, chemical and pharmaceutical, and recycling industries [[13], [14], [15], [16], [17]] has been studied using techniques at different scales. At the microscopic or grain scale, most work has focused on the investigation of the particle size, shape, and density; whereas at the macroscopic or bulk scale, attention has been paid to robust physical measurements including the compressibility, defined in terms of uniaxial compression stress, and shear testing in the quasi-static regime [18]. Moreover, flowability for specific applications—for instance additive manufacturing or die filling—has been researched respectively by avalanching and indentation [19,20]. Other methodologies exist that provide conventional parameters, albeit with indirect physical interpretations, such as the discharge rates, compressibility in terms of tapping densities, or the angle of repose [21,22].
Over the last two decades, granular column collapse experiments have received rising attention, aiming at understanding natural and industrial granular flows [23]. Fig. 1 shows the experimental set-up consisting of a reservoir in which the granular column is prepared and pre-conditioned. The reservoir wall is instantaneously removed, allowing the granular material to flow over the base, driven by gravity, until the final deposit configuration is attained at rest.
We distinguish different types of granular column collapse experimental set-ups by their main features, as found in the literature:
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The geometry of the initial column has been considered to be either quasi-two-dimensional [[24], [25], [26], [27], [28], [29], [30]], assuming plane strain conditions inside a rectangular channel, or axi-symmetrical [23,24,28,[31], [32], [33], [34], [35]], which does not allow inspecting the internal structure of the mobilised mass during flow propagation. So-called semiaxisymmetric geometries have been explored to circumvent such drawbacks with consistent results compared to cylindrical set-ups [25]. For a quasi-two-dimensional set-up, we define the initial column aspect ratio as a = h0/l0, with h0 the average initial granular column height after pre-conditioning, and l0 the reservoir base length, see Fig. 1. The explored values of a range typically between around 0.5 [24,25,30] and 10 [29,30].
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In the case of quasi-two-dimensional set-ups, the procedure for material release generally consists in the instantaneous removal of a vertically lifted gate, ensuring that the time to completely separate the gate from the granular material is shorter than the elapsed time for the onset of flow [31]. Alternatively, some authors have resorted to swinging gates [26,27,36].
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The basal surface geometry and properties have been investigated. Beyond the usual horizontal surface configuration, the special case of a rotating horizontal table has been analysed in [33]. A smooth basal surface has been adopted in most cases, whereas experiences with rough surfaces— e.g. covered with sandpaper of a roughness of the same order as the tested granular material— have shown little effect on the results [23]. Furthermore, flows down rough inclined surfaces have been studied primarily in the field of earth sciences [37,38] to understand phenomena such as landslides or debris flows. Other works have presented results from inclined plane observations with rough [39] and smooth [40,41] basal surfaces. The maximum reported inclinations with respect to the horizontal range from 15 to 35°. Erodible beds, formed by layers of variable thickness of a granular material, have also shown negligible difference in the flow behaviour and deposit morphology on horizontal set-ups [31], whereas the flow dynamics and run-out have been confirmed to be controlled by erosion in the case of inclined channels or steps, as reviewed in [42].
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The interstitial fluid surrounding the granular material, either gas or liquid, has been also taken into account. Dry granular flows have been mostly researched, without control of the packing state of the material. Air fluidisation of granular columns both previous to and during flow has been reported in [43,44]. The inclusion of a liquid phase, in the form of capillary water in the pendular state, has been examined in [[45], [46], [47]]. Finally, fully saturated granular samples, immersed in distilled water or in various mixtures of water with soluble agents, have been tested in [[48], [49], [50]]. The pore fluid pressures at the basal surface have been controlled in the cases of air fluidisation and fully immersed set-ups [43,48].
We have developed a new fully-instrumented granular column collapse apparatus [51,52] that provides for a direct observation of granular flow regimes generated in actual handling conditions [53], and suitable for a wide range of powders and grains with particle sizes from the scale of μm to mm. The apparatus allows us to characterise the effect of their varying physical and mechanical properties at the grain and bulk scales on their flowability. Few researchers have addressed the question of the granular column collapse of fine-grained cohesive powders—for instance gypsum plaster [30]—and have largely focused on studying free-flowing non-cohesive coarser materials such as monodisperse spherical glass beads or quartz sand. We have equipped our experimental apparatus with complementary measurement techniques to visualise granular flow by looking at: the fluidisation and deaeration of the granular columns, the basal load distribution after collapse, the near-wall kinematics during flow propagation, and the free surface morphology of the final deposits. With the instrumentation redundancy, we seek to circumvent the eventual operational issues, as well as the problems associated with the material properties, such as the particle colour and granular texture affecting the feasibility of the image analysis of the flows.
This paper is organised as follows. First, we describe our experimental apparatus and the integrated instrumentation in Section 2. Next, we present three representative granular materials, and we detail our testing protocol in Section 3. We illustrate the capabilities of the apparatus by following the testing protocol to analyse the chosen materials. We show and discuss a selection of the obtained results in Section 4. Last, we summarise the highlights of our work and draw our conclusions in the final Section 5.
Section snippets
Experimental set-up
Fig. 2 shows views of our new fully-instrumented granular column collapse apparatus, consisting of a horizontal rectangular channel (1) of width 160 mm and length 2150 mm, which comprises a smooth anodised aluminium plate at the base, and vertical glass walls of height varying between 350 mm to 150 mm for ease of operation. The prismatic configuration permits the thorough visualisation and instrumentation of the set-up, by exploiting the quasi-two-dimensional nature of the generated granular
Materials and testing protocols
We have chosen three materials representative of common industrial practice to illustrate the capabilities of our experimental apparatus, namely: oat flakes, copper sulphate fertiliser, and talc powder. Table 1 shows material properties of the selected materials.
We report poured bulk density ρp values corresponding to samples gently funnelled into the reservoir. The funnel is gradually lifted during filling to maintain a maximum distance of 150 mm between the release point and the surface of
Results and discussion
In this section, we present selected results on three representative granular materials to display the main features of our experimental apparatus. We explore the pre-conditioning state of the granular columns by fluidisation and deaeration before collapse in Section 4.1. We use the profile sensor to analyse the free surface morphology of the samples at rest, before and after collapse, to find out the run-out lengths and the slopes of the final deposits in Section 4.2. The data gathered by the
Summary and conclusions
We have presented our new fully-instrumented granular column collapse apparatus responding to the need for an experimental methodology to characterise granular flow of a wide range of powders and grains. Our experimental set-up and the approach followed to interpret the results can be used as a reference framework to inform decision-making strategies for the adequate selection of bulk solids handling equipment, based on a quantitative evaluation of flowability of granular materials. Moreover,
Latin symbols
- A
Cross-sectional area of the granular column (m2)
- a
Initial column aspect ratio (−)
- Cc
Circularity coefficient (−)
- d
Particle size by sieving, percent mass fraction passing in subscript (mm)
- Ekin
Kinetic energy of the granular system (J)
- Ekinrot
Rotational kinetic energy of the granular system (J)
- Ekintrans
Translational kinetic energy of the granular system (J)
- Epot
Potential energy of the granular system (J)
- Etot
Total energy of the granular system (J)
- f
Force transmitted to the load cells (mN)
- g
Acceleration of
Acknowledgements
This work was supported by the Industrial Doctorates Plan of the Government of Catalonia [Project 2014 DI 075: Optimization of dosing systems for bulk solids using experimental and numerical techniques]. The authors would like to thank Joan Caba, Xavier Arderiu, Josep-Manel Padullés, and Juanjo González at TMI for their valuable contribution to the design and start-up of our experimental apparatus. The first author would like to acknowledge the support received by the Geotechnical Laboratory at
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