Tools Request permission Export citation Add to favorites Track citation. Share Give access Share full text access. Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Abstract The flowability of powders with different mass median diameters ranging from micrometers to nanometers was measured using the vibration shear tube method.
Citing Literature. Volume 29 , Issue 1 May, Pages Related Information. Close Figure Viewer. Browse All Figures Return to Figure. Previous Figure Next Figure. Each time yield locus is valid for only one consolidation period and one consolidation stress. Since unconfined yield strength usually increases with increasing consolidation period, flowability, ffc, will decrease with increasing storage period see Fig. In accordance with [3. If the time yield locus is approximated as a straight line, this value is identical to the slope of the time yield locus.
The explanation of this is given in Sect. Since time consolidation tests are time-consuming, it is common practice to measure only one shear point of a time yield locus. The time yield locus is then approximated by a parallel to the linearized yield locus running through the measured shear point. When this procedure is applied, the 3. If such a simplified test procedure is applied, it has to be ensured that the results are on the safe side regarding quantitative application e.
Slope angle of the time yield locus here: time yield locus approximated as a straight line 3. The wall friction angle is important for silo design for flow and for silo design for strength, but also for the design of chutes and other equipment, where the bulk solid will flow across a solid surface. The procedure corresponds to the procedure recommended for the Jenike Shear Tester [3. The principle of the test setup for a wall friction test is shown in Fig. The bulk solid specimen is subjected to a vertical normal stress. In order to measure the wall friction, a bulk solid specimen is moved across the surface of a wall material sample with constant velocity, v.
This 70 3 Flow properties of bulk solids process is called shear similar to the yield locus test. With time, the rate of increase of the wall shear stress becomes less until finally a constant wall shear stress is attained steady-state shear stress. Since wall friction is often dependent on wall normal stress, wall normal stress is varied incrementally during the test.
Thus the normal stress is adjusted to another value after steady-state flow has been observed. In this way values of steady-state wall friction at several wall normal stresses are measured. The curve or line running through the measured points is called the wall yield locus. Since 3. Thus the wall yield locus could more exactly be called a kinematic wall yield locus [3.
The larger the wall friction angle or coefficient of wall friction, the greater is wall friction. If the wall yield locus is a straight line running through the origin Fig. In this case wall friction is independent of wall normal stress. The wall yield locus shown in Fig. In this case one finds a different wall friction coefficient and wall friction angle for each point on the wall yield locus according to Eqs. In this case the wall friction angle is not equal to the slope of the wall yield locus. When the wall friction angle is used for a certain application, e.
The relevant wall normal stress must be assessed and then the wall friction angle for this stress can be determined from the wall yield locus. Wall yield loci; a. In analogy to the time yield locus the time consolidation at a surface is characterized by a time yield locus. In contrast to the wall yield locus, which describes kinematic wall friction, the time wall yield locus represents static wall friction static wall yield locus resulting from storage of a bulk solid on the surface of a rigid wall under a static normal stress over a given period of time [3.
The test setup is the same as for a wall friction test Fig.
Measurement begins with preparation of the specimen, i. The described step is called preshear in analogy to a yield locus test. After preshear, shear stress is reduced to zero. Then the specimen is stored at rest for the selected storage time. This is called shear or shear to failure in analogy to a yield locus test.
This maximum is interpreted as static wall friction. The time wall yield locus represents the static wall friction after a certain storage time at rest, t. In most cases the time wall yield locus is not a straight line running through the origin. If the relative displacement is translational, the shear tester is called a translational shear tester.
The Jenike shear tester, which is described in Sect. Principle of the shear deformation in a translational shear tester A shear tester, where the relative displacement is achieved by rotation of the top of the bulk solid specimen relative to the bottom, is called a rotational shear tester. The bulk solid specimen in Fig. Furthermore, by rotating the circular plate around its vertical axis the bulk solid specimen is subjected to shear deformation. Shear testers according to this principle are called torsional shear testers. Deformation of the bulk solid during shearing varies with the radius.
It is zero in the center and increases linearly with the radius. Principle of rotational shear testers: a. Thus the deformation of the bulk solid specimen is more homogeneous, but still dependent on the radius. In the following the test procedure is described regarding two common shear testers, the Jenike shear tester and the ring shear tester. These two types of shear testers have been investigated in science more than other testers. These testers have been built in a diversity of research institutes in many countries in order to investigate, for example, the stress distribution in a bulk solid specimen and the influence of the geometry of the shear cell.
Thus quite a lot of information is available about the shear process in the bulk solid specimen. At first the Jenike shear tester was mostly applied for silo design. It was developed on basis of direct shear testers known from soil mechanics e. The shear cell of the Jenike shear tester is shown in Fig.
The base of the shear cell is fixed to a stationary bearing plate. The shear ring is placed on the base. Base and shear ring contain the bulk solid specimen, which is 4. The shear lid and thus the bulk solid specimen are loaded centrically by a normal force, FN, by means of a weight hanger the weight hanger is a device for carrying weights, which is set on the central tip of the shear lid and weights.
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Principle of the shear cell of the Jenike shear tester dimensions in mm In Fig. In addition, shear cells with smaller or larger dimensions are possible, for example for the case that only a limited amount of bulk solid is available for testing, or if a bulk solid with large particles has to be tested. The latter follows from the condition that the specimen must contain a sufficient number of particles to ensure that it behaves like a continuum. If the number of particles is too small, the measured shear force fluctuates, since the stress is transferred through a small number of force chains which undergo a permanent change force chains: see Sect.
Furthermore, the measured shear stresses are too large due to the restricted mobility of the particles [4. With a shear cell as shown in Fig. If particles are hard and sharpedged, the maximum particle size is somewhat smaller.. To shear the bulk solid specimen, the upper part of the shear cell, i. This is caused by a stem that presses against the bracket attached to the shear lid.
The stem is attached to the drive system through a force transducer which measures the shear force, FS. The shear force is transferred to the bulk solid specimen through the bracket and the shear lid as well as through the small pin attached at the bracket and the shear ring. For the preparation of a test the base along with the shear ring is placed on the bearing plate Fig.
A mould ring is then placed on the shear ring. Shear ring and mould ring are then pressed against locating screws not shown in Fig. The offset is equal to the thickness of the wall of the shear ring. After the shear cell has been filled with the bulk solid, excess material is scraped off level with the top of the mould ring and, thus, a plane surface is attained.
Shear cell in initial position: The shear ring is in the offset-position, i. After filling, excess material is removed by scraping off with a spatula. The shear displacement of the Jenike shear cell is limited to twice the wall thickness of the shear ring, i. Therefore at preshear, steady-state flow has to be attained after a sufficiently small shear displacement. This is only possible when the bulk solid specimen is close to critical consolidation consolidation attained at steady-state flow prior to preshear, so that only a relatively small shear displacement is necessary until steady-state flow prevails.
Thus the bulk solid specimen has to be preconsolidated prior to preshear. With the hanger and appropriate weights the bulk solid specimen is loaded with the same normal force, FN, which has been selected for preshear. For the case that the shear tester is provided with a twisting device as shown in Fig. Then the twisting lid is twisted by means of the twisting device. Due to friction between the smooth underside of the twisting lid and the bulk solid, shear stresses develop in the circumferential direction.
The shear stresses along with the normal stress created by the normal force, FN, consolidate the bulk solid specimen. If the shear tester is not provided with a twisting device, the twisting lid is rotated with a wrench, whereby the procedure is in principle the same as described above. Shear cell; setup for preconsolidation twisting The required number of twists depends on the bulk solid and the stress level selected for the yield locus.
If a very compressible bulk solid is tested, it may happen that as soon as the weight hanger has been placed on the twisting lid, the bulk density increases significantly and thus the twisting lid moves downwards well into the filling mould. In this case hanger and twisting lid have to be removed and the shear cell has to be filled further. This has to be repeated until a sufficient amount of bulk solid is in the shear cell, so that even after twisting the bulk solid surface is above the top 80 4 Practical determination of flow properties of the shear ring.
If the latter is not the case, then it is necessary to prepare a new test specimen. After twisting the twisting device and weight hanger are removed. Then the mould ring is carefully lifted and subsequently the twisting lid is slid off the bulk solid specimen in direction of the stem. Excess material is then scraped off in small quantities to be flush with the top of the shear ring similar to Fig. Care has to be taken that neither a downward force is exerted by the spatula nor the upper shear ring is moved relative to the base. The last step of the preparation is to place the shear lid centered on the shear ring on the bulk solid specimen Fig.
In this position the width of the gap between the pin and the shear ring should be about 0. Then the hanger with weights is placed on the central tip of the shear lid to apply the normal force, FN. In order to ensure that the shear ring is not in contact with the base and thus shear and normal stresses are transferred between the rings, the shear ring is carefully rotated around its axis and simultaneously lifted until the distance between the base and the shear ring amounts to about 0. Now the shear cell is ready for preshear.
This plane is called the shear plane, and for the stress calculation it is assumed that the shear deformation takes place in this plane. The normal stress at preshear is calculated from the normal force, FN, resulting from the hanger and weights on the hanger, the weights of all other parts above the shear plane shear lid, shear ring and the bulk solid within the shear ring.
For preshear the stem is driven with constant velocity in direction towards the shear cell Fig. The position of the shear cell relative to the stem must be such that the stem acts on the bracket in the shear plane. Only in this way the shear force does not exert a moment on the shear plane which can be easily shown by equilibrium of forces and moments of the upper part of the shear cell shear lid and shear ring with bulk solid [4.
The measured shear force, FS, is recorded during the test chart recorder, data acquisition system. At preshear the shear force should at first increase with a steep slope, than become flatter and finally attain a constant value Fig. Thus steady-state flow is attained. The stem is then driven backwards until the shear force, FS, is reduced to zero.
For this the normal force, FN, is reduced by removing weights from the hanger. The hanger must not be lifted because the bulk solid specimen should not be disturbed or unloaded completely. Subsequently the specimen is sheared by driving the stem in the forward 4. In the case of a fine-grained, stiff bulk solid specimen the shear force increases quickly until it reaches a maximum.
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After the shear stress maximum has been recognized, the stem is driven backwards to reduce the shear stress to zero. The filled shear cell is then removed from the tester and weighed in order to determine the overall bulk density under consideration of the known weight and volume of the shear cell. Since here the total internal volume of the shear cell is used, the calculated bulk density is the overall bulk density directly after twisting. After measurement of the first point of the yield locus, more points have to be measured by repeating the procedure described above.
Powders and Bulk Solids
For each individual test one should use a fresh bulk solid sample. If the material has not been changed by the shear test e. In this case the material should be well loosened before each test. A course of the shear stress as shown in Fig. The maximum, which can be less pronounced than in Fig. Although at further shear steady-state flow prevails, the specimen is not in the same condition at the initially underconsolidated specimen described in Fig.
Thus only the bulk solid close to the failure plane has properties corresponding to steady-state flow. The rest of the specimen remains in the state of overconsolidation. Thus, the specimen is nonhomogeneous, and the measured overall bulk density is too high compared to the bulk density corresponding to steady-state flow. Instead, for subsequent shear tests the number of twists has to be reduced.
Thus it may be necessary to repeat preshear several times until the appropriate number of twists has been found out. Sometimes a shear stress maximum at preshear can also be observed when shear is continued even after the shear stress has become constant for a certain time interval shear stress plateau. This maximum, which is usually less pronounced than described above, is often caused by the height of the shear zone decreasing shear localization, see Sect.
These processes lead to a decrease of the shear stress. In addition, when coarse particles are presheared, dilation can be observed in the first part of preshear thus resulting in a shear stress maximum see Sect. Sometimes the number of twists is not sufficient to attain steady-state flow within the available shear displacement, i.
In this case the number of twists has to be increased. If this is done, care has to be taken in order to avoid the bulk solid specimen becoming overconsolidated, but the overconsolidation is not recognized because of the limited shear displacement. Especially when very fine-grained bulk solids dry or moist are tested, overconsolidation can lead to a shear stress maximum developing very slowly as shown in Fig.
If this specimen requires an extended shear displacement, the operator will be happy to have attained steady-state flow within the available shear displacement when seeing that the shear stress does not increase further with time apparent steady-state flow. Thus the operator will stop preshear and proceed with shear to failure. But, as can be seen in Fig. Due to the limited shear displacement of the Jenike shear tester it is usually not possible to measure the broken curve in Fig. This makes is sometimes difficult to identify an overconsolidated specimen. Possible course of the shear stress when preshearing an overconsolidated specimen requiring a large shear displacement It is not possible to quantify the time required to measure a yield locus since it depends on the bulk solid, the number of trials until the optimal number of twists has been found out, and the skill of the operator.
The principle of the ring shear tester was developed by Hvorslev [4. Since naturally in soil mechanics high stresses have to be applied, the tester was accordingly heavy and not suitable for the small stresses applied in bulk solids technology. Other ring shear testers have been built in universities for research purposes [4. The main difference to earlier designs is the lighter construction, a shear cell which can be removed from the tester with lid and bulk solid specimen, the option of running wall friction tests, and the application of very small stresses.
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A computer-controlled version allows automatic measurement and evaluation. The ring-shaped annular bottom ring of the shear cell contains the bulk solid specimen. The annular lid is placed on top of the bulk solid specimen and attached to a crossbeam. Two parallel tie rods are connected to the crossbeam. Each of the tie rods is connected to a load beam not visible in Fig. To shear the bulk solid, the lid and the bottom ring of the shear cell must rotate relative to each other.
The bottom of the shear cell and the lower side of the lid are rough in order to prevent the bulk solid from sliding relative to these surfaces. Therefore, rotation of the bottom ring relative to the lid creates a shear deformation within the bulk solid. The roughness of the bottom and the lid is realized, for example, by radially-oriented bars vanes. During shear the shear force, which is the sum of the forces F1 and F2, is recorded. The shear force is directly proportional to the shear stress acting in the bulk solid specimen in the circumferential direction.
Shear cell of the Schulze ring shear tester [4. Thus a bearing for the lid, as used for earlier ring shear testers, is not necessary. The advantage of this construction is that the lid can tilt somewhat and thus can adjust to the bulk solid specimen like the shear lid of the Jenike shear tester , which results in a more uniform stress distribution in the bulk solid specimen. Furthermore, similar to the Jenike shear tester this design allows one to remove the shear cell along with the lid and the bulk solid specimen, for example, for time consolidation tests with external storage.
The vertical normal force, FN, is exerted on the crossbeam which is fixed at the lid. This can be accomplished with weights as used with the Jenike shear tester placed on a hanger which is attached to the crossbeam, Automatic ring shear testers are provided with a device for the computercontrolled adjustment of the normal force. The weights of the lid, hanger, crossbeam, and tie rods can be compensated by a counterbalance force, FA, which is directed upward and acts at the crossbeam.
The result of the counterbalance force which is created, for example, by a counterweight, is to make possible the application of normal stresses smaller than the stresses resulting from the weight forces of the lid and the parts connected to the 86 4 Practical determination of flow properties lid. In principle, this way normal stresses smaller than Pa and even negative normal stresses can be applied on the bulk solid specimen [4. The shear force is recorded versus time chart recorder, data acquisition system, control system. If the lid of the shear cell is connected to a displacement transducer, the vertical position of the lid can also be measured.
Similar to the Jenike shear tester, the size of the shear cell is a limiting factor for the particle size of the bulk solid to be tested. Following the experience of the author, in a ring shear cell with mm outer diameter and cm3 specimen volume, bulk solids with particles up to a diameter of 5 mm in case of a very narrow particle size distribution, and up to 10 mm in case of a wide particle size distribution e.
If very fine-grained bulk solids have to be tested e. Only cohesionless, incompressible bulk solids can dilate at the beginning of preshear which results in the height of the specimen increasing somewhat see Sect. Measurement of a yield locus by preshear and shear to failure with a ring shear tester where several points are measured with one bulk solid specimen When the shear stress does not increase further and, thus, steady-state flow is attained, the direction of rotation of the bottom ring is reversed.
Then the bulk solid specimen is sheared until the maximum value of shear stress can be identified. The shear stress maximum represents incipient flow failure. It is interpreted as a point on the yield locus same assumption as with the Jenike shear tester, see previous section. Thus with bulk solids which do not change their properties due to the shear deformation true for nearly all bulk solids , a complete yield locus test can be performed with one specimen.
This greatly reduces the time required for a shear test [4. For the automatic measurement the ring shear tester presented here is connected to a PC running the control and test software. The hanger and weights are replaced by a device for the computer-controlled adjustment of 88 4 Practical determination of flow properties the normal force, FN. Furthermore, the computer controls the shear cell rotation and measures shear force and specimen height.
The control software must be able to identify steady-state flow as well as incipient flow in order to terminate preshear or shear to failure when appropriate.
Thus control, measurement and evaluation are done by the computer. This reduces the time that an operator is required to about five minutes per yield locus [4. The ring shear tester is used increasingly as an alternative to the Jenike shear tester. Especially for bulk solids which cannot be accurately tested with the Jenike shear tester because of its limited shear displacement, the ring shear tester is advantageous, for example, for testing soft elastic plastics powder, rubber granules [4. Furthermore, with the ring shear tester smaller stresses can be applied than with the Jenike shear tester [4.
Also better reproducibility [4. The latter may be the reason for the growing number of users in other fields than silo design, for example, in quality control or product development, where the Jenike tester is rarely applied. First a bulk solid specimen is presheared. After preshear the specimen is not immediately sheared to failure Fig. This can be done on the shear tester, whereby in this case the tester cannot be used for other tests during the storage period, or apart from the tester, for example, on a special device called a time consolidation bench Fig.
In this device the shear cell with the bulk solid specimen is loaded vertically with weights. The weights are adjusted so that the stress state in the specimen is similar to the stress state at the end of consolidation, i. Time consolidation bench with covers version for Jenike shear tester The time consolidation bench in Fig.
Sometimes it is desired to store the specimen at defined conditions, e. In this case one would store the specimen without cover. However, under all circumstances it has to be ensured that the specimen is not subjected to vibration or unwanted temperature changes due to heating equipment or sunlight. As with shear without time consolidation measurement of a point on a yield locus, Fig.
If consolidation time affects the bulk solid under consideration, after the consolidation period the shear stress maximum will be larger than it would have been without a consolidation period between preshear and shear. It is common practice to measure only one shear point on a time yield locus, i. The time yield locus is then approximated by a parallel to the linearized yield locus running through the measured shear point Fig.
Yield locus with time yield loci approximated as parallels to the yield locus 4. Therefore it is described here for both testers in this section. For measuring wall friction with the Jenike shear tester the base of the shear cell is replaced by a sample of the wall material Fig. Setup to measure wall friction with the Jenike shear tester The shear cell is prepared similar to a yield locus test Sect. The mould ring is placed on the shear ring, and shear ring and mould ring are filled with the bulk solid. Excess material is scraped flush with the top of the shear ring. Then the twisting lid is placed on the bulk solid filling, the hanger is placed on the lid, and weights are placed on the hanger, corresponding to the largest normal stress of the intended wall friction test.
Then the lid is twisted several times to homogenize the specimen and increase its bulk density thus ensuring that the shear lid will not move downwards too much when being loaded with hanger and weights. Since the dependence of wall friction angle on bulk density can usually be neglected, the time-consuming procedure for determination of the optimum number of twists, which is an important part of the preparation of a yield locus test, can be omitted.
During the test the bulk solid specimen is moved relative to the wall material surface. Since wall friction is usually smaller than the internal friction of the bulk solid, the complete bulk solid specimen moves relative to the wall material. This is possible because the influence of bulk density can be neglected and thus it is not necessary to prepare a new specimen for every stress level. When using the Jenike shear tester, appropriate weights are placed on the hanger. Then the stem is driven forward in order to move the shear cell across the wall material sample.
When the shear stress reaches a constant value, weights are removed from the hanger until the normal stress is reduced to the next level. This is the wall yield locus of the tested bulk solid on the specific wall material. From the wall yield locus the wall friction angle can be determined according to Sect.
Wall friction test: Shear stress vs. The annular bottom ring contains a sample of the wall material to be tested. On top of the wall material sample is the bulk solid specimen, which is covered with the annular lid of the shear cell. A normal force, FN, is applied to the bulk material specimen with the lid of the shear cell as with a yield locus test, Fig. Since the layer of bulk solid located between the lid, which has a rough underside, and the surface of the wall material is also prevented from rotating, 4. The test procedure is the same as described above for the Jenike shear tester Fig.
Measurement of wall friction with a ring shear tester [4. Therefore wall friction testing with many different wall materials, which are replaced by new samples very often, is less expensive with the Jenike shear tester. In addition, the dependence of wall friction angle on the shear direction, e. On the other hand the ring shear tester, which provides unlimited shear displacement, allows one to study the long-term behavior of the wall friction, e.
The unlimited shear displacement is also an advantage for combinations of bulk solid and wall material requiring large shear displacements. If such combinations are sheared with the Jenike tester, always after the maximum shear displacement is reached the stem has to be retracted and the shear cell pushed back to its initial position by hand [4.
Therefore in the following only a short description of the test procedure is given. The preparation and procedure of a wall friction time test are similar to a wall friction test. The main difference is that after steady-state wall friction has been attained the specimen is unloaded from shear stress and then stored at rest consolidation time on the wall material sample while the normal stress is kept constant Fig. For this the shear cell with the bulk solid specimen can remain on the shear tester, but the tester cannot be used for other tests during the consolidation time. Thus it is advantageous to store the specimen under static load on a time consolidation bench Sect.
After the storage time the shear cell with the bulk solid specimen is placed on the shear tester and sheared again under the same normal load as before the consolidation time. The maximum shear stress defines a point on the time yield locus for more details refer to Sect. With this kind of test products can be compared regarding their sensitivity to attrition, or the maximum stress for the storage of a specific product in order to minimize attrition can be determined [4.
It is important that the stress level of an attrition test 4. Fines are generated when particles are subjected to stresses, but a static load has to be distinguished from shear deformation kinematic load. Commonly — and not unexpected — more fines are generated by kinematic load than by static load at the same stress level. For attrition testing at kinematic load a device is required where a bulk solid specimen can be subjected to an adjustable normal stress and a large shear deformation. This is fulfilled with a rotational tester like a ring shear tester [4.
The procedure of an attrition test with a ring shear tester is as follows with other testers the procedure has to be adjusted corresponding to their specific features : Particles smaller than a specific size are removed by sieving e. The prepared bulk solid sample is filled into the shear cell Fig. The specimen is sheared similar to preshear during a yield locus test to a certain shear displacement selected by the operator.
Shear displacement is the relative rotational displacement of the bottom ring and lid, measured at the mean radius of the specimen. The relative displacement follows from the shear velocity times the duration of shearing. After shearing the specimen is sieved with the same sieve used for preparation of the specimen, or with a sieve of a smaller mesh size. It can be useful to divide the mass of the fines by the total mass of the specimen. Alternatively to the analytical procedure described in the previous paragraph, one can measure particle size distribution before and after shearing.
A comparison of both particle size distributions may give more insight into the attrition processes. Attrition tests provide only qualitative data. Among other reasons this is because during the shear process essentially only the bulk solid in the shear zone is subjected to a kinematic load, and the exact volume of the shear zone is unknown.
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The thickness of the shear zone for not too fine bulk solids is on the order of magnitude of five to twenty particle diameters see Sect. However, even if attrition could be measured quantitatively and independent of the test device, this would not be a significant 96 4 Practical determination of flow properties advantage, because the shear deformation in silos, hoppers etc. One reason for this is that shear deformation is concentrated in shear zones see Sect.
After a sufficient shear deformation the fines content attains a nearly constant level, since at the given test conditions no further attrition is possible. This state has been reached in Fig. If one selects a series of stresses for attrition tests, which are large relative to the strength of the particles, it can happen that all particles are destroyed independent of the applied stress.
Attrition test: fines content as a function of normal stress and shear displacement qualitative Before attrition testing, preliminary tests to determine optimal shear deformation are recommended. If there is too little shear deformation, the quantity of fines generated might be too small to be precisely measured. If shear deformation is too large, all particles in the shear zone may be completely destroyed, so one cannot determine differences between various samples of a bulk solid or between different levels of the applied normal stress.
During preliminary tests, therefore, several identical samples of a bulk solid should be subjected to different shear deformations. The results amount of fines generated during the test should show at least in a limited range of the applied shear deformation a measurable fines content and increased fines content with shear deformation. Such a range is indicated in Fig. A shear deformation within this range should then be selected for the attrition tests. This ensures that a measurable amount of fines is produced and that shear deformation is not so large that all particles within 4.
Thus one can distinguish between the attrition sensitivity of individual samples. The more bulk density increases, the more compressible the bulk solid. For some applications it is of interest to know a characteristic value for the degree of compressibility. Other applications require knowledge of the dependence of bulk density on stress e. The bulk solid is filled loosely in a mould, scraped off flush with the top of the mould, and then subjected to a vertical force, F, through a platen of area A Fig.
From the height, h, and the mass of the specimen the bulk density is calculated. A source of error is the friction at the side walls of the mould. This friction reduces the normal stress from top to bottom see Sect. Thus for a simple test as shown in Fig. Thus, the dependence of bulk density on consolidation stress can be obtained by measuring several yield loci at different consolidation stresses. The bulk density resulting from a yield locus test is typically somewhat larger than that from a compressibility test where the specimen is not sheared, but uniaxially consolidated see Sect.
Compressibility can be an important parameter also for comparative tests. At both consolidation stresses the bulk density is measured, e. The advantage of this procedure over the comparison of the bulk density of a loose specimen to its tap density is that here the bulk density is a result of a well-defined stress, whereby the loose density depends on how this loose state has been prepared Sect. If the bulk density as a function of the consolidation stress is of interest, several pairs of values of bulk density and consolidation stress must be measured in the relevant stress range.
The results should be indicated then in form of an equation adapted to the measuring points, which indicates bulk density as function of the consolidation stress. One finds an overview of meaningful equation types in [4. A function, which can be adapted simply and usually describes bulk density in a limited stress range sufficiently well, is: 4. They both have the same units as the bulk density.
It is recommended that stresses similar to the stresses acting on the bulk solid in the application under consideration be selected. This can be the maximum stress in a silo, the stress in the hopper of a silo especially for silo design for flow , the stress associated with storage of the bulk solid in IBCs or on pallets, the stresses in small containers e. If similar materials must be compared on the basis of the test results, the stress level usually has no influence on the qualitative ranking of a set of products in terms of their flowability.
The semicircular shape reduced model seemed to be suitable for viewing the flow profile and variations occurring during the flow. Draft code of practice for the design of silos, bins, bunkers and hoppers. Berkshire: BMHB, Powder Technology , New York, v. A novel theory on the arching and doming in mass flow hoppers. Bergen: The Michelsen Institute, Flowability and handling characteristics of bulk solids and powders - a review with implications for DDGS. Biosystems Engineering , London, v. Storage and flow of silos. Salt Lake City: University of Utah, Bulletin, Flow and shear descriptors of preconsolidated food powders.
Journal of Food Engineering , Essex, v. The shape of the cohesive arch in hoppers and silos - Some theoretical considerations. Stresses in bulk solids in wedge hoppers: A flexible formulation of the co-ordinate specific, Lame-Maxwell equations for circular arc, principal stress systems. RIPP, M. Chemical Engineering Science , New York, v. Steel silos with different aspect ratios: II - behavior under eccentric discharge.
Journal of Constructional Steel Research , London, v. Powders and bulk solids. Behavior, characterization, storage and flow. Berlin: Springer, An approximate theory for pressures and arching in hoppers. All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License. Services on Demand Journal. Paulo Donato Castellane, km 5