The Sevilla Powder Tester: A Tool for Characterizing the Physical Properties of Fine Cohesive Powders at Very Small Consolidations †

We present a ﬂuidized bed apparatus that enables us to test the bulk mechanical properties such as the yield stresses and compressibility of ﬁne cohesive powders. Every measurement is preceded by driving the powder into the bubbling regime in which the material loses memory of its previous history. Then the gas ﬂow is set to a given value to take the powder into a well deﬁned and reproducible initial state of low consolidation. Reverse ﬂow is used to exert high compressive stress. A cornerstone of our technique is that the procedure is automatized, thus making results operator insensitive. Besides being a practical tool to diagnose the ﬂowability of experimental powders, the Sevilla Powder Tester (SPT) also provides us with a powerful technique to research fundamental problems in powder mechanics.


Introduction
The mass f low of fine particles is relevant in many industrial fields. It is estimated that 60% of products in the chemical industry are manufactured as particulates and a further 20% use powders as ingredients [1]. In spite of this, most industrial powder processes are dependent on empirical correlations since the link between the physics of local grain interactions and their global mechanical behavior is still poorly understood. A clear example are fluidized beds, which are extensively used whenever a good solid-fluid contact is needed such as in the catalytic cracking of oil, the combustion of coal, drying, mixing, transport, etc. A precise knowledge of the fluidized bed structure and behavior is quite relevant not only from a theoretical point of view but also from the practical point of view.
The behavior of powders can be significantly inf luenced by particle size, particle deformation, distribution of forces, cohesive and frictional interaction, contact restructuring, aggregation, interstitial gas, etc. The presence of these multiple and usually cooperative features makes the problem of investigating powder behavior from a fundamental perspective a rather complicated challenge, thus empirical ap-proaches prevail. Most of the empirical studies to characterize powder flow yield numbers which are not clearly related to the fundamental physical properties. More importantly, due to the hysteretic nature of interparticle contact forces, uniform powders are hard to create and the packing arrangement is a strong function of the previous history. Generally speaking, the techniques employed lack a satisfactory way of initializing the powder in order to have an initial reproducible state in which the memory of the powder has been erased. Moreover, the more cohesive the powder, the larger the memory effects are. Consequently, the wide experimental variations in bulk properties at low consolidations measured by the traditional testers preclude a reliable estimation of interparticle forces [2], which are ultimately responsible for the ability of a powder to f low [3].
In this paper we review a Powder Tester apparatus [4] in which the powder sample is conveniently initialized by the use of fluidization. This Powder Tester enables us to investigate fluidization properties such as bed expansion, sedimentation, aggregation of fine particles within the fluidized bed, onset of bubbling for sufficiently large gas f low, transition to a solid-like regime for gas flows smaller than a critical one, etc [5]. For the solid state, in which particle contacts are permanent, the tester measures the uniaxial tensile yield stress of the powder and its average particle volume fraction as a function of the consolidation stress, which can be controlled in a range spanning from a few to thousands of Pascal by means of forward and reverse controlled gas f low. The behavior of powders during compaction yields information about the mechanism of density increase. From the bulk stresses, we estimate the interparticle contact forces that are well correlated to direct measurements of forces between isolated particles made using a Scanning Force Microscope (SFM) [6]. All the measurements can be done under complete computer control and are fully automated. A further advantage of the SPT for testing experimental powders is that the instrument only needs a small volume of powder (typically around 20 g.).

Some techniques of analysing powder flowability
Schwedes recently made an extensive review on testers for measuring the bulk flow properties of granular materials [7]. In this section, we highlight some of the most-used techniques in powders from a critical perspective.

Empirical techniques
A traditional way of testing powder flowability is to measure the ability of the powder to flow through standard devices. For example, we find in the Book of the American Society for Testing and Materials Standards a technique that consists of measuring the time that a given mass of powder takes to discharge through a hopper [8]. Even though this technique has been proved to be useful for metallic powders, an external energy source such as tapping is needed for very cohesive powders to help powder flow [9]. Vibration, however, may consolidate the powder and, especially in the case of fine particles, this enhances cohesiveness. A similar technique, frequently used for pharmaceutical tabletting applications, consists of forcing the powder to pass through rings of decreasing diameters [10]. The f lowability index is defined as the diameter of the smaller ring through which the sample can discharge three consecutive times. There is also a commercial rheometer similar to the ones employed to measure the viscosity of liquids, but that has been adapted to test powder flow [11]. The rheometer incorporates a blade with different sections in the opposite sides of a rotation shaft. The first section has its surface parallel to the rotation shaft whereas the second section is twisted relative to the rotation shaft. The Hosokawa Powder Tester [12] is another instrument that has been extensively employed in the xerographic industry to measure toner f lowa-bility. In the Hosokawa test, a number of screens of different sizes are placed vertically and are vibrated. An estimation of the toner flowability is given by the relative mass of powder that passes through each screen.
The success of these techniques is hindered by the difficulty of initializing the powder in an initial reproducible state. Therefore, results are dependent on the history of the powder: i.e. the filling procedure, previously applied stresses, etc. This is particularly important in the case of fine cohesive powders for which interparticle attractive forces may increase by several orders of magnitude with the applied external load [13]. An additional problem is that the interaction of the powder with mechanical parts, such as the blade of a rheometer, may produce a "heterogenous" cohesiveness since the load and shear applied can change abruptly from point to point within the sample. Thus the results achieved depend on the particular design of the device and on the experimental procedure. In addition, the correlation of the experimental results to fundamental physical parameters of the powder remains rather obscure. Therefore, it would be desirable to measure properties more directly linked to fundamental parameters, thus yielding more robust and confident results.

Techniques of analysing powder flowability based on fundamental properties
The powder compressibility has usually been taken as a measure of powder flowability [14]. Granular materials that f low well end up in very dense packings that are quite difficult to compress, whereas poorly f lowing powders pack in open structures that can be further compressed with ease. Compaction tests in which a cylindrical plug of powder is compacted axially by a piston are commonly used in civil engineering [15]. A proposed number to classify powder f lowability is the Hausner ratio, defined as the ratio of the tapped powder density to the untapped powder density [16].
Most of the situations involving the flow of powders imply the presence of shear stresses. Therefore, some techniques to test powder flowability are focused on measuring the yield stress as the powder sample is sheared. Consider an arbitrary plane through the powder sample and a shear stress t acting on that plane; there will be a value of stress that will cause the powder to shear off in the plane and cause the powder to f low. This yield stress depends on the normal stress s acting perpendicular to the plane. In general, t increases with s, and the relationship between t and s defines the yield locus of the powder. At high stresses the yield locus can be approximated by a linear function known as Coulomb's law [17] t҃s tan Φѿc (1) where c and Φ are the cohesion and the angle of internal friction. For many coarse granular materials c is negligible.
The point of the yield locus on the negative s axis is the ultimate tensile strength s t . The linear theory is, however, inadequate to describe the behavior of fine cohesive powders at low values of s and t that occur in practice. Traditionally, the Jenike shear cell [18] has been used by engineers in powder technology to estimate the angle of internal friction of highly consolidated granular materials. Essentially, the technique consists of compacting a powder sample with a known external load into a cylindrical cell composed of two metal rings one upon the other. With the compaction load still applied, the minimum steady state shear stress necessary to displace the upper ring horizontally with respect to the lower one is measured. Steady state f low means f low at constant density and constant shear stress. These values of normal and shear stresses define the end point of the yield locus. Then the normal load on the powder is decreased and the new horizontal force necessary to initiate shearing of the powder is measured. In order to minimize the inf luence of the operator, the Jenike cell is commercialized with a reference material with which researchers can check both their equipment and experimental technique. The reference powder consists of " 3 kg of limestone powder packed in a polyethylene jar" and is accompanied by a certificate that supplies the limiting shear stress for four different powder normal stresses [19]. However, in a great deal of powder processing equipment there is no significant compressive force while the Jenike cell is inappropriate for low consolidation stresses. The recently developed ring shear tester represents a technical improvement on the Jenike tester in order to measure the yield locus at smaller loads (ȁ100 Pa) [20]. An experimental problem that besets the Jenike cell technique and its modified versions is the lack of a reliable method of producing reproducible initial states. Interparticle contact forces are very sensitive to small variations of the previous external loads. As a result, errors due to poor preparation methods can easily arise. Further disadvantages of the Jenike test are that it must be accepted that the slip plane coincides with a horizontal plane and that the shear process takes place uniformly throughout the sample in order to relate the stresses to the real stresses inside the material. This is known to be false for overconsolidated materials [21]. A commercial alternative to the Jenike shear cell is the Peschl annular shear cell, in which the shear stress is applied by rotating the top part of an annular shear box containing the powder sample [21]. While this test allows for a constant area of shear and unlimited shear distance, making it useful for quantifying powder flow after failure, wall effects and strong uncertainty in stress distribution are major drawbacks.
Another property that has been employed to quantify powder f low is the angle of repose of a pile of powder [22]. Even though the angle of repose is a well defined property of noncohesive granular materials, it is meaningless when cohesive interaction becomes important. We may remember from our childhood that sand castles can sustain 90°slopes but when we tried to increase the size of the castle, landslides would probably happen that decreased the angle of repose to well below 90°. The inf luence of the size of the powder sample on the avalanching behavior of fine powders is well documented in the literature [23]. Therefore, the size of the pile, which is indeed an external parameter, must be specified in the testing procedure when dealing with cohesive powders.
A common tool to analyse the avalanching behavior of powders is a horizontal rotating drum partially filled with the granular sample [24]. In this device, intermittent and nearly reproducible avalanches are observed at low rotation speeds. For low-cohesive well-behaved granular materials, avalanches occur quite regularly with nearly uniform size and time spacing, whereas in the case of poorly flowing cohesive powders, the time spacing and size of avalanches shows a noisy behavior [24]. A rotating drum-based unit, developed by Kaye and coworkers [25], is now commercially available. In this device, avalanches are automatically detected by a change in the light intensity captured by a grid of photocells placed behind the drum. The avalanching behavior is characterized by the time interval between consecutive avalanches. The scatter of the points is a measure of the regularity of the avalanche process. With this technique, a gas conditioning system can be implemented [26] in order to control gas conditions inside the chamber that may have a profound effect on powder f lowability. Testing cohesive powders is, however, difficult and the test usually yields inaccurate results. A source of error is that the powder sticks easily to the walls of the drum and this reduces visibility. As a result, the light intensity series can easily become non-stationary whereas the number of avalanches per unit time detected decreases, thus complicating analysis of the data. In the case of ver y cohesive powders it is also likely that the powder slips as a whole. A further criticism is that merely the data on the time interval between consecutive avalanches cannot be enough to analyse cohesive systems with complex dynamics. For instance, Quintanilla et al. [24] have seen that for a class of cohesive powders, there is a regular sequence of large avalanches preceded by a number of two or three small precursors. In such cases, an in-depth statistical analysis is needed.
Since f lowability is closely linked to interparticle forces, it can be thought that a good bulk test is to measure the powder tensile yield stress for which the interparticle attractive force is responsible. The split cell tester is a commercial device able to measure a tensile yield stress [21]. The sample is held in a ringshaped cell and is compacted vertically using a plunger. Then a horizontal tensile stress is applied and steadily increased until the sample is pulled apart. In this way, the tensile yield stress for a given consolidation stress is measured. In the lifting lid tester, the sample is pulled vertically in the same direction of compaction [21]. These techniques present some inconveniences when applied to fine cohesive powders. One of them is again the lack of a mechanism for initializing the powder into a reproducible state of consolidation. As a consequence, results are of poor reproducibility. Another is the difficulty of measuring the tensile yield stress of fine cohesive powders at low consolidation stresses by means of piston consolidation [27]. It must be remarked that the way of preparation and compaction of the powder in the cell does not produce an isotropic state of stresses. Therefore, the tensile yield stress does not have to coincide with the tensile strength. Research tools such as triaxial tests achieve an approximated isotropic behavior by using hydrostatic compaction, but is applicable only to high compression loads.

Direct measurement of interparticle
forces A good estimation of the powder flowability should be based on direct measurement of the interparticle forces. The adhesion force between individual particles can be measured directly using a Scanning Force Microscope [6]. With this instrument, a probe particle is attached at the end of a V-shaped tipless cantilever. The probe particle is brought close to an isolated substrate particle under computer control and a loading-unloading cycle is applied. The largest down-ward def lection achieved by the cantilever during unloading gives the adhesion force. Figure 1 shows the statistical distribution of the adhesion force measured between two micrometer-sized toner particles. Another apparatus recently reported to measure interparticle forces [28] comprises a sensor unit composed of a contact needle that comes into contact with the powder and dislodges particles, measuring the adhesive force between the particle and sample substrate. This technique, however, does not have a way to control the previous load force on the particle that modifies adhesion substantially for plastic contacts [6]. The same criticism applies to the well-established centrifugal method [28].
As can be seen in Fig. 1, the SFM data obtained for the adhesive force between irregularly shaped particles such as xerographic toners has a broad dispersion. This is mainly due to the dependence of the adhesive force on the local surface properties of the contact. When two irregular particles are brought into contact, we can expect a wide range for the adhesive force measured depending on the exact location of the contact that determines the asperity size. This problem gets worse when flow conditioner additives are dispersed on the particle surface.

The fluidized bed method
A method to obtain the uniaxial tensile yield stress of the powder with high reproducibility consists of supplying a gas flow into a powder bed [27,29]. The layout of the experimental system is shown schemati- cally in Figure 2. Powder samples are supported on a porous plate in a vertically-oriented cylindrical vessel. Our experimental materials are xerographic toners made of polymer and with typical particle size ȁ10 µm. Pore size of the distributor plate is ȁ5 µm to ensure that toner particles do not penetrate into the pores and that the gas stream is distributed uniformly over the lower boundary of the bed. A controlled f low of dry nitrogen is introduced into the lower part of the vessel. By using dry nitrogen, the complicating effect of humidity, which is known to affect particle adhesion [30], is minimized. The gas flow is controlled by a mass f low controller while the gas pressure drop across the bed ∆p is measured by a differential pressure transducer. Readings of the pressure drop across the porous plate (without toner in the cell) are taken before each series of powder measurements. In all the range of gas f lows we used, there is a linear dependence of the pressure drop across the plate on the gas f low velocity. The powder sample is weighed and then placed in the vessel; at this stage the sample is quite inhomogeneous, with some loose and some compacted areas. To homogenize the sample, the bed is driven into the freely bubbling regime by imposing a large gas f low. Once in the bubbling regime, the bed loses memory of its previous history [31]. In the case of highly cohesive powders, such as toners with very low additive concentration, it is necessary to shake the sample in order to break up channels that conduct f luidizing gas away from the bulk of the powder and prevent f luidization. For that purpose, an electromagnetic shaker can be incorporated into the set-up in the base of the bed [4]. The bed is allowed to bubble during a time period large enough to reach a stationary state and after that the gas flow is suddenly returned to zero. This gives a repeatable start-ing condition for the powder. The height of the bed h provides an average value of the particle volume fraction where m s is the powder mass, r p is the particle density that must be known beforehand, and A is the cross-sectional area of the vessel. h is measured by means of an ultrasonic sensor placed on top of the vessel. The consolidation stress s c at the bottom of the bed is assumed to be the total weight of the sample divided by the area of the gas distributor. To measure the uniaxial tensile yield stress s t we subject the vertical layer of powder to an upward-directed f low of gas that is slowly increased to put the bed under tension. The total pressure drop is measured and the pressure drop across the gas distributor is subtracted from it. This is shown in Figure 3. When the gas passes through the packed bed of particles, the gas pressure drop is due to frictional resistance and increases linearly with increasing gas flow at low Reynolds numbers as described in general by the Carman-Kozeny equation [32] ҃ where x is the vertical coordinate measured downward from the free surface of the bed, µ is the dynamic gas viscosity (µ҃1.89҂10 Ҁ5 Pa·s at ambient temperature for dry nitrogen), v g the superficial gas velocity, and Eȃ180 is an empirical constant. There is a critical  gas velocity at which the powder fractures and the gas pressure drop across the bed ∆p falls abruptly. In order to find the tensile yield stress it is important to know how the powder fails. Close observations reveal that fracture of the bed always starts at the lowest point, the bottom of the bed. This was already predicted theoretically and later observed by Tsinontides and Jackson [33]. In their one-dimensional analysis, they neglected the wall effect and considered the uniaxial stress s, local particle volume fraction f and gas pressure depending only on the vertical coordinate x. Next, we give a slightly modified analysis from that of Tsinontides and Jackson [33] to show explicitly that the condition for tensile yield will be first met at the lowest point of the bed as the gas flow is progressively increased.

Location of fracture in the fluidized bed
In the consolidated equilibrium state, prior to the application of a gas flow, there are no external forces acting upon the particles except for the gravity force. Then we have a compressive stress s c (x) across the bed that obeys the simple equation The vertical coordinate x is measured downward from the free surface of the bed. When the gas is forced to pass through the bed, we must also consider the drag force per unit total volume F s exerted by the gas on the particles, which is given by the gas pressure drop per unit length F s ҃dp/dx. Then the force balance equation is Since in fine powders, the gas flow is usually at small Reynolds numbers, it is admitted that F s is proportional to the gas velocity F s Ϸb(f)v g . For a sufficiently large gas velocity, the negative contribution of the drag force will turn the stress s negative and equal to the tensile yield stress s t at some point within the bed. In order to find the yield condition, Eq. 5 must be integrated. There are several empirical equations in the literature for b(f). Tsinontides and Jackson found it reasonable to adopt the Richardson-Zaki equation [34]: where n is ȁ 5 for small Reynolds numbers and v p0 is the sedimentation velocity of a single particle, v p0 ҃

(1Ҁf) nҀ1
rpfg v p0 dp dx ds dx ds c dx (1/18)(r p Ҁr g )d 2 p g/µ (r g is the gas density), in the Stokes regime. While Eq. 6 describes well the behavior of f luidized beds at small values of the particle volume fraction, the Carman-Kozeny equation (Eq. 3) gives the best results for f0.3 [35]. Since we are looking for the yield point of the granular solids at large values of f, Eq. 3 seems more appropriate to us for the pressure gradient. The integration of Eq. 5 yields where we have used E҃180 and the gas density has been neglected as compared to particle density. Let us consider first the simplest case of a homogeneous bed in which f҃f 0 and s t ҃s t0 0 are constants throughout the bed. Then we have s(x)҃r p f 0 gx 1Ҁ (8) i.e. the uniaxial stress across the bed will increase linearly with a slope that decreases as the gas velocity is increased. Eventually the slope becomes negative and with a sufficiently large gas velocity, s will equal s t0 at the point where s is maximum, which is always the bottom of the bed. Note that if s t increases with the depth of the bed (due to an increase in consolidation, for example) the fracture will occur also at the base of the sample as long as there is a non-vanishing s t0 , at the free surface (tensile yield stress at zero consolidation).
A more realistic approach is to take into account that f(x) increases with the depth of the bed as a result of the increase of the local consolidation stress. In the whole range of consolidations tested, we obtain a good fit to the experimental data on the average particle volume fraction ͗f͘ by the modified hyperbolic law (see as an example Figure 4) ͗f͘(x)҃aҀ For the commercial toner Canon CLC700, we have a҃1.366, b҃1.088, c҃3.968, and d҃0.02454 with a regression coefficient R҃0.9954. To apply this formula, we need to assume that the average particle volume fraction ͗f͘(x) from the free surface to a depth x in a bed of total height x is equal to the measured ͗f͘ in a bed of total height x. From the definition of ͗f͘ we derive the local particle volume fraction f(x) seen that the deviation between the results is within the experimental scatter (Ȁ1 Pa).
to be used in Eq. 7. Figure 5 shows the new profiles of the uniaxial stress obtained by numerical integration of Eq. 7 for different values of the gas velocity. The essential difference with respect to the uniform case is the convex shape of s(x) due to the increase of the drag force with depth. The consequence is that the yield condition is more neatly met at the base of the sample. According to Eq. 5, the total gas pressure drop across a bed of height h at yield, (∆p) Y , is given by the powder weight per unit area plus the tensile yield stress at the bottom (∆p) Y ҃r p ͗f͘ gh ѿ  s t (h) (12) Thus the overshoot of ∆ p beyond the bed weight per unit area when the powder fails gives us a quantitative measure of the uniaxial tensile yield stress s t (h). For practical purposes, we checked that the tensile yield stress is not sensitive to the rate of increase of the gas flow. Figure 6 shows results of s t for a given sample obtained using different rates. It is

Fig. 5 Continuous lines: Uniaxial tension (s) across a non-homo-
geneous bed of powder as the gas flow is increased (the ratio of the gas velocity to the sedimentation velocity of an individual particle v g /v p0 is indicated for each curve). The free surface is at x҃0 and the bottom at x҃4 cm. The calculation is performed for a non-homogeneous bed with average particle volume fraction ͗f͘ ҃1.366Ҁ1.088/(1ѿ 3.968x) 0.02454 (fit curve to Canon CLC500 toner experimental data) and particle density r p ҃1199 kg/m 3 . The dotted line is the experimental tensile yield stress (s t ҃1ѿ5.5x Pa) for Canon CLC500. The yield condition (s҃s t ) is met at the bottom of the powder (x҃4 cm) for v g /v p0 ȃ 0.087. As noted by Tsinontides and Jackson [33], the condition for tensile yield can be met either at the lowest point within the powder bed or at the contact between the bed and the gas distributor plate. However, we have consistently observed that the gas distributor surface remains always covered by a thin layer of powder after the break. Thus the measurement is indeed that of the tensile yield stress of the powder rather than a measure of the interface strength between the distributor plate and the powder. As further proof, we present in Figure 7 experimental measurements of s t using both metallic and ceramic gas distributor plates. Within the experimental scatter, the results fit to a single curve.
The yield condition will be more neatly met at the base of the powder for the most cohesive toners (  s t  large) while a large portion of powder remains far from the yield condition. In contrast, for low-cohesive systems ( st small), the uniaxial stress will be close to the tensile yield stress throughout all the material at the yield point, therefore, in practice, the fracture will be less clearly visible at the base. In our experimental work, we observe a variety of behaviors at the yield point depending on the magnitude of the tensile yield st (Pa) m҃7 g (gas) m҃4 g (gas) m҃7 g (centrifuge) ceramic filter (variable mass) Fig. 7 Uniaxial tensile yield stress as a function of the consolidation stress for an experimental xerographic toner with 0.2% concentration by weight of additive. The data from different tests using consolidation by gas (two tests with samples of different masses) and centrifuging in a bed with a metallic gas distributor are plotted jointly with data obtained in a bed with a ceramic gas distributor where consolidation was increased by adding new mass to the sample.
stress and in agreement with this theoretical prediction. For most cohesive powders, the fracture at the bottom is clean and the powder rises in the bed as a plug. Furthermore, the bottom of the plug does not erode as it rises in the bed. The toner without flow additives behaves in this way. For powders of mediumlarge cohesiveness, fracture of the bed is still clearly visible and plugs are still formed, but the plug erodes as powder agglomerates fall away from its lower surface. The plug then becomes unstable and collapses at a certain height. Examples of this behavior are the toners with 0.01% and 0.05% Aerosil concentration by weight (12.5 µm particle size). For powders of low cohesiveness, plugs are rarely visible. After the break at the bottom of the bed, the fracture propagates until it reaches a certain height. Then, the gas escapes from the powder through channels which erupt like miniature volcanoes. The lower the cohesiveness of the toner, the less stable are the channels. These effects are observed, for example, in the toners with 0.1% and 0.2% Aerosil concentration. Finally, for the least cohesive powders, for example, the experimental toner with 0.4% Aerosil concentration or the Canon CLC500 toner, plugs do not develop, channels are very unstable, and a state of homogeneous fluidization is easily reached. We note, however, that this type of behavior depends also on the consolidation stress s c that inf luences the tensile yield stress Ҁ as we will see. In that sense, beds of small s c favor the formation of channels, whereas highly consolidated beds favor the formation of stable plugs. Valverde et al. [27] found that wall effects are negligible for particles with a typical size of ȁ10 µm in beds with typical heights not larger than their diameter, as can be seen in Figure 8. Data of the average particle volume fraction from circular beds and from a rectangular bed fit within the experimental scatter to a single curve.
In our early investigations, two techniques were employed in order to test the powder under different consolidation stress. In the first one, the powder mass was varied by adding powder to the bed [27] (see, for example, Fig. 8). In the second one, the vessel with the powder inside was centrifuged prior to measuring the tensile yield stress [36], thus increasing the apparent gravity by g a ҃( g 2 ѿw 4 r 2 ) 0.5 , where w is the angular velocity and r the average radius at which the bed is rotating (see, for example, Fig. 7). These techniques needed to be performed by human operators and therefore none of them allowed for automation of the measurements. Furthermore, there are some difficulties related to testing the powder under very In Figure 10 a schematic view of the automated SPT is shown. The main novelty is that by means of a series of computer-controlled valves, a controlled dry nitrogen f low can be pumped upward or downward through the bed while the gas pressure drop across the bed is read from the differential pressure transducer. In this way, the gas f low can be used to automatically vary the consolidation stress on the powder while at the same time avoiding wall effects and inhomogeneous gas distribution through shallow layers.
To compress the powder over the sample weight per unit area after the powder has settled, the valves are operated to change the gas flow path to the reverse mode. Then the downward-directed gas f low is slowly increased from zero to a given value. The gas imposes a distributed pressure over the granular assembly pressing it against the distributor plate. The consolidation stress at the base of the bed is thus increased up to s c ҃W ѿ∆p 0 (13) where W҃r p ͗f͘ gh and ∆p 0 is the downward-directed gas pressure drop. Further increasing the compressing gas f low imposes further pressure on the sample. low/high consolidations. For very small consolidation stresses, beds of extremely low height must be used. In such cases, it was likely that non-uniform consolidation allowed the gas to flow preferentially through regions of high porosity such as channels. In the other extreme, if we wanted to achieve high consolidations by adding mass to the bed, its height should be increased up to values larger than the bed diameter for which wall effects are not negligible. In those cases, the tensile yield stress measured had an important contribution from the wall friction as shown by Figure 9. We will see that these inconveniences are solved by using the gas f low as an agent to compress or decompress the powder.  unit area (i.e. the uniaxial tensile yield stress) also increases. Conversely, when the sample consolidation On the other hand, the automatic Powder Tester provides us with a useful technique to test the powder under very low confining pressures like in microgravity. To decrease s c below the powder weight per unit area, we allow the powder to settle under a remaining upward-directed f low. In this way, s c is lowered down to where ∆p 0 is the pressure drop of the remaining gas f low reducing consolidation. As before, the uniaxial tensile yield stress of the consolidated sample is measured by slowly increasing an upward-directed gas flow that subjects the bed to a tensile stress. The bed height is automatically measured by means of an acoustic pulse technique. Figures 11 and 12 show the gas pressure drop across the bed during the breaking process for overconsolidated and underconsolidated states, respectively. As consolidation is increased, it is clearly seen that the slope of the linear part increases as a consequence of the increase of the average particle volume fraction. The overshoot of the pressure over the weight per powder sample is held in a 4.45-cm diameter, 17-cm high cylinder made of polycarbonate, the base of which is a sintered metal gas distributor of 5 µm pore size. The cylinder is placed on a shaker used to help powder fluidization. Dry nitrogen is supplied from a tank of compressed gas and a mass flow controller is used to adjust the f low. The pressure drop across the bed is measured by a differential pressure transducer. A series of computer-controlled valves are used to control the gas flow path through the bed. The bed height is read from an ultrasonic sensor. All these components are connected to a computer by means of a data acquisition board. A filter is placed upstream of valve 3 to catch elutriated particles and prevent valve 3 from damage.  (Figure 13b). This is directly related to the increase in interparticle force with decreasing additive concentration [6].
The SPT has been fully automated and yields highly repeatable results [4]. This was also shown previously in Fig. 7, where the experimental curves s t Ҁ s c , obtained by means of gas consolidation and centrifugation, overlap. The data plotted in Figure 14 also show that we cannot differentiate the results for the average particle volume fraction as a function of the consolidation stress obtained from both compaction techniques. Figures 15 and 16 give an idea of the sensitivity of the SPT to differentiate the f lowability of apparently similar powders. In Fig. 15, we present the phase diagrams yielded by the aerof low meter for two samples of different color of the toner Canon CLC700 (magenta and cyan). It is difficult to establish a quantitative difference in the f lowability of both samples. Fig. 16 shows the average particle volume fraction of both samples as a function of the consolidation stress applied by the downward gas f low (Eq. 13). Now both toners are well separated. As a consequence of their better ability to f low, the magenta toner particles are able to pack in a more compact structure for the same consolidation stress and this is clearly captured by the SPT. A straightforward extension of the SPT consisting of using nitrogen with controlled relative humidity enables the characterization of powder flow under well-controlled ambient conditions. is subsequently decreased, the average particle volume fraction decreases and hence the slope of the linear part decreases and the uniaxial tensile yield stress decreases. Figure 13a is an example of the complete diagram than can be obtained from the SPT. It shows the interdependence between the consolidation stress, the tensile yield stress and the particle volume fraction for two powders with different levels of surface additive coverage, SAC, concentration. Clearly, a higher consolidation implies larger particle volume fraction and tensile yield stress. In the upper part of the figure it is seen that for a given consolidation stress, the particle volume fraction has a larger value for a higher additive level. This is a direct result of the increase in f lowability with increasing additive, which increases the ability of the toner particles to rearrange themselves at a given stress. For a constant value of the consolidation stress, the tensile yield stress increases 76 KONA of view, the increase of strength with time of consolidation during storage is a relevant issue. Our measurements for xerographic toners indicate that the estimated adhesion force [6] rises exponentially to a maximum in a time scale that depends on the load imposed and on the surface additive coverage. Figure 17 indicates that as the load is increased while keeping the surface additive coverage constant, the relative increase of the adhesion force becomes more

Viscoplastic flow of interparticle contacts
An interesting experiment that can be performed automatically with the Powder Tester is to subject the sample to a fixed value of the consolidation stress for a controlled period of time. After this time period, the consolidation stress is removed and the tensile yield stress is measured. The increase of the tensile yield stress gives us an insight into the viscoplastic behavior of the interparticle contacts. From a practical point   of failure decreases and for zero tilt, we recover the measurement of the uniaxial tensile yield stress s t . Thus, by combining gas f low and tilt, we can generate a range of conditions of shear stress and normal stress. Figure 18 shows the incipient yield locus obtained in this way for the Canon CLC500 toner. Two sets of experimental results obtained with experimental toners of different cohesivity are shown in Figure 19. For the cases illustrated in Fig. 19, the Aerosil concentrations are 0.02% and 0.2% by weight. Clearly, the yield loci of the two materials at low stresses are very different. For a given normal stress, the critical shear stress needed to make the powder f low decreases when the flow additive is increased as a consequence of the decrease of adhesion force. Another remarkable feature of the yield loci is their convex shape at small stresses. This is a well-known pronounced. A similar behavior is obtained if the surface additive coverage is decreased while keeping the load constant. Therefore, not just the actual value of the adhesive force for a given load force but also the time of application of the force plays a role in the compression process, suggesting a viscoplastic deformation of the contact in large time scales. To avoid viscoplastic f low, the data presented in the previous sections of this paper were taken from measurements made within a short time scale (t ȁ5 min.).

The tilted fluidized bed: a technique for measuring the incipient flow of a sheared cohesive powder
Our f luidized bed technique provides a convenient method of generating a reproducibly consolidated powder and can be adapted to measure the limiting shear stress of the powder subjected to a controlled and small consolidation stress. After initializing, the next step is to apply a shear stress to the sample by slowly tilting the bed. As the angle of tilt increases, this generates a shear stress in the powder layer. For deep beds, the location of the shear plane and the angle of tilt a at which failure occurs depend on the width of the bed D [23]. If we restrict our samples to shallow layers of height h D, it is observed that the width of the bed has no major influence and that powder failure occurs near the base of the sample. We then have t 1 ȃr p ͗f͘ gh sin a (15) Similarly, the consolidation stress is related to the weight of the sample and to the angle of tilt s 1 ȃr p ͗f͘ gh cos a (16) Thus, from the angle at which the sample fails in shear, we calculate the coordinates of one point (s 1 ,t 1 ) on the yield locus. In order to generate more data for the yield locus we need to be able to vary the compressive stress on the sample. As before, we do this by means of a small remaining gas f low reducing consolidation. If we now tilt the apparatus, the shear stress at the bottom of the sample is given by Eq. 15 since the component of the buoyancy force acting on the shear direction is zero. On the other hand, the consolidation stress s acting perpendicular to the shear plane is reduced by the gas pressure drop ∆p, and so Eq. 16, modified to take account of ∆p, becomes sȃr p ͗f͘ gh cos aҀ∆p (17) As the consolidation stress is decreased, the angle   common aspect of the yield locus of fine powders at low stresses [7]. Moreover, we see that the cohesion c of the powder, defined as the critical shear stress for zero consolidation stress, is comparable to the uniaxial tensile yield stress. If we approximate the yield loci obtained at high stresses by a Coulomb's linear law (Eq. 1), we see in Fig. 19 that our results predict an increase of the angle of the internal friction with the percentage of f low conditioner, as observed by Steeneken et al. [37] in potato starch powders, due to the roughening of the powder particles by the additive. We derived the same trend on the effect of additive on the angle of internal friction from experiments where the angle and depth of avalanches were measured in tilted beds of varying width and the results were fitted by a wedge model [23].
In the tilted fluidized bed technique, the yield locus is not defined for a "presheared" sample and the end Mohr circle for steady state flow cannot be determined. Therefore, the initial states in the classical shear testers and our tester are different. Nevertheless, a comparison of the yield loci obtained using our technique with the yield loci obtained from other standard testing devices such as the recently developed ring shear tester [20] is of great interest, and no doubt it will contribute to deepen our understanding of the behavior of powders subjected to very small shear and normal stresses.

Conclusions
In this paper we have described a Powder Tester instrument whose main advantages are i) results are operator-insensitive since measurements are automatically taken, and ii) fluidization provides a convenient method to have the sample in a reproducible initial state. Every step in the process is determined by gas f low, and by means of a set of valves and flow controllers, we are able to run the entire process by a computer. The measurements involving gas flow velocity, pressure difference, and bed height are accessed by the same computer, and from these sets of measurements, the values of consolidation stress, average particle volume fraction, and uniaxial tensile yield stress are automatically calculated. An upward/downward-directed gas f low is used for deconsolidating/ consolidating the powder, and an ultrasonic device measures the bed height giving an average value of the particle volume fraction. By quasistatically tilting the bed, the SPT also serves to measure the yield shear stresses. This technique is especially feasible to measure the yield locus of cohesive powders, which are difficult to initialize, subjected to very small consolidation stresses.
As a concluding remark we want to stress that the usefulness of the SPT is not just restricted to f lowability diagnosis. Our experimental work shows that the tester is a powerful instrument of research in powder technology.