Powder Flow Function

Obviously, the unconfined 5deld stress, ffy, of the solids varies with compacting stress, ac- 

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If the hopper-flow factor lies above the powder-flow function, cohesive arching is not possible with the material in that hopper. If the hopper factor lies below the powder-flow function, arching of material in the hopper is possible even for large-outlet sizes. 

This relationship is determined experimentally and is usually presented graphically (Figure 10.6). This relationship has several different names, some of which are misleading. Here we will call it the powder flow function. Note that it is a function only of the powder properties. 

This may be plotted on the same axes as the powder flow function (unconfined yield stress, Gj and compacting stress, gq) in order to reveal the conditions under which flow will occur for this powder in the hopper. The limiting condition gives a straight line of slope 1 /ff. Figure 10.7 shows such a plot. 

Where the powder has a yield stress greater than Gc/ff, no flow occurs [powder flow function (a)]. Where the powder has a yield stress less than Gc/ff flow occurs [powder flow function (c)]. For powder flow function (b) there is a critical condition, where unconfined yield stress, Gy, is equal to stress developed in the powder, Gc/ff. This gives rise to a critical value of stress, Gcyh, which is the critical stress developed in the surface of the arch ... 

Knowing the hopper flow factor and the powder flow function (cFy versus ac) the critical stress in the arch can be determined and the minimum size of outlet found corresponding to this stress. 

These yield loci characterize the flow properties of the unaerated powder. The following section deals with the generation of the powder flow function from this family of yield loci. 

Pairs of values of dy and gq are found from each yield locus and plotted against each other to give the powder flow function (Figure 10.6). 

The powder flow function which can be represented by the relationship, ay = a, where Oy is unconfined yield stress (kN/m ) and gq is consolidating stress (kN/m ) Determine (a) the maximum semi-included angle of a conical mild steel hopper that will confidently ensure mass flow, and (b) the minimum diameter of circular outlet to ensure flow when the outlet is opened. 

What is the powder flow function Is the powder flow function dependent on (a) the powder properties, (b) the hopper geometry, (c) both the powder properties and the hopper geometry ... 

Shear cell tests on a powder show that its effective angle of internal friction is 40 and its powder flow function can be represented by the equation [Pg.289]

A powder has an effective angle of internal friction of 60 and has a powder flow function represented in the graph shown in Figure 10E2.1. If the bulk density of the powder is... 

One way which relies upon the fundamental knowledge of the stress-strain-volume behaviour of bulk solids is dependent upon the development of testers such as the biaxial and triaxial shear testers as well as the now universally accepted Jenike shear cell, or the standard shear test tester. Other instruments, such as the annular shear cells and the cross-sectional Peschl and Colijn (1977) tester, use the same stress-strain-volume principle. These annular shear cells may also be used to evaluate a bulk powder flow function. The powder flow function, having been discussed previously, still requires a family of yield loci before cohesion can be evaluated. 

Johanson claims that this new approach produces a similar powder flow function in one tenth of the time required by the Jenike test. However, Enstad and Maltby (1992) and Schwedes and Schulze (1990, 1992) criticised the Johanson method and doubted whether the measured failure stress was representative of a material s unconflned yield strength, even after the application of a correction factor. This observation was confirmed by Marjanovic et al. (1995, 1998) with five powders (Table 1.13). 

Geldart, D., Harnby, N. Wong, A.C. (1984) Fluidization of cohesive powders. Powder TechnoL, 37, 25-37. Gerritsen, A.H. (1986) A Simple Method for Measuring Powder Flow Functions with a view to hopper design. Partec 86. Nuremberg, Germany, Part 3, pp. 257-279. 

A powder s strength increases significantly with increasing previous compaction. The relationship between the unconfined yield stress/, or a powder s strength, and compaction pressure is described by the powder s flow function FE The flow function is the paramount characterization of powder strength and flow properties, and it is calculated from the yield loci determined from shear cell measurements. [Jenike, Storage and Flow of Solids, Univ. of Utah, Eng. Exp. Station Bulletin, no. 123, November (1964). See also Sec. 21 on storage bins, silos, and hoppers.]... 

In an effort to put powder flow studies and hopper design on a more fundamental basis, Jenike [45] developed a powder shear tester and methodology that permits an assessment of powder flow properties as a function of consolidation load and time as well as powder-hopper material interactions. The methodology has been used extensively in the study of pharmaceutical materials [39,58-61]. From the yield loci obtained using this method, several parameters can be determined that influence powder flow, and discussions of these points are well documented in the literature [49,62,63]. 

Table 6 Powder Flow Properties of Several Materials as a Function of Relative Humidity...

By measuring the force required to shear a bed of powder that is under various vertical loads, a relationship describing the cohesive strength of the powder as a function of the consolidating pressure can be developed (4). This relationship, known as a flow function, FF, can be analyzed to determine the minimum outlet diameters for bins to prevent arching and ratholing. 

If gravity discharge is used, the minimum outlet size required to prevent arching is dependent upon the flow pattern that occurs. Regardless of the flow pattern, though, the outlet size is determined with the powder s flow function, which is measured by way of the cohesive strength tests described earlier. 

The flow function illustrated in Fig. 1 reveals a singular behaviour of the powders which may be associated with the process or with the high percentage of PVC. In fact, even if the curves were obtained by linear regression, a marked dispersion may be seen, particularly for the compaction of the mixture and, curiously, for the wet granulation powder. 

Regarding the flow function values, powders may be classed in two groups ... 

G(< )t) is also a derived function and is given by Figure 9. /c(ct1), the unconfined yield strength of the material, is determined by the flow function (FF) at the actual consolidating pressure al. The consolidation pressure al is a function of the head or height of powder above the outlet of the bin, as given by Janssen s equation ... 

In essence, the test battery should include XRPD to characterize crystallinity of excipients, moisture analysis to confirm crystallinity and hydration state of excipients, bulk density to ensure reproducibility in the blending process, and particle size distribution to ensure consistent mixing and compaction of powder blends. Often three-point PSD limits are needed for excipients. Also, morphic forms of excipients should be clearly specified and controlled as changes may impact powder flow and compactibility of blends. XRPD, DSC, SEM, and FTIR spectroscopy techniques may often be applied to characterize and control polymorphic and hydrate composition critical to the function of the excipients. Additionally, moisture sorption studies, Raman mapping, surface area analysis, particle size analysis, and KF analysis may show whether excipients possess the desired polymorphic state and whether significant amounts of amorphous components are present. Together, these studies will ensure lotto-lot consistency in the physical properties that assure flow, compaction, minimal segregation, and compunction ability of excipients used in low-dose formulations. 

The flow function that describes the cohesive strength (unconfined yield strength, F ) of the powder as a function of the major consolidating pressure (cti). The flow function is one of the parameters used to calculate the minimum outlet diameter/width for bins, press hoppers, blender outlets, etc. to prevent arching and ratholing. The calculation of the minimum outlet diameter/width is discussed in more detail below. 

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