What is powder rheology?

LEARN MORE ABOUT THE RHEOLOGY OF POWDERS

Problems with powder related to gravity flow behavior

A typical industrial powder processing line will include several storage containers (e.g. bins, hoppers, silos, hoppers, intermediate bulk containers or IBCs, bags, etc.), feed steps or handling (eg belt conveyor, screw conveyor, pneumatic conveyor, gravity chutes, etc.) and processing steps (eg, grinding, mixing, drying, bagging, etc.). A major industrial problem is to ensure that the powder reliably discharges from storage to the next stage of the process. Therefore, to understand the application of powder flow measurements, it is helpful to have a basic knowledge of the flow patterns and flow obstructions that can occur inside storage tanks on a processing line.

What are the powder flow patterns that can occur in a process storage tank?

There are mainly two different flow patterns that can occur:

Central flow (shown in Figure 1a) can be considered the default flow model and is characterized by powder discharge through a preferential flow channel above the outlet drawdown point. The powder is drawn into the flow channel from the upper free surface of the inventory. This results in a first-in-last-out discharge regime and, if it is operated in a continuous mode (rather than a batch mode), the powder around the walls of the lower section will remain static in the container until such time as it is drained. to empty.

Mass flow (shown in Figure 1b) is the desirable flow pattern for powders that flow poorly or are time sensitive, but need to be specifically designed for. Here, the entire contents of the container are "alive", resulting in a first-in, first-out unloading regime. To do this, the walls of the hopper must be sufficiently stiff and smooth. For a given wall material / convergence angle, the friction of the powder wall must be less than a critical value. Additionally, product discharge should be controlled by a valve or feeder that allows powder to flow through the entire cross section of the outlet. (It is this last point that prevents many vessels from operating in mass flow.)

A wall friction test will be able to give a rough estimate of whether a given hopper geometry will withstand mass flow (provided the outlet area is fully active). For an exact calculation of the maximum half-angle of the mass flow hopper, wall friction and flow function tests must be performed.

What are the powder obstructions that can occur to prevent the flow:

Mainly, there are two flow obstructions that can occur:

The "rat hole" (shown in Figure 2a) is the main obstruction of the flow in a central flow vessel where the powder in the flow channel above the outlet discharges and leaves a stable internal structure.

Arching (shown in Figure 2b) is the obstruction of flow in a mass flow vessel, where a stable powder arc forms through the outlet or converging walls of the hopper, thereby preventing flow.

For a given powder, there is a critical output dimension which must be exceeded to ensure reliable discharge from a central flow or mass flow vessel. These are the critical diameter of the rat hole D rh and the critical arch diameter DC or D p (depending on the geometry of the hopper - see Figure 3). The AMETEK Brookfield Powder Flow Tester (PFT) can calculate these critical dimensions as a result of a flow function measurement. Accurate dimensioning also requires a wall friction test. Note that for a given powder, the diameter of the rat hole is significantly larger than the diameter of the vault.

Main differences between powders and fluids

For Newtonian fluids, the shear strength (viscosity) is independent of normal pressure but depends on the shear rate. In powders, the effect of these factors is reversed so that the shear stress of a powder is strongly dependent on the normal stress but independent of the shear rate. Thus, during the characterization of the powders, the tests are carried out at a single speed but over a range of normal stresses. The other key difference is that powders are anisotropic, so the stresses are not equal in all directions and are frictional so that they can generate shear stresses at the boundaries of the walls (see section Wall Friction ).

Flow function test

The primary measure of powder flowability is the powder flow function - which gives a measure of how much resistance the material retains on an unstressed surface after consolidating to a given stress level. The simplest way to explain the flow function is to use the uniaxial unconfined failure test shown in Figure 4, which measures the resistance of a freestanding powder column. This condition is analogous to the condition of the powder arch through a hopper outlet shown in Figure 2b.

1) Consolidation of the sample.

The powder is placed in a cylindrical cell and compacted under a normal stress s1.

2) Unconfined sample.

The mold is now carefully removed to reveal a column of compacted powder.

3) Unconfined failure of the sample.

The normal stress acting on the powder column is gradually increased until failure occurs, and the maximum normal stress sc is recorded.

The unconfined uniaxial failure test is conducted over a range of consolidating stresses and the flow function is constructed by plotting the unconfined breaking strength against the consolidating stress, as shown in Figure 5. More the value of the flow factor (ff) is high, plus the flow of the powder (Table 1).

Intended Uses of the Brookfield PFT Powder Rheometer

- Measure the flow properties on all raw powders and mixtures to determine if there are any differences in their flowability and if these are consistent with plant experience.

- New materials - Test new ingredients / mixtures against existing ingredients / mixtures to determine if the alternative material is likely to be easier or more difficult to handle. This potential cost of handling can be factored into the purchasing decision.

- Reverse Engineering - If you have factory experience with powders on a given process line, you can use the PFT to determine the flow properties of each powder and use it as a flow benchmark for future batches.

- Design- Design the geometry (convergence angle and outlet size) of new hoppers / silos for reliable throughput.

Alternative methods of displaying the results of the flow function test

To demonstrate the fluidity of the powder, the flow function can be presented graphically (as in Figure 5) to describe the behavior over the stress range of about 0.3 kPa to 13 kPa. This range of stresses is representative of that experienced by the powder in small to medium-sized silos. However, describing fluidity with a function can complicate the analysis because it is sometimes found that the flow functions of two different materials intersect, so their relative ordering changes with stress levels. Alternatively, the fluidity ratings for specific stress levels can be determined by calculating the following parameters:

Estimated critical vault diameter [m]: The minimum silo outlet size for reliable gravity discharge in mass flow, calculated using the arch equation in Figure 2b. The stress value is the intercept of the flow function with a line ff = 1.4. These are the default throughput factor settings, but can be adjusted by the user within a range of 1.0 to 1.8 for silo design applications.

Estimated critical diameter of the "rat hole " in [m] : The minimum outlet diameter to prevent the formation of a stable "rat hole" in a center flow vessel. The outlet diameter is calculated using the rat hole equation in Figure 2a. The stress value is the intercept of the flow function with a line ff = 2.5 and can be user defined at any stress level.

Flow index: The gradient of a line from the origin to the last point of the flow function, usually between 0.1 and 1.0. This index will give a comparison of the behavior of materials at intermediate compaction stresses greater than one meter of powder depth.

Flow intercept : The interception of the best fitted linear failure function with the unconfined fracture strength axis giving a number in kPa. This gives a number which reflects the fluidity of the powder at compaction stresses generally less than 0.15m powder depth.

Note that a consolidated flow function test over time allows the user to determine if the material is gaining strength during long term storage.

Wall friction test

The friction acting at the wall / powder interface has a significant influence on the distribution of stresses in treatment tanks, silos and hoppers.

The higher the wall friction, the more powder weight is transferred down through the silo / tank / container walls, rather than compacting the bulk solid below. The lower the friction, the more the powder's own weight is transmitted through the bulk solid. This 'Janssen effect' is illustrated in Figure 6, which shows how the vertical pressures in the vertical section of a silo would vary if the wall friction were increased from zero to a high value of 400. The presence of the friction of the wall has a negative feedback effect on the increase in pressure with depth, so that the stresses generally approach constant values at a depth of about 4 container diameters.

Software can be used to estimate the pressures in a container based on measurements of bulk density ρ, wall friction, internal wall friction symbol δj, and container diameter D. The main consolidation pressure 1 at depth Z is given by the equation:

The wall friction angle symbol of wall friction represents the angle at which a wall surface must be tilted as shown in Figure 7 to slide the powder. The wall friction angle is typically on the order of 10 to 45 degrees. The wall friction angle is also called the slope angle.

While the results of the wall friction test can be graphically displayed as a location of wall failure as shown in Figure 8a (representing the limiting shear stress that the powder can withstand at a wall), or as a function of wall friction angle as shown in Figure 8b (showing how the wall friction angle changes with reduction in stress), one of the four indices d The following flow derived from the locus of maximum wall friction is generally adequate. These wall breaking properties are:

θ c θ p = The maximum mass flow rate of the half - angle hopper (measured vertically) for conical or plane hoppers.

wall friction symbol = The maximum wall friction angle to determine the minimum drop angle for gravity flow (see Figure 8b).

Grad = The maximum wall friction angle displayed as a coefficient.

cw = The wall cohesive shear stress in kPa that can be supported at the wall under zero normal stress (see Figure 8a). This determines "stickiness", that is, whether the powder is likely to stick to the wall surface under a stress close to zero. that is, the powder will accumulate on the walls of the chutes around the unloading / transfer points.

An extended wall friction test allows the wall sample to be subjected to large shear displacements (on the order of 30 meters) to establish whether long term powder buildup on the wall is expected.

Bulk density test

It is the powder's own weight, its bulk density, which controls the stresses acting on the powder during flow or when it is static in processing lines / silos, etc. Bulk density is measured during the flow function test (and is needed to calculate critical outlet dimensions) and the wall friction test, but it can also be measured in a single separate test for bulk density. alone.

Bulk density is usually displayed as a bulk density curve (Figure 9). In general, a free flowing material will be incompressible, so it will only show a small increase in density with stress. In comparison, a very cohesive, low flow bulk solid will show a large increase in bulk density with increasing stress.

ρ filling = The apparent filling density to be expected when the powder is poured into a container

ρ comp = The packed bulk density gives an indication of the bulk density to be expected if the material is poured and compacted at high voltage

Summary

The Brookfield Powder Flow Tester offers four standard tests:

Flow Function Test - Measures internal force, flow function, internal friction function and bulk density function - used to characterize the flow force and bend / rat hole potential of powders .

Time Consolidated Flow Function Test - Same as above but after static storage for a user defined period.

Wall Friction Test - Measures the friction between the powder and a given wall surface and the bulk density function - used to evaluate the half angles of the mass flow hopper and the angles of the gravity flow chute.

Bulk Density Test - Measures the bulk density curve of the powder.

Note that to undertake a complete silo design, the user must run and combine the results of tests 1, 2 and 3.