Modeling wall friction

It turns out that the measured wall friction, when plotted against the ratio of groove volume to particle volume (in a logarithmic scale), behaves like a three-part function. Even for crushed glass (an amorphous particle) the behavior is similar. The data distributes into three regions, two of them remaining flat and a third one having a slope. The most intriguing part is that if we divide the measured wall friction angle by the measured effective angle of internal friction, we reduce this plot to a two-part function. It starts flat and then jumps to a step that remains constant to higher values of the mentioned ratio.


But there is not an evident function that can relate these two variables clearly; there are no continuum equations from which these results can be derived. But there might be a way out, if we look at what DEM (discrete element method) does. DEM tracks every particle in the simulation, because each particle has a dynamic equation that is being solved. DEM solves thousands of dynamic equations at every pre-established time step, using the initial conditions at the boundary and then applying these values into force-displacement laws that determine the corresponding contact forces. The acceleration is determined from the forces using the dynamic equation (Newton’s Second Law), which is later integrated to find velocity and then displacement of the particles, the positions of these particles are updated, the displacement computed, and the cycle starts again.


To be continued…

Modeling of wall friction (a.k.a. What is Wall Friction? Part 6)

The mentioned previous studies produced clear trends in the measured wall friction, as it varied with respect to a parameter (such as particle size, plate roughness, etc.). But the conclusions in many of these projects were qualitatively in nature. In only a couple of studies I found, a model was proposed. So the question comes: why has nobody come up with a model, given all the data that has been produced? The answer came to me until recently: there is no clear way of deriving a model from first principles (say a continuum equation). Other than just fitting a curve to the data, given the know parameters that affect wall friction, there is no evident method that would lead us to a function that could be used for predicting and modeling wall friction.

Another problem I found with these previous research results is related to the lack of consistency in the behavior of the data. In some of the provided plots, there was no clear trend in the data. This makes it hard to find any model. The reason this is happening, at least in my opinion, is that in many of these cases things like particle shape and size (sometimes they used a wide number particle size distribution), or plate roughness were not controlled at all. The plate surface had whatever grain direction the fabrication process provided, the bulk material had any particle shape the manufacturer was able to deliver, and the researchers did not pay attention to any of these details at all.

In order to produce consistent results, especially for problems like wall friction which depend on a lot of variables, a control is needed of these parameters. In my study, spherical particles were used (sphericity above 90%) with a narrow number particle size distribution, and the roughness on the plates was simulated by machining triangular sawtooth (like inverted V shape) grooves on one surface. The height of the groove was varied, but the periodicity remained constant.

To be continued…

What is wall friction? Part 5

Selection of the samples, used as wall material, was made based on the fabrication process of the surface. It would be far easier to work on aluminum than on steel plates, although the action of the particles could cause wearing, but this could be accounted for later on (as a correction factor, maybe). Previous researchers have made similar studies by using plates with a standard finish. There is a table (that you can find on the internet) that lists standard machined finish characteristics, which include the roughness values measured with a profilometer (either mechanical or optical), different values are given in this table (one of these is called RMS, or root mean square) that one could use to establish the roughness of the finish on your plates. There are manufacturing procedures that ensure that the surface would have the corresponding standard finish and, consequently, the corresponding surface roughness.

But the problem with this approach is the lack of consistency in the orientation of the so-called grain. It is an experimental fact that grain (which is the structure above the mean wall surface, such as peaks) plays an influential part in friction. If the flow of the powder is against the grain (picture this as particles finding obstacles as they move along the surface), the wall friction increases. But if the powder flows along the grain (particles move along the peaks, instead of going over the peaks), then wall friction reduces appreciably.

To be continued…

What is wall friction? Part 4

Finally, we have come up to one of the many subjects I am hoping to talk about in this blog: modeling of wall friction based on micromechanical parameters such as wall surface roughness, particle shape, particle size distribution, and microfriction values. Wall friction in fact depends on other parameters such as temperature, humidity, particle roughness, etc., but I want to restrict the study to only a few simple and measurable variables.

I hope this is going to be received well by the particle science community since I will be publishing these results pretty soon. One main concern I found during this process is the fact that I used a different tester to measure wall friction. This tester (I am not sure I should talk about it) has the ability to measure static friction, for dynamic friction the procedure has to be changed a little. In both instances the pattern was the same, the measured data had the same trend in the static case as it did in the dynamic case, that problem was solved.

We selected spherical glassbeads as the sample of bulk material because we have a lot of options in the choice of particle size from vendors. Also, the sphericity of these particles (how round they really are) is above 90%. Their particle size distribution by number of particles per size has a small standard deviation (how wide this curve is, I will talk about particle size distribution in another post). We looked at these particles under the microscope and they indeed showed a large amount of sphericity (although it was not measured), the size distribution was measured using laser scattering methods.

To be continued…

What is wall friction? Part 3

Now, after measuring your wall friction angles, and selecting your hopper, and having it fabricated and installed, you go ahead and test your new hopper. Theory says the new hopper will work, and in many instances it will, but if you find yourself in the situation that It would not work, that you get hang-ups, or maybe ratholes, it is time to go back and retrace the whole process to find the culprit.

Although there could be other causes for hopper problems, wall friction is one of them, and I will concentrate on this problem for the time being. What many designers fail to recognize is that wall friction is not a static value. Many things can change the wall friction angle. The fabrication process might have affected the wall characteristics, there is also the possibility that the hopper is being used with a different material, since it is not unusual to have a silo handling other kinds  of bulk materials. The hopper and silo walls will sustain wearing, this changes the wall friction. The bulk solid is affected by humidity or temperature, even if the wall friction was measured taking those into account, you might still have problems during discharge, this is so because the influence of humidity on wall friction is not well understood at this point.

Of course, the best solution, after the fact, is to install a flow-promoting device. This adds cost to the original silo project, a little design sense can go a long way. You could use some criteria to make sure variations of the wall friction can be accounted for. Unfortunately, other than empirical methods, there is not a formal procedure than would help on this.

Previous researchers have identified the many variables that can affect wall friction, this makes the wall friction angle a mutivariable problem, which complicates matters a lot. But in some cases, some parameters might be important and others not so much. Of course this gives hope to investigators like me. In summary, many people have attacked the problem but a few have come up with a model to estimate wall friction.

Most of the studies out there are essentially presentations of collected data from which they make qualitative analysis to find trends when a variable is changed. I have only encountered three papers (as recent as 1980, before that I am not considering, since so much has changed since the 1970s) that suggest a model, and all of them obtained the model from macro parameters from the bulk testing...

But...What is wall friction anyways? Part 2

Now, Jenike proposed a measuring device to determine wall friction, that device is now known as the Jenike tester, other testers have sprung up which could be used to determine wall friction, but the Jenike cell has become the industry standard. The basic method consists of taking a sample of the powder and a sample piece of the hopper or silo wall, the powder is then poured into a ring (usually metallic) and then a normal load is applied (by placing dead weights on the cell), then the ring is pushed by an actuator and the shear force is measured. The ring displacement can be measured too. This is done for different loads so as to cover a wide range of normal loads.

If one plots shear force (or shear stress by dividing over the area of the cell) against normal force (or normal stress), a line is usually formed, but this is not always the case. For solids this line is straight, most of the times, but not for powders (at least not that often). I have seen more than one publication where the shear stress is plotted against the normal stress and a line is created for each point (the second point being the origin), and an envelop of lines is presented. Other times, the researchers have reported their wall friction by fitting a line to the data, which could produce a low linear correlation value.

A better way to understand the data is by plotting the wall friction against the applied normal stress. The wall friction angle is calculated by taking the arc tangent of the ratio of shear stress to normal stress. Usually, a decaying curve is obtained so that at low normal stresses, a high friction angle is obtained. This plot is then used to determine the wall friction at a certain normal stress.

To be continued...

But...What is wall friction anyways?

Yes, that's my thesis topic. The problem with this concept (experimentally determined) is that no predicting method or model exists that could help design equipment given known parameters. It is a very old problem, many people have tackled it, but so far, no explicit, extensively used solution exists.

Now, why is this so important? To answer that question, we have to go back to the 1960's when Andrew Jenike published his now extensively cited report. But even before, people like Janssen had understood that powders did not behave like liquids when they are stored in containers. Janssen found that unlike liquids where the pressure is proportional to the height of the container (so that as the container becomes higher, the pressure at the bottom increases), the pressure increases and at some point it becomes constant so that no matter how high the silo is, the pressure will be constant at the bottom. Janssen found that the reason this is so, it's because of friction, the powder and the wall develop friction at contact, which helps in supporting the whole mass of the powder.

Then Jenike came along and used this previous findings to develop a comprehensive method for designing silos, bunkers, and any vessel that may contain powder. But wall friction is one of the main parameters needed for the selection of the correct hopper for the silo. Since the powder has to flow by gravity, the hopper has to be used in aiding the powder flow out of the silo, this hopper can have many converging geometries. The correct angle of this hopper depends strongly on the wall friction created by the contact of the powder and the wall.

To continue...