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…