Warren-Spring equation

In a slightly different form, Eq. (6) is commonly referred to as the Warren spring equation. Representative yield loci determined utilizing the simplified shear cell are shown in Fig. 7 for spray-dried lactose, bolted lactose, and sucrose. The yield locus for each material relates the shear strength to the applied load. 

Geoffroy, J.-M. Carstensen, J.T. Modified warren-springs equation. Powder Technol. 1993, 76, 135-140. 

It is now believed, however, that more powder flow properties can be incorporated into this simple relationship of C = 2T. Incorporation of the parameters of particle size, bulk and powder densities leads to the relationship expressed as the Warren Spring equation... 

The shear flowability index, n, was found, from past observations (Farley Valentin 1965, 67/68), to be independent of the bulk density of sheared compacted powder. Because of this independence of particle size from bulk density it is now realised that the shear flowability index, n, from the Warren Spring equation and the Jenike internal angle of friction may be the preferred parameters to eharacterise and quantify the flowability of powders. Jenike and others (Williams et al. 1970/71 Williams Birks 1965 Hill Wu 1996 Cox Hill 2004) selected the Jenike failure function to be one of the best indicators to predict the ease of powder movement and powder flowability. 

The well-known failure hypotheses of Tresca, Coulomb-Mohr and the yield locus concept of Jenike [1] and Schwedes [2] as well as the Warren-Spring-Equations [3 to 7] were specified from Molerus [8, 9] by the cohesive steady-state flow criterion. The consolidation and non-rapid, frictional flow of fine and cohesive particulate solids was explained by acting adhesion forces in particle contacts [8]. 

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