Janssen theory

The previously mentioned Janssen theory (Janssen, 1895) includes, possibly, the oldest reported attempt to calculate pressures in silos. Janssen derived an equation for the calculation of vertical and horizontal pressures and wall shear stresses. He assumed a vertical force balance at a slice element spanning the full cross section of a silo being filled with bulk solids, and determined the wall friction coefficient with a shear tester as well as the horizontal pressure ratio from pressure measurements in a model bin. He also assumed... 

The Janssen theory is the main descriptor of filling pressures in all standards. 

The Janssen theory describes pressures in a parallel-sided vessel. The corresponding theory for a converging channel came much later, and is normally attributed to Walker (1964, 1966), though it was first derived by Dabrowski (1957) and was probably also found by Jenike and others in the late 1950s. 

Chosen diagrams of silo wall circumferential forces in Fig. 7 are presented. The curve (1) represents only the static forces due to bulk solid horizontal pressure calculated according to Janssen theory. The diagram (3) shows values of tensile horizontal forces obtained experimentally for static pressure coupled with phase of cooling and it can be compared with corresponding theoretical curve (2) predicted from the appropriate FEM analysis for the same combination of actions. 

D. L. Massart, C. Janssens, L. Kaufman and R. Smits, Application of the theory of graphs to the optimalisation of chromatographic separation schemes for multicomponent samples. Anal. Chem., 44 (1972) 2390-2399. 

Meijer, H. E. H., and Janssen, J. M. H., Mixing of immiscible liquids, in Mixing and Compounding of Polymers—Theory and Practice. (I. Manas-Zloczower and Z. Tadmor, Ed.). Hanser Publishers, Munich, 1994, pp. 85-147. 

Janssen and Hoogland (J3, J4a) made an extensive study of mass transfer during gas evolution at vertical and horizontal electrodes. Hydrogen, oxygen, and chlorine evolution were visually recorded and mass-transfer rates measured. The mass-transfer rate and its dependence on the current density, that is, the gas evolution rate, were found to depend strongly on the nature of the gas evolved and the pH of the electrolytic solution, and only slightly on the position of the electrode. It was concluded that the rate of flow of solution in a thin layer near the electrode, much smaller than the bubble diameter, determines the mass-transfer rate. This flow is affected in turn by the incidence and frequency of bubble formation and detachment. However, in this study the mass-transfer rates could not be correlated with the square root of the free-bubble diameter as in the surface renewal theory proposed by Ibl (18). 

Raes, F. and Janssens, A., Ion-Induced Aerosol Formation in a HpO-H Ojj System - I. Extension of the Classical Theory and Search for Experimental Evidence, J. Aerosol Sci. 16 217-227 (1985). 

Valeev, E.F., Janssen, C.L. Second-order Moller-Plesset theory with linear R12 terms (MP2-R12) revisited auxiliary basis set method and massively parallel implementation. J. Chem. Phys. 2004, 121, 1214-27. 

Neukermans S, Janssens E, Chen ZF et al (2004) Extremely stable metal-encapsulated AiPbio and AlPbi2 clusters mass-spectrometric discovery and density functional theory study. Phys Rev Let 92 163401... 

Janssen, C. L., Allen, W. D., Schaefer, H. F., and Bowman, J. M., The infrared spectrum of the hydrogen hifluoride anion Unprecedented variation with level of theory, Chem. Phys. Lett. 131, 352-358 (1986). 

Figure 15 is a graph from Janssen and Hoogland27 which is the basis of their arguments for the hydrodynamic theory of mass transfer in the absence of coalescence. Note the slope change, around 30 mA/cm2, which corresponds to a change in bubble size for these oxygen bubbles evolved in basic solution and is indicative of the onset of coalescence between bubbles on the electrode. 

Nielsen, 1. M. B., and C. L. Janssen. Local Moller-Plesset perturbation theory A massively parallel algorithm. /. Chem. Theor. Comp. 3 71-79,2007. 

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