106 BELL SYSTEM TECHNICAL JOURNAL 



a cylindrical sample of a viscous material is compressed between 

 parallel plates at a rate given by: 



dt 3v V^ ' ^^^ 



where r? is the viscosity. This equation is of the form of Equation 2 

 with b — 5. In the solder tests, the values of b obtained were in 

 general much larger than 5.0, so that these materials are not strictly 

 viscous. On the other hand, the fact that the results are independent 

 of the initial sample height indicates that the rate of flow is inde- 

 pendent of the strain; while the fact that the curves of log dh/dt vs. 

 log /; continue to be linear at very low rates of flow indicates the 

 absence of any yield point, or minimum stress required for flow. 

 Hence the stress required for compression appears to be of the type 

 which has been called quasi-viscous — wholly dependent on the velocity 

 gradient. 



Flow of this type, of which viscous flow is a special case, has been 

 observed in colloidal solutions tested by the capillary tube method. 

 In such solutions deW'aele ^ found the rate of efflux proportional, not 

 to the pressure (as in strictly viscous fluids^), but to a power of the 

 pressure. Porter and Rao ^ have shown that this would be the case 

 if it were assumed that the shearing stress (r) is proportional to a 

 power of the velocity gradient (dv/dx), or t — ri' {dv/dxY''^, where 77' 

 and n are constants; dv/dx is the velocity gradient normal to the 

 plane in which t is the tangential stress. Assuming this relation, the 

 case of compression between parallel plates has been shown ' to be 

 given by: 



5(«-|-l) 



dh ^TT'"A 2 



di = ^-—E±r' (^) 



V 2 



where C is a constant inversely proportional to ??'. The development 

 of Equation 4 employs approximations corresponding to those used 

 in obtaining Equation 3, involving the assumption that the diameter 

 of the sample is large compared with its height. 



As a matter of at least theoretical interest a series of runs were made 

 on one solder (No. 2) employing different loads and sample volumes, 

 and the data thus obtained were analyzed with reference to their 

 agreement with Equation 4. This analysis is given in an appendix 



6 A. de Waele, /. Oil & Color Chem. Assn., 6, ii (1923). 

 ^Bingham, "Fluidity and Plasticity," McGraw-Hill. 

 ^ Porter and Rao, Trans. Faraday Soc, 23, 311 (1927). 



