MKCHANICAL lMi( )1'KUT1KS OK I'OLYMKliS 127 



wave is equal to" 



Z.) = Vrfrip (1 + ./■) = /^u + ./A' ,w (4) 



This causes a change in resistance, and a change in tVcMnioiicy in a 

 crystal generating a shear wave in the licjuid ecjnal to 



A/?,. = /vi/e.u; A/' = -A',X,, (5) 



where A'l anil K^ are constants of the crystal which can be oljtained 

 approximately from the dimensions and piezoelectric constants of the 

 crystal but which are more acciu"ately obtained by calibration in known 

 li(iuids. The constants A'l and Ko vary slightly with temperature and 

 should be calibrated over a temperature range. 



The first instrument to use a vibrational method for measuring vis- 

 cosity was the vibrating wire method of Phillipoff. In this method a 

 wire was \'ibrated in a lifiuid and the damping rate was used as a measure 

 of the viscosity. Another method also applicable in the low freiiuency 

 range is the transducer method of Ferry. In this method wires are 

 ^•ibrated by electromagnetic transducers and the resistance and reac- 

 tance drag on the wires are measured by the change in the electrical 

 resistance and reactance of the transducer. From the constants of the 

 transducer, the equivalent viscosity and stiffness of the licjuid can be 

 measured. 



In the medium freciuency range a torsional crystaf method was 

 devised by one of the writers which has been applied in the freciuency 

 range from 10 to 150 kc. The torsional crystal is shown by Fig. 2. For 

 these types of measurements the crystal usually is made of cjuartz with 

 four electrodes of gold evaporated on the surface. Four wires are soldered 

 on the surface and serve as supports as well as electrodes. The motion 

 is all tangential to the surface and tests at Bell Laboratories and at the 

 Franklin Institute, where a precision study of the torsional crystal has 

 been made, have shown no observable longitudinal waves from the 

 crystal surface. The process of measurement consists in measuring the 



* W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 

 D. Van Nostrand, 1950, p. 340. 



3 W. Phillipoff, Physik. Zeits, 35, 1934, pp. 884-900. 



■• T. L. Smith, J. I). Ferry and F. W. Schemp, "Measurement of the Mechanical 

 Properties of Polvmer Solutions hv Electromagnetic Transducers," J. App. 

 Phys., 20, Xo. 2, Feb. 1949, pp. 144-153. 



* W. P. Mason, "Measurement of the Viscosity and Shear Inelasticity of Liquids 

 hv Means of a Torsionallv Vibrating Crystal," A.S.M.E., 69, May 1947, pp. 359- 

 367. 



^ P. E. Rouse, Jr., E. D. Bailey, and J. A. Minkin, "Praetors Affecting the 

 Precision of Viscosity Measurements with the Torsional Crystal," Laboratories 

 of the Franklin Inst., Report 204S, presented to Am. Petroleum Inst., May 4, 

 1950. 



