Gupta, N C Sen

Mukherjee, J N

English

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THE VELOCITY GRADIENT METHOD FOR THE MEASUREMENT OF VISCOUS PROPERTIES OF NON-NEWTONIAN LIQUIDS*By J. N MUKHERJFEANDN. C. SEN GUPTA*(Recnveif for pitblicaiioUf September /, ig^i)ABSTRACT A method has been dtscTifitii which admits of a direct measurement of velocities tit different depths in a flowing liquid. The liquid is contained in a rectangular cell of depth of the order of 1 mm. and the velocities measured with a microscope using an objective with a large working distance. Velocity distribution curves have been obtained with a sugar solution, two gelatin sol.-^  and a bentonite suspenLsion. The advontages of the metht^ d are discu.ssed,A large miniber of liquids, especially concentrated colloids, do not obey Newton’s linear relation between shearing stress and rate of shear. They are designated as non-Newtonian liquids. A systematic study of the viscous pro­perties of sucli liquids has b'lth theoretical and practical ii.nere.st. The earlier work of Hess,'Halschek," Bingham,'* UstwakC and others has been considerably extended in recent years'*’"’’ * and several accounts are available.* Newton’s equation for viscous fluids is :dvjdz~ V h i ■■■ (i)where dvjdz is the rate of shear .(velocity gradiciil) in cm./sec./cm., F  the shearing stress in dynes/sq. cm. and n the coefficient of viscosity in dynes.sec./sq. cm.Ostwald^ assumed that in colloids like gelatin sols a structure exists in the undisturbed sol which is progressively broken down as the rate of shear is increased so that the apparent fluidity (reciprocal of viscosity) of the system gradually rises.Ostwald’s relation i s ;d v i d z ^ ¥ ” h '  ... (2)w'here n is a constaiit greater than unity and has been called the “ coefficient of structure ”  and is a constant whose dimensions arc different from that of the coefficient of viscosity.* Communicated by the Tndmii Physicftl Society,7— 1433P — I ■50 J. N. Mukherjee and N, C. Sen GuptaAccording to Bingham” a minimum shearing stress is necessary to start flow in "  plastic ” systems beyond which the rate of shear is proportional to the shearing stress. Bingham proposed for them an equation of the form :d v ld z = (¥ (3)He called, f, the yield value’ of the system.Many examples of both ‘ structure-viscous ’ and ‘ plastic ' systems have been found in the literature while some show intermediate behaviour."In viscomelric measurements, especially by the capillary method, the rate of shear varies from layer to layer over wide limits. \Miile this variation can be easily taken into account in Newtonian liquids where the coefficient y is constant and has a definite significance, it is not easy to do so in the case of non-Newtonian liquids where the values given by different viscometers of such quantities as the yield value, apparent viscosity or mobility depend on the method and also on the dimensions of the apparatus where the same method is used. It is obviously desirable <0 measure the rate of shear (velocity gradient) at different layers in the viscometer. Pichot'" and Philippoff" have described methods which permit observations of the velocity gradient, but these methods do not give the velocity gradient in absolute units. Kroepelin”  uses a pitot tube for this purpose but his method is applicable for rather high rates of shear whereas mca.surements at low rates of shear are of especial interest, e.^., in distinguishing between equations(2) and (3). His method also involves the use of fairly wide tubes which may complicate the conditions of flow. A flat cell of the type used in the micros­copic measurement of cataphoretic velocities of colloids is a convenient form of apparatus which has been used liy us at low rates of shear.The flat cell used had the following dimensions : length—8.0 cm., breadth— j,o cm., height—0.0644 cm.For Newtonian liquids in a rectangular flat cell,dv/dz= — nz/y (4)where ir is the pressure gradient (negative in this case) and z the d^tauce from the central plane.From equations (a) and (3) w'e have for non-Newtonian liquids respectivelyd v Id f= ^ ft "z ” Iy' (5)and d v ld z = ~ n {z -z ^ )!y  (6)z« is the distance along the normal to the direction of flow measured from the central plane, up to which the fluid flows as a solid plug,®-irg.; gives a measure of, and is equal to, the lower yield value.®Measurement of Viscous Properties 51Measurements have been made on the following systems ;(a) a saturated sugar solution {67% ),(b) two gelatin sols, and(c) a hydrogen bentonite suspension, tFinely powdered pure sugar charcoal was suspended and the speeds of the parti­cles at different depths v\ere measured.(a) As is to be expected, the sugar solution (Fig. i) gives a perfect ijarabolic distribution of velocities which is characteristic of Newtonian liquids. The pressure gradient was, however, very small and in the present form of the1 A very fine suspension of a bentonite, obtained by means of a Sharpies .snpercentrifuge, w as elertrodialysed to give the hydrogen bentonite. The methods of preparation and other experimental details willfie described el.sewhere.52 /. N- Mulzherjce and N. C, Sen Guptaappamtus could not be measured very accurately. The coefficient of viscosity obtained from the approximate pressure gradient is about 2 poise. The viscosity of the same solution measured by means of a rotary viscometer is 1.7 poise which agrees with the value given in Internalional Critical Tables.ib) The velocity distribution in concentrated gelatin sols gives curves of a liigher degree than the parabola. The value of 'n inequation (5) calculated from the curves in Fig. 2 is about 2.8. Curves given in Fig. 3 are however parabolic in nature, and the behaviour of gelatin sols depends on concentration mid other fnrlors.(t) The bentonite suspension (Fig. 4, curves i and ii) shows a parabolic distribution of velocities with a central fiat legicn whose depth diminishes with increase in the pressure gradient. is evidently equal to half the depth of the flat region. The yield values calculated from the two curves are 27 and 30 dyiies/sq.cm. respectively. The yield value of the same suspension obtained by means of a capillary viscometer is 88 dynes/sq.cm. which is more than three times the value obtained from Fig. 4 while a rotary viscometer gives values nearly equal to those obtained by the flat cell.It is evident that the melhcd described here gives curves which are signi­ficantly characteristic of the \aiiation of the velocity giadienl with shearing stress. These curves aic capable of yielding on mathematical analysis veiy useful information nut obtainable by the usual viscometric methods. The appa­ratus is being modified for mote asenrate nuasureinents at low rates of she^r and at constant temperature.J ‘MVSiCAC Chkmjstkv L auokatorv,UNlVIlRSlI'V CoCtK<Uf. OF SCIKNCK92, Pppivu CiRcucAK R oad, CAU-um.Measurement oj Viscous Properties '5iR E F R R K N C E SJ Hess, see for references Kolloid-X., 27 ,1:54 (1930).* See Hatschek, “  The Viscosity of Liquids," Hell and Hons (1938/.* See Biughain, *' Fluidity and Plasticity," McGraw-Hill Co. ^1933'.< Ostwald, Kolloid-/., 86, 99, 157, 348 (1935); and a series of papers afterwards; see also de Waale, /. /Itin'r. Chem. Soc.* Buckingham, J. /Imer. Soc. Test Mah., 21 (il). 11,S4 (1921).*■' vSeott Blair and Crowlher,/. P/iys. f'/inn,, 38,321 (1929); Schofield and Scott Blair, /. PliySi  ^Cheni., 34, 248,1505 (1930); 3S, i2i2 (1931); 86, 973 (1935); Schofield, Physics, i, 122 (i 9 3 3 )-’ RtiiKT, A'o//()ii/ / ., 3 9 , ,80 iu ;26) ; Reiner and Riwilin, Kolloid-Z., iS, 1 (1937)! Reiner and Umer. Kolloid-Z., 68, 44 (193,3); Reiner, Physics, 6, 331, 342 (1934).“ P h ilip p o lf, Physik. Zeii., 22, 8 8 4 , 900 ( 1 9 3 4 ) ;  K o I / o id -Z ,,  71, 1  U93.S) i 78, 14 a , 1 5 5  (1936); 83 , 163 U93S).First Report on Viscosity and Plasticity, ilcadcmy ol Sciences, Amsterdam (i935 i^ ,Sfcond Repoit on Vi,scosity and Plasticity, Academy of Sciences, /Uiiilfrduw (1938); Evans and Reid, luillinfi Mnd\ Its Manufacture and Terting, Tians. Min. Geol. Inst. India, 3% 11936]; Hour'ink, Bilasticity, rifcsticity and Structure of Matter, Cambridge (1937)1 Scott Blair, Introduction to Industrial Rheology, Churchill (1938); Goodeve, The Viscosity of non-New­tonian Liquid,s, Refu/ils on Pi ogress of Physics, 5,20 (193SI,Pichot,P/iy.w'fs, 6,200 119341.F Philippoff, Kolloid-Z,, 83, 163 (1938).IK Kroepelin, Z. Physik. Chan., 140, 291 (1930).Jilt. Cl it. Tables, Y, 23 <1929).

The Velocity Gradient Method for the Measurement of Viscous Properties of Non-Newtonian Liquids

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The Velocity Gradient Method for the Measurement of Viscous Properties of Non-Newtonian Liquids

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