P A U L W . K I N N E Y , A r m s t r o n g C o r k C o m p a n y , L a n c a s t e r , P e n n a .
T
H E rheological properties of various plastic soft solids as reported by use of the mobilometer have never been stated in absolute units and, therefore, comparison with the results obtained with other instrum ents is not easy. I t is th e purpose of this paper to show how one mobilometer has been calibrated to give results in absolute units. A comparison of the results obtained when several materials are measuredThe mobilometer was first described by Gardner and Parks (6) for the control of the flow properties of paints, enamels, and pig
mented lacquers. Its dimensions were later standardized in the Gardner laboratory by Sward and Stewart (13). I t has been used by numerous workers to report the Theological properties of several systems of materials. Gardner and Van Heuckeroth (7) have applied the instrument to food products, mineral oils, petrolatum, coal tar, etc. Gray and Southwick (8) have used the instrument in their studies of the mayonnaise emulsion, Turnbull (13) and McIntyre and Irwin (11) have used it to study the flow properties of ceramic clay slips. Baldeschwieler and Wilcox (1) have utilized the instrument as a viscometer for viscous mineral oils. The writer has found use for it. in a study of the rheological properties of adhesives, particularly those used in the installation of various floor coverings.
An ideal instrum ent for use in th e study of the flow proper
ties of industrial materials should satisfy the following requirements:
3. I t should be adaptable to a rather wide range of consisten
cies.
tem being measured is altered more than is slightly incidental to the consistency being controlled. The results so collected are usually of no value as research date.
An industrial research instrum ent m ust m eet all the above requirements, w ith emphasis on the first four. T he Gardner mobilometer is a control instrum ent which can be m ade to satisfy all points if the degree of precision is known and if the results are calculable in absolute units. I t can, therefore, be used as an industrial research instrum ent.
Description of the G ardner mobilometer has been ade
quately covered in the literature. Essentially, no funda
m ental changes have been made in the shape or size of the disks or cylinders of the commercially available instrum ents.
Combes, Ford, and Schaer (4) have replaced th e disks by a
perforated cone for use in measuring the consistency of greases.
The writer has found a glass tube fitted in a stopper on the top of the cylinder helpful in dealing with materials containing volatile solvents. Continued exposure of such materials to the air currents of the room causes loss of solvent which sometimes results in deleterious skinning of the exposed surface. High loss of solvent will, of course, produce inaccuracies. The use of the tube decreases this source of error to a large degree. The tube consists of a piece of standard 20-mm. glass tubing 180 mm.
long, drawn down a t the upper end, and fitted into a No. 9 roofing putties and fibrous roof coatings, and was developed w ithout knowledge of th e existence of the mobilometer. In construction, the Clarvoe instrum ent varies essentially only in th a t the diam eter of the cylinder is greater and no disk is used on the end of th e plunger rod when measuring stiff putties. M aterials of lower consistency are measured w ith a ball on the end of th e rod. The perforated disks of the Gardner instrum ent are n o t suitable for use w ith fibrous materials, b u t it has been suggested th a t the ball tip principle be borrowed from th e Clarvoe instrum ent, for this purpose.
P r o c e d u r e
A standard procedure has been employed in all calibrations and observations. All work was performed in a constant- tem perature room held a t 22 ± 0.5° C., although an effort was made to keep the tem perature of the m aterial being measured more closely adjusted. This eliminated th e necessity of a water bath, b u t decreased th e accuracy of calibration and ob
servation in varying degrees, depending on the tem perature coefficient of the material.
The sample was brought to temperature and poured into the cylinder of the mobilometer to a height of within 2 cm. from the top. In the case of a viscous liquid the air bubbles were expelled by merely allowing the cylinder to stand undisturbed for a time.
In the case of highly plastic materials, the entrapped air was eliminated by gently and steadily tapping the bottom of the cylinder on a resilient surface for several minutes. The cylinder was screwed into the base and the rod-guide was clamped in place. The top of the guide clamp in contact with the cylinder was kept at approximately the same height as the level of the contents of the cylinder. In adjusting the weights producing the flow (the weight of disk, rod, and weight pan plus the added weight) no attem pt was made to keep the minimum weight of the system 100 grams, as is usually done. In fact, an effort was made to have available a lower minimum shearing weight in some cases, so th a t the instrument could be applied to more fluid materials.
This was done by removing the weight shot from the hollow rod (the shot is placed in the rod by the maker in order to standardize the weight of disk, rod, and weight pan, so th at this combination will weigh 100 grams). In this manner, a shearing weight of less than 50 grams was available. At a chosen shearing weight, the time for several plunges was recorded, having the plunger in a different position radially for each determination. At certain positions, the frictional forces of the instrument appear to be at a minimum. Reference is made below to means of minimizing the effects of friction due to the crudity of construction. The position of minimum time was chosen and an effort was made to keep this same radial position in subsequent calibration and
M arch 15, 1941 A N A L Y T I C A L E D I T I O N 179 observation. The time was recorded for a fall of 10 cm., this 10
cm. being chosen so that the disk will fall through that volume of material in approximately the middle section of the cylinder, in order to minimize any end effects which might be inherent.
In the case of true liquids, after each plunge the rod was not wiped clean of adhering material, but at least 2 minutes’ draining time was allowed, so th a t the material could flow from the rod before the next plunge was made. This practice was adopted because the use of the glass air current shield in certain cases made wiping after each plunge impractical. The amount of liquid ad
hering to the rod after 2 minutes’ draining time was usually less than 1 gram for 10 cm. of exposed rod. In the case of plastic soft solid materials of considerable yield value, frequent wiping was necessary, as layers of the material tended to build up with successive plunges and withdrawals. This point of procedure was not particularly desirable but seemed practical. An average time for a t least three falls for each shearing weight was used in partially operative in the cases of the disks in which there are holes. We m ay consider th e operation of the blank disk, as applying flow between cylinders. Observation shows th a t the disk, however, does not travel coaxially to the cylinder, measurable by means of ordinary stop-watch technique.
I t can be seen th a t in the mobilometer the types of flow are complicated, and th e results of calculations based purely on the dimensions of the instrum ent would probably mean very little.
Newton’s fundam ental law of viscous flow states th a t when two parallel planes separated by distance s are sheared by a force, F, per unit area, the velocity, v, which one plane travels w ith respect to th e other will be proportional to th e coefficient of viscosity, jj, of th e material separating th e planes.
Thus,
K, in this case, cafi be evaluated either by calibration against a liquid of known viscosity or from the dimensions of the which the more complicated formulas of all instrum ents may be transformed.
also applies, although the value of K cannot be obtained from dimensions of the instrum ent b u t m ust be evaluated by calibration against a standard liquid. Here again, however, the dimensions of K F are dynes per sq. cm.
The mobilometer has been designed to measure the flow properties of m aterials which do not behave as true liquids—
i. e., those materials which behave as plastic soft solids or non- Newtonian liquids. In the case of plastic solids, Bingham abscissa of the straight line asym ptotic to the curve obtained when the rate of shear, V /t, is plotted as the ordinate against the shearing stress, P, as the abscissa. The yield value, p, has the same dimensions as P. The mobilometer gives curves such th a t the points measured, for the m ost part, fall on the section of the curve which is coincident w ith the asym ptote. In fact, it is impossible in m ost cases to detect curvature graphically in this section of the curve, so it m ay be considered to be a straight line.
Equation 8 m ay be given the same treatm ent as E quation 5 to give
»(.KF - Kf) (9)
Equation 4 is specific for application in the m easurem ent of the viscosity of a liquid. Equation 9 is for application to the mobilometer in th e case of a plastic solid. The value of K for the mobilometer, obtained from calibration w ith a standard liquid, is an instrum ental constant and it can, therefore, be used in E quation 9. The actual values of K obtained in the cases of the different instrum ents (parallel plates, capillary tube, or mobilometer), of course, will not be equal.
The values of ¡x and K f, necessary as physical constants to express the flow characteristics of a plastic solid, can be calcu
lated by th e m ethod of averages {10) using values of 1 /i and K F obtained experimentally. Only those values which occur
180 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y V ol. 13, No. 3
F i g u r e 1 . C u r v e o p T a b l e I
V isc o sity s ta n d a r d 0 , v 10 35.74 poises a t 2 2.0° C ., N c y lin d e r, a n d 0 - 4 d isk
need of which is attrib u ted mainly to th e buoyant effect;
and A = straight line equation constant.
I t will be noted th a t
(1 2)
The value of C can be approxim ated b y calculation from the dimensions of th e submerged parts and the specific gravity of the m aterial under measurement.
The above statem ent has not taken into consideration any frictional forces due to contact of the moving disk and th e inside of the cylinder, which are in opposition to the weight and are therefore in the same direction as the buoyant force.
These frictional forces cannot be calculated from dimensions of the instrum ent and m ay be disregarded in the cases of well-machined disks and cylinders where the friction, if effective a t all, is very small. The frictional forces arise from poorly machined working parts; those disks and cylinder walls which appeared to be rough had higher values of C than the smoother appearing ones. If accurate results are desired, the moving parts should be accurately machined and care
fully finished. I t was noted th a t those disks which had been used for some time had lower values of C than th e newer ones.
If careful technique is practiced, it is logical to conclude th a t any gross discrepancies in measurem ent or low precision may be accredited to large values of frictional forces.
on th e linear portion of the curve should be used in the calculations.
C a lib r a tio n
A Bureau of Standards calibrated viscosity standard liquid having a viscosity of 35.74 poises at 22.0° C. was used to calibrate the instrument and thus obtain the instrumental constants for various combinations of disks and cylinders. Two sets of three disks—i. e., one blank, one 51-hole, and one 4-hole disk in each set—were calibrated. One set had been in use for some time and one set was recently purchased from the Gardner laboratory;
the former set is identified by the prefix O- and the latter, by N-.
Five cylinders were calibrated, four old and one recently obtained, identified by the symbols I, II, III, IV, and N. The practice followed has been outlined above under the heading of Procedure.
C o rre c tio n s
In Table I are given th e times necessary for a 10-cm. fall of the plunger rod fitted with a four-hole disk, using various weights to produce the shear. I t was found th a t the straight line obtained when the rates of fall—i. e., the values of 1 /i—
were plotted against the shearing weights in grams, did not go through the origin, b u t instead had an intercept a t a small value on the abscissa. Inspection shows th a t the total weight producing the shear is not ju st overcoming the viscous re
sistance of the liquid, b u t a portion of the weight is being used to overcome the buoyant force of th e submerged disk and rod.
In order to have the shearing weight corrected so th a t it will equal the weight producing shear, the buoyant effect cor
rection m ust be subtracted from th e shearing weight. E qua
tion 3 can be expressed
n « K(IF - C)t (10) where F — W
Figure 1 shows the curve obtained when the values given in Table I are plotted. Constants A and C of the equation representing the curve were calculated by the m ethod of averages.
IF a } + c (1 1)
T a b l e I. Ca l i b r a t i o nw i t h Bu r e a u o f St a n d a r d s Vi s c o s i t y St a n d a r d
(ii “ 35.74 po ises a t 22° C .; t = tim e of fall of 10 c m . w ith w e ig h t W , u sin g a 4 -h o le d isk )
A - 1.645, C - 5 .4 , K - 0 .02173
W t 1/i F - W - C C a lc d . E r r o r
G ram Sec. %
4 9 .3 3 7 .3 0 .0 2 6 S 1 4 3 .9 3 5 .5 8 0 .4
6 5 .9 2 7 .2 0 .0 3 6 7 6 6 0 .5 3 5 .7 6 0.1
8 5 .9 2 0 .5 0 .0 4 8 7 8 8 0 .5 3 5 .8 6 0 . 3
1 1 5 .9 1 4 .8 0 .0 6 7 5 7 1 1 0 .5 3 5 .5 4 0 .6
1 3 5 .9 12.6 0 .0 7 9 3 7 1 3 0 .5 3 5 .7 3 0 .0
1 6 5 .9 1 0 .3 0 .0 9 7 0 9 1 6 0 .5 3 5 .9 2 0 . 5
A v . 3 5 .7 3 0 . 3
T a b l e I I . Va l u e s o f In s t r u m e n t a l Co n s t a n t s
C y lin d e r D isk K ** — A v e ra g e
N o . N o . A C A A D e v ia tio n
% N N -B 2 20,600 1 6 .6 0 .0 0 0 1 6 2 0 i 0 .0 1 9 2 5 1 .9
N N -51 16,120 1 6 .7 0 .0 0 2 2 1 7 0 .2 6 3 4 1.0
N N -4 1,931 6 .4 0 .0 1 8 5 1 2.200 1 .5
N O -B 57,820 - 0 . 2 0 .0 0 0 6 1 8 1 0 .0 7 3 4 5 0 .4
N 0 -5 1 14,600 2.1 0 .0 0 2 4 4 8 0 .2 9 0 9 0 .3
N 0 - 4 1,645 5 .4 0 .0 2 1 7 3 2 .5 8 3 0 .3
I 0 - 4 1,702 2 .9 0.02100 2 .4 9 5 0 . 5
I I 0 - 4 1,705 3 .3 0 .0 2 0 9 6 2 .4 9 1 0 .9
I I I 0 -4 1,639 4 . 7 0 .0 2 1 8 0 2 .5 9 1 0 .4
IV 0 -4 1,691 3 . 0 0 .0 2 1 1 3 2 .5 1 1 0.1
A v erag e 0 - 4 D is k 1,676 3 .9 0 .0 2 1 3 2 2 .5 3 4 0 .4
where IF = shearing weight—i. e., the weight of disk, rod, and weight pan plus added weights; C — correction constant, the
The error introduced by not wiping the rod clean of adher
ing liquid between determ inations is not large if sufficient time is allowed for drainage. In the case of the calibrating liquid less than 1 gram of m aterial adhered after 2 m inutes’
draining time. As plastic soft solids do not drain properly and consequently add considerably more weight, they should be wiped after each determ ination if high precision is desired.
The percentage error introduced by not removing the adher
ing film, however, in the case of these plastic materials, may not be very large, since the weights necessary to produce flow in these m aterials are usually rather high.
There is a different value of th e instrum ental constant for each combination of disk and cylinder. Table I I gives the values of the instrum ental constants, K , along with the value
M arch 15, 1941 A N A L Y T I C A L E D I T I O N 181 of A from Equation 11 which is used in calculating K and k.
In order to calculate k it is necessary to know the value of V, the volume of flow. This value, calculated from the dimen
sions of the instrum ent, is 118.8 cc. for 10-cm. fall.
The constants are given for the combination of one cylinder and different disks and for one disk and several cylinders.
The wide variation in the values of K, for the disks which are supposed to be interchangeable, makes the necessity of calibration of the various disks immediately apparent, if results of measurem ent of flow properties w ith one mobil- ometer arc to be compared w ith those of another. The values of K obtained when the different cylinders are used inter
changeably do not vary so widely as do the values of K using the “interchangeable” disks.
The average value of the buoyant force correction, C, for disk 0-4 in combination with the various cylinders is 3.9 grams. This value compares veiy well with the value
calcu-Fi g u i i e 2 . Ma n i l a Co p a l Re s i n So l u t i o n i n Al c o h o l
5 8 .4 % b y w e ig h t
T a b l e III. G a r d n e r M o b i l o m e t e r D a t a f o r 5 8 .4 P e r C e n t A l c o h o l i c S o l u t i o n o p M a n i l a C o p a l R e s i n
(0 - 4 , 0 - 5 1 , a n d 0 - B d is k s w ith N cy lin d e r. T e m p e r a tu r e , 2 2 ° C . C, 5.7) D e v ia tio n fro m M ean TV
G ram s t Sec.
F K F
D yn es/
sq. cm . D isk 0 4 , K
-1 / i
0 .02173
V a lu e of n
%
4 9 .3 2 4 .3 4 3 .6 0 .9 4 7 0 .0 4 1 2 3 .0 0 . 0
7 4 .2 1 5 .2 6 8 .5 1 .4 8 9 0 .0 6 6 2 2 .6 1 .8
7 9 .2 1 4 ,1 7 3 .5 1 .5 9 7 0 .0 7 1 2 2 .5 2 .2
8 9 .2 1 2 .4 8 3 .5 1 .8 1 4
D is k 0 - 5 1 , K « 0 .0 S 1
0.002448 2 2 .5
A v.
2 .2 1 .5
3 9 .1 2 8 6 .7 3 3 .4 0 .0 8 1 8 0 .0 0 3 4 9 2 3 .4 1 .7
6 4 .0 16 4 .1 5 8 .3 0 .1 4 3 0 .0 0 6 0 9 2 3 .4 1 .7
8 4 .0 1 2 3 .2 7 8 .3 0 .1 9 2 0 .0 0 8 1 2 2 3 .6 2 .5
1 0 0 .0 1 0 1 .2 9 8 .3 0 .2 4 1 0 .0 0 9 9 2 4 .3 5 .3
1 5 0 .0 6 4 .6 1 4 8 .3 0 .3 6 3 0 .0 1 5 5 2 3 .4 1 .7
2 0 0 .0 4 7 .9 1 9 8 .3 0 .4 8 5 0 .0 2 0 9 2 3 .2 0 .9
2 5 0 .0 3 7 .5 2 4 8 .3 0 .6 0 8 D is k 0 B , K
-0 .-0 2 6 7 0.0006181
2 2 .8 A v.
0 .9 2 .1
1 5 0 .2 2 6 2 .8 1 4 4 .5 0 .0 8 9 3 0 .0 0 3 8 0 2 3 .5 2 .1
2 0 0 .2 1 8 8 .1 1 9 4 .5 0 .1 2 0 2 0 .0 0 5 3 1 2 2 .6 1 .8
2 5 0 .2 1 4 8 .3 2 4 4 .5 0 .1 5 1 1 0 .0 0 6 7 4 2 2 .4 2 .7
3 0 0 .2 1 2 2 .2 2 9 4 .5 0 .1 8 2 0 0 .0 0 8 1 8 M e a n v a lu e
2 2 .2 2 3 .0 poises
A v.
3 .6 2 .5 2 .0
Fi g u r e 3 . Ma n i l a Co p a l Re s i n So l u t i o n i n Al c o h o l
5 8 .4 % b y w e ig h t, p lo t te d in a b s o lu te s y s te m u n its
lated from the dimensions of the submerged parts, the mean volume of the submerged parts being 5.7 cc. This would give 4.9 grams’ buoyant force, since the specific gravity of the calibrating liquid is 0.86. The 1.0-gram difference between average C and buoyant force calculated from the dimensions is attributed to the weight of calibrating liquid adhering to the rod.
The frictional force is negligible in the case of disk 0-4, as it is with the other older, smoother-surfaced disks 0 -B and 0-51. Higher frictional force is, of course, associated with rougher working surfaces. Also, as summarized in Table II, the average percentage deviations between th e known viscosity of the calibration liquid and the values of viscosity, calculated using Equation 3, are higher for th e new disks than for the smooth ones. I t will be noted th a t the value of C for disk 0-B is —0.2. This out-of-line value is attributable to calibration inaccuracy, b u t since the shearing weights used in this case were in the range of 350 to 1100 grams, the resulting percentage deviation between —0.2 and 3.9 values of C was not excessive. The percentage deviation in this case was of the same order as for the other O-set disks.
D e te r m i n a t i o n s
The viscosity of a clean, concentrated solution of M anila copal resin in denatured alcohol (Special D enatured Formula No. 1) was measured. The solution was prepared by dissolv
ing the C N E grade of this natural resin in the alcohol, allow
ing the d irt and other insoluble m aterial to settle, and using the clear supernatant liquid. Analysis of this solution showed its concentration to be 58.4 per cent by weight.
Table I I I presents the d ata obtained when the viscosity was measured using 0-4, 0-51, and 0-B disks and N cylinder.
In Figure 2, the reciprocal of the tim e required for 10-cm.
fall of the plunger is plotted against th e weight producing the fall. Each numerical value of t is an average of th e times of a t least three falls a t the same weight. In order to calculate the viscosity from the data, it is necessary to subtract from the shearing weight a correction for th e buoyant force. For purposes of calculation, the average submerged volume will be taken as 6 cc. To calculate the shearing force—i. e., the weight overcoming viscous resistance—from th e shearing weight, Equation 13 is used.
182 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y V ol. 13, N o. 3
F = W - 6 p (13)
where p = specific gravity of the m aterial being measured.
In the case of this solution where the specific gravity equals 0.95, th e buoyant force correction is equal to 5.7. After calcu
lating the force, F, necessary to shear the liquid, the calibra rates of flow, along w ith the per cent deviation from the mean calculated value of viscosity. The average deviation is 2.0 per cent. I t will be noted th a t those values of viscosity corresponding to low rates of flow tend to have a greater deviation than the higher rate values; th a t those viscosities obtained using the O-B disk have higher deviation than those obtained w ith 0-51 and 0-4; and similarly 0-51 has higher values than 0^4. The explanation of this is th a t probably the incalculable frictional forces are present and are exerting a greater influence a t the lower rates of fall.
If to this M anila copal resin solution is added some con
siderable q u antity of a mineral filler, the flow properties will change from those of a viscous liquid to those of a plastic soft solid and the rate of shear will no longer be proportional to curves resulting when th e rate of 10-cm. fall is plotted against the shearing weight. If by using th e calibration constants we
siderable q u antity of a mineral filler, the flow properties will change from those of a viscous liquid to those of a plastic soft solid and the rate of shear will no longer be proportional to curves resulting when th e rate of 10-cm. fall is plotted against the shearing weight. If by using th e calibration constants we