c -4 SIhlPLI.: PLXSTOMETEII FOR COXTROL USE
W T H DESTA41, CREA4;\IS.* BT E. M O N E A ~ I~D
P.
v.GIESY
In April, 192.3, before the Division of Industrial and Enginecliing ('hemistry at the S e n Hax cn Meeting of the Xmerican Chemical Society, Rinpham suggested that plasticity measureinents could lie inade iq timing the flow of a plastic inaterial over successive increnients of length of a capillary, this being equivalent to determining the speed of flow through capillaries of the same diameter and varying lengths Since the niaintenance of uniform consistency is important in the manufacture of dental cream, n e clecicled to use this principle in the development of a simple plastoineter n hich niight bc used for plasticitv nieasurenients on dental creams. The use of gas pressme inx olx es coiiiplicatetl and expensive apparatus for keeping the prewire constant and measuring it IT-e decided to t i y to use a iiierciiry coliiinn to supply pressure, measuring the pressure by the height of the column The dental cream is pushed hy the pressure of the mercur\ throoph the graduated capillary. and the tiim at which the head of t h r coliiinn pasies alternate centimeter divisions is noted T-ndei thcsc conditions A1 At- nherc A1 = 3 ciii and A t is the a r tual time taken by the dental cream to trax erse this length of capillary, is a variable nhich iq a linear function of P 1. where P is the total pressure applird ailti 1 the mean lenyth of capillary fillcd by the niatcrial cluiing thitimc. So, when a curre is plotted nith 1 1 A1 as ordinate antl P 1 abscissa, a straight line should result, thc
18.9 22.6
0.0076 0.0096
25.8
0.0101
30.2
0.0128
This seeiiied to he due to flon--resistance iiot in the capillary, but in the reservoir, which had the effect of an additional length of capillary. K e therefore modified the insti*uiiientto the form first described. Runs with varying pressures pave the follon ing results. 1'1es.uie (cni H g
>lope
Ij
0
20
1
o 0156 o 0162 o 0166
26 6
The curves of these runs are shown
\-Itlt?I((pt 0
24
0
24
0 22
111 Fig.
1.
It will be noticed that even here the effect of the internal resistance of the reservoir shows itself somen-hat. It should be pointed out that it will be inipossible to eliminate this entirely with any type of capillarjr tube instrumeiit. K i t h more fluid illaterials I'cr its effect is less noticeable. In working with fairly thick aqueous emulsions we were able to use the Type I11 instrument with entire satisfaction : varying the applied pressures did not affect the slopes :
Theoretical Part Bingham and Murray1 calculated the average shearing stress over the interval l?-ll by iiitepratiiip [PR 211 dl between these limits, and found it to be [PR 2(lL-ll)] log,, 1 2 ll. They then stated that the volume of flow was evidently 7rR2(12-11), and plotted the speed of flow for different intervals as a function of thr average shearing stress. Green in his discussion of this paper, stated that nR2(1,-ll) was eczdently not the correct V t to use (he obviously meant T7)$ but gave no reason for the statement. This method is not rigorously correct. for the reason that 1-is not proportional t o F, but to F-f. which has not been calculated. Our own method is ilia thematically less rigorous, since we plot average rate of flow over an interval as a function of inean shearing stress over the Proc. Am. SOC Twtiiig llateiials, 23 11, 6;s (1923)
1286
E. MONESb AND P. hl. CiIESY
same interval. To determine whether this if-as justifiable, we calculated t aa function of 1 from the equation
P 1
=
a
+ (1,’s)dl//dt
(1)
which is the equation of a straight line espressirig the ekperimental results. This cannot be integrated as it stands, but hy making the substitution 1 = I , / z , the equation reduces to the form dz, dt
=
Sz2(a-Pz)
(2)
Integrating and resubstituting me obtain
t
=-
P P-loa 1-1, log, - Sa2 P-la Sa
(3)
~
FIG.
4
Plastirit y Curve3 for Dental Cream using varying pressures
where t = t, when 1 = 1,. In this equation we ha\-e substituted the figures from an actual run on a sample of dental cream:
P
= 21 8cm.Hg s = o 0086 a = 017 1, = 3 cni.
and have czlculated the following values of t , using 8-place logarithms (6place give an accuracy of only about I percent.): 1 icm
3
t
1%(’
1
0
44
O i j
I
111
256
9
310 318 046
3 r
I1
202
1287
A SIMPLE PLASTOMETER
F'rom these values n e have calculated AI A t , and froin equation with the following results: 1 (cm
1 1 At
)
04537 7
(11 clt,
dl dr
4
0
6
o 029770
o 029748
s
o 021965 o 017281
0 0219j3
IO
(I)
0
04.i4C8
o 017286
From this it is obvious that while the inatheiiiaticsl method 1s not rigorous. its errors are far less than the experimental ones. ,111 this, of course, is based on the assumption that a linear relation bctween F' antl T7 t really exists. But even if this is iiot strictly ho, it mill not vitiate the results of this calculation. The differences hetwecn A1 At antl dl d t depend only on the curvature of the 1-t curve, and it i.i evident that it nould lalie a great increase in curvature t o inake thrsc (lifere1Tces as large as the experimental errors. Our measurements have shown that when the
