May, 1962
SLIDISG OF
LIQUIDDROPSO N SOLID
883
SURFBCES
TABLE I CONCENTRBT[OX O F SURFSCE COMPOUNDS AFTER \'ARIOUS
TREATMENTS (NUMBER
OF
ADSORBED IONS PER SURFACE LEAD
-
ATOM) --SampelCOa
SlnOn dd. as either 804 or SOa
0.4. 0.9 0.7 Before treatment .5 .2 .9 After KEX trea+tment(water treatment for control) .4 .2 .7 After acetone wash PbS sample heated in air to 150" for 6 hr. Before treatment 1.9 12.0 7.6 After KEX treatment (water treatment for control) 0.4 4.4 2 . 6 After acetone wash .5 2.1 1.4
measure surface OH ion excha:nge. Such measurements inight be possible but mould call for Preicautio13sin drying PbS samples and in excluding atmospheric moisture picked up by the KBr while t,he sample pellet,s are made. Both of these factors -cl.ould have to be examined to determine an ion balance.
--
EX
COa
4.8 1.2
0.9 1.5 1.7
33.4 1.3
1.9 3.6 3.1
Control--
SmOn calcd. as either or SOa
SO4
0.7 .9 .9 12.0 13.3 11.2
0.4 .6 .6
7.6 8.4 7.1
Acknowledgments.-The author wishes to thank bfr. Robert J , Wagner, Edwin S. ROuSSeau, and Jtr. Donald F. Lowe for helpful discussions and aid in the preparation of samples, and Dr. James R. Huff and Dr. Raymond J. Jasinski for making t,he surface area measurements.
THE SLIDING OF LIQUID DROPS ON SOLID SURFACES BY DOUGLAS A . OLSER',POWELL A. JOYKER, AKD NIARVIYD. OLSON Minnea polis-Honeywell Research Center, Hopkins, Minnesota Received November 6 , 1061
The equations for predicting the tilt angle at which a liquid drop begins t o slide on an inclined solid surface have been developed. The validity of these equations has been verified experirnentally.
Introduction The sliding motion of liquid drops on inclined surfaces originally was studied by Frenkel. I n this study Frenkel reported an equation which mould predict the angle, a , at which a liquid drop would begin to slide down an inclined surface. The equation is mg sin
CY
=
+
~ ( Y L V
YSV
-
YSL
1
(1)
where m
=
g
=
a
=
w
=
~ L V =
y s = ~ y s = ~
mass of the liquid drop gravitational acceleration tilt angle maximum width of the contact area between the drop and the surface liquid-vapor interfacial tension solid-vapor interfacial tension solid-liquid interfacial tension
+
The expression (YLV ysv - ~ S L )in the righthand side of eq. 1 is recognizable immediately as the reversible work of adhesion. I n a later study Aron and Frenke12 determined from eq. 1 values for the reversible work of adhesion of liquid drops on several different surfaces. They also showed that in order for a liquid drop to slide down an iiiclined surface the following inequality must be true (since sin a caiinot be greater than unity) m > -WE, 9
where E,
=
(2)
reversible work of adhesion.
(11 Ya. I. Fienkel, Zhur. Eksptl z Teoret Fzz , 18, 659 (1948). ( 2 ) Y a B Aron and Y a I. Frenkel, zbqd., 1 9 , 807 (1949).
In the entire study, however, no definitive experimental verification of eq. 1was given. I n the present study it has been shown that the previous conclusions can be expanded upon so as to permit estimation of tilt angles from readily measurable quantities. The equations which are developed also are experimentally verified. Theory If it is assumed that the entire initial resistance to sliding of the liquid drop is at the rear of the drop, then eq. 1 can be derived. Consider a liquid drop on an inclined plane surface (Fig. 1). As,wme the drop will begin to move a t an angle, a, where the accelerating force exceeds the retarding force at the rear of the drop. From Fig. 1 the work, dW, a t the rear of the drop due to the retarding force, f ~ acting , through a distance, ds, is given by dW = f~ ds (3) At the trailing edge of the liquid drop a new liquid surface and a new solid surface are formed and the interfacial surface is destroyed (or more rigorously there is exposure of liquid-vapor and solid-vapor interfaces and destruction of a solid-liquid interface). Consequently the work done a t the rear of the drop as an area dA of the solid surface becomes exposed can be given by dW
= (YLV
+
YSV
- rst)dd
(4)
Since dA = w ds where w is the width of the drop and since eq. 3 and 4 may be equated, the retarding force is given by
D. A. OLSCN,1’. A. JOYNER, AND ,If. D. OLSON
884
where 8 = equilibrium contact angle. If eq. 7 be substituted in eq. 6 then
VAPOR
m g sin
I/
I
motion of a liquid drop.
I
I
I
I
I
2
3
4
5
6
-.rn W
of m/w us. l/sin a! for water drops sliding on polytetrafluoroethylene.
Fig. 2.-Graph fR
= (YLV
+
YSV
-Y
S L ds ~ =
ds
(YLV
+
YSV
-
YSLh
(5)
Equation 5 for the retarding force also can be equated with the accelerating force mg sin a to give mg sin
a!
= W(YLV
+
YSV
- YSL)
(6)
which can be solved to give a, the angle at which the drop begins to slide on the inclined surface. Data are not generally available for solid-vapor, ysv, and solid-liquid, y s ~ ,interfaces; however, they are related by the theoretical relation3 YSV = YSL
+
= WYLV
(1
+ cos e)
+
+
END VIEW
0 0
(Y
YLV COB
6
( 3 ) T. Young, Trans. Roy. Sac. (London), 96, 65 (1805).
(8)
The often used expression y ~ v ( 1 cos 0) which appears in eq. 8 is rigorously true only if one can neglect the adsorption of the liquid vapor upon the solid ~ u r f a c e . ~However, this should be a good approximation for the case of water in contact with low energy solid surfaces such as polytetrafluoroethylene (Teflon )and polyethylene. Thus, it has been demonstrated that the tilt angle, a, at which the drop begins to slide can be calculated if values are available either for ( y ~ v ysv - YSL) or for YLV (1 cos e), which are expressions for the reversible xork of adhesion, Ea. However, the latter expression is only applicable within the limita,tions discussed in the previous paragraph. Equation 8 is of considerable importance in that it allows measurements of the equilibrium contact angle, 8, to be made on a flat surface and then to be applied to the prediction of the tilt angle, a. Equations 6 and 8 can be stated more generally by mg sin a = WE, (9) Thus, the work of adhesion also is related to the tilt angle. The general validity of eq. 6 and 8 can be tested by the behavior of a series of liquid drops of different size sliding on a given surface. This is discussed further in the following sections. As noted earlier the preceding equations predict the tilt angle at which the drop begins to slide. Several authors5, have investigated sliding drops and have derived appropriate equations for drops already in motion at any given tilt angle. Other authors’ have described the minimum tilt angle in terms of parameters n.hich are not easily measured. However, there is no provision in any of these equations for predicting the minimum tilt angle from simple measurements. Experimental Procedure
SIDE V I E W
Fig. 1.-Sliding
Vol. 66
(’7)
+
Three cases were chosen for investigation, water on polytetrafluoroethylene (Teflon), glycerol on polytetrafluoroethylene, and water on polyethylene. Materials.-The polymers used were thin translucent sheets about 0.025 in. thick. The sheets were mounted in shallow troughs with lined paper beneath them to facilitate measurement of drop dimensions. The polymer sheets were rinsed in a chromic acid cleaning solution followed by an aqueous cleaning solution of “Alconox” detergent. The sheets then were rinsed in distilled water. Several sheets were cleaned only in “Alconox” solutions; no apparent differences in tilt angles were observed. The liquids used were water and reagent grade glycerol. The surface tensions of each were determined using the sessile drop methods on Teflon. Our experimental values all were within 1% of the accepted value of 72.75 dynes/cm. for water and within 2.5% of the accepted value of 63.4 dynes/cm. for glycerol. Procedure.-The inclinometer for measuring tilt angles was constructed of the following components: light source, (4) D. H. Bangham and R. I. Raaouk, Trans. Faraday Soc., 3 3 , 1463 (1937). 15) G. Macdougall and C. Ockrent, Proc. Royal Sac. (London), IEOA,
151 (1942). (6) K. Kawasaki,
J. Colloid Sci., IS, 402 (19601. (7) E. Baer and T. F. McLaughlin, J. A p p l . Polymer Sei., 5, 240
(1961).
(8) A. M. Worthington, Phil. Mag., 20, 51 (1885).
SLIDING OF LIQUID DROPSox SOLID SURFACES
May, 1962
lens (focal length 1 m.), in. diameter mirror with cross hairs, graduated scale with increments of 3 min. which could be estimated to 1 min., and tilting plate. Located axially with the plate, the mirror reflects its cross hairs onto a scale t o give direct readings of the tik angle. The trough lined with the polymer sheet was placed on the tilting plate. A known volume of the appropriate liquid was added to the trough and the plate then was tilted through the necessary angle to obtain sliding of the drop at constant velocity. The tilt angle was observed with an accuracy of i l min. All data were observed in a room thermostated at 70°F. The relative humidity range was 35 f 2%.
4-cos 6 )
(10)
g
From Fig. 2, 3, and 4 it is seen that a straight line does result which indicates a verification of the theory discussed above. As further verification of the tlheory the contact angles have been calculated frorn eq. 10 and are shown in Table I along with the observed contact
I
1
I
I
1
I
i
Results and Discussion Representative data for each system are given in Fig. 2, 3, and 4. In each case several sets of measurements were made to determine that the data were reproducible. The values for the observed tilt angle, olobs, were determined directly from the inclinometer discussed in the previous section. Equation 8 predicts that a graph of m/w plotted us. l/siiz a for a series of drops of different size on a given surface should give a straight line through the origin with a slope of YLV (1
i
i
885
0
2
I
I
I
I
I
3
4
5
6
m W
of m/w us. l/sin a for glycerol drops sliding on polytetrafluoroethylene.
Fig. 3.-Graph
I
I
I
I
I
I
I
,,,i
TABLE I CALCULATED ALSDOBSERVED CONTACT ANULES Liquid/solid h o d &bad
Water on polytetrafluoroethylene Glycerin on polytetrafluoroethylene Water on polyethylene
105' 95' 114'
103f.2' 1oo=k2° 9Gf2'
angles. There is excellent agreement for water and glycerol on polytetrafluoroethylene. Eomewhat poorer agreement is obtained for water on polyethylene; however, this could be expected since eq. 8 neglects the adsorption of the liquid vapor upon the solid surface and its consequent effect upon the ,angle.g I n this instance better agreement is obtained by considering eq. 6 . Normally eq. 6 gives intractable results, since values usually are not available for the surface tension of the solids, ysv, and the interfacial tension, YSL. However, the difference between these quantities can be determined. From eq. 61 and the graphs of m/w us. l/sin a the resulting straight line has a slope of YLV
+
YW
- YBL
9
which can be solved to give (ysv - YSL). For polyethylene and water, ('YSV - ~ S L )was found to be -29.9 dynes/cm. In a few limited cases, direct estimations of these quantities are now possible. Fox and ZismanlO (9) An alternate explanation may be found ii:! the faot that, as shown by A . J. G . Allan ( J . Polymer Sci., 38, 297 (1969)). surface oxidation inoreases the wettability of polyethvlene. Increased wettability will reduce the observed contact angle. Since the polyethylene used in this study was rinsed in chromic acid cleaning aolution, surface oxidation probably occurred which could account for the low contact@angle. (IO) H. W. Fox and W . A. Zisman, J . CoEZoid Sci., 7, 428 (1952).
0
I
I
I
I
I
I
I
2
3
4
5
6
m _.
1
W
Fig. $.-Graph
of m/w us. l/sin cy for water drops sliding on polyethylene.
have developed the concept of the critical surface tension, yc, of a solid which is the best estimate available at the present time for the surface tension of a solid, YSV. They found a value of 30 dynes/ cm. for polyethylene. This value, along with an interfacial tension of 55.6 dynes/cm. i1 between high molecular weight hydrocarbons and water, permits an estimation of (YSV - y s ~ for ) the polyethylene-water system. A value of -25.6 dynes/ cm. was obtained, which is in good agreement with the value of -29.9 dynes/cm. obtained graphically. (11) D. J. Donahue and F. E. Bartell, J . Phys. Chem., 66, 480 (1952).
886
LEWISL. ASDERSONA N D MILTOPI; KAHX
I n conclusion it has been shown that the equations developed in the previous sections predict linear plots of m/w us. l/sin a. This has been shown to be experimentally true. As a further verification of theory the observed and calculated values of the contact angles were shown to be in generally good agreement. The calculated and
T’ol. 66
estimated values of (ysv - y s ~ )were shown to be in good agreement for the polyethylene-water system. Thus, the predicted results are consistent with those observed. Acknowledgment.-The authors wish to thank Professor George Gubareff for his aid in translating references 1 and 2.
ARSENIC (111)-ARSESIC(V) EXCHANGE REACTION I N HCl SOLUTIOSS’ BY LEWISL. AKDERSOX~ AKD MILTONKAHS Department of Chemistry, The University of New Mexico, Albuquerque, N . M . Received November 10, 1961
A measurable exchange has been observed between As(II1) and As(V) in 10.8 to 12.6f HCl a t 29.7”, and in 10.9.f HCl a t 48.6 and 67.3’. Complex exchange curves were observed at each temperature. The complexity is attributed to the slow interconversion, via hydrolytic reactions, among two or more forms of $s(V) which exchange at different rates with As(1II). Spectrophotometric studies revealed that As(V) species in 10.9f HC1 were not in chemical equilibrium even after 19.3 days of aging a t room temperature. There is spectrophotometric evidence for the existence of polymeric forms of As(V) in 10.9f HC1.
Introduction This paper deals with the As(II1)-As(T7) exchange in HC1 solutions. I n the course of a study of the “hot atom” chemistry of arsenic, Maly and Simanova3 observed exchange on heating a mixture of As(II1) and As(V) in concentrated HC1. We hare observed an easily measurable exchange at 29.7, 48.6, and 67.3” in 10.9 f HC1. This exchange, however, is generally complex; that is, the exchange curves are not straight lines. This system is complicated further by the slow attainment of chemical equilibria at room temperature among species of As(V) over several weeks as evidenced by the dependence of exchange curves on the age of the As(V) solutions. Spectrophotometric studies corroborated this aging phenomenon and revealed an extreme dependence of the equilibria among As(V) species on the HC1 concentration. Although the data presented here do not permit the postulation of a mechanism for exchange, we are able to report a number of interesting observations which point up the complexity of this system. Experimental Tracer.-The 17.5-day As74 tracer was obtained from Abbott Laboratories, Oak Ridge, in the form of high specific activity sodium arsenate solution. This solution was made 11 to 12fin HC1 and distilled in a stream of Clz to one-fourth its original volume (-20 ml.). Excess Clz was removed from the cooled residue by either a stream of nitrogen or the addition of excess owdered FeC12-4HzO. The residue then mas saturated wit% HCl at 0” and rapidly distilled for 2 min.; the distillate was received in 5 ml. of.12 f HCl at 0” and served as the stock solution of high specific activity 4s(111). The As(II1) tracer solutions used in runs 1-8 were prepared by inoculation of inactive As( 111) solutions and used directly; for subsequent runs, the inoculated ks(II1) was oxidized, reduced, and distilled as described above. The As(V) tracer solutions were prepared by exchange in (1) This communication is based on work done under the auspices of t h e Los Alamos Scientific Laboratory a n d the Atomic Energy Commission (Contract No. A T (11-1)-733) a n d submitted i n partial fulfillment of t h e requirements for the degree of Doctor of Philosopy i n the Graduate School of the University of New Mexico, June, 1961, b y Lewis L. Anderson. (2) E a s t m a n Kodak Fellow, 1959-1960. (3) J. Maly and R. Simanova, Chem. Listy, 49, 814 (1955).
10.9f HC1 betmeen inactive As( V) and high-specific-activity As(II1) at 95’ for 4 hr. in a sealed Pyrex tube. To test for radiochemical purity, a sample of purified highspecific-activity ils(II1) was sealed in a test-tube and counted from time to time, over a t least 5 half-lives of AsT4,on a scintillation counter. The decay curves contained 17.5and 71-day components which correspond to 17.5-day As74 and 76-day As73. Also, the specific activity of an aliquot of an inoculated As(II1) solution was within 2y0of that of an aliquot subjected to oxidation, reduction, and distillation. Reagents and Analyses.-The HC1 solutions were prepared by dilution ot Analvtical grade 37% HC1 a i t h doublydistilled water. The Bs(II1) stock solutions were prepared by dissolving C.P. AsoO? in HC1. The solutions were analvzed for As(11II by titrating aliquots with standard KBrOj solution to the methyl orange end-point in 2.4fHCl.4 Stock solutions of As(V) were prepared by dissolving C.P. As206 in HC1. The As(V) concentration was determined by thiosulfate titration of the iodine liberated from K I by aliquots of the solution.6 All stock solutions except those used in runs 1-4 were stored at room temperature under the normal fluorescent light of the laboratory; the solutions used in rune 1-4 were stored in the dark. Chloride analyses were performed by a modified Volhard method .6 The acid concentration of a stock solution was calculated from the concentrations of As(II1) or As(V) and total chloride assuming that As( 111) and As( V) exist in these solutions as AsCll and AsCla-, respectively. It is noteworthy, however, that whereas >98yo of As(1II) should exist in 10.9 f HC1 as AsC&,~there is no evidence for the existence of AsC16-.* Because the extent of hydrolysis of As(\?) in HC1 solutions is unknown, the actual HC1 concentration of an As(V) stock solution probably was somewhat greater (
