A Simple Explanation of the Salt-Water Oscillator Richard M. Noyes University of Oregon, Eugene, OR 97403 Yoshikawa et al. (1)have described a simple device that undergoes repeated'o$cillations and that can also illustrate some of the principles essential to the oscillators driven by chemical reactions. I was privileged to see the original manuscript as a reviewer and concluded that the system would be enjoyed by both students and teachers and that it would be quite instructive. However, I was concerned that the manuswipt as submitted offered no explanation for the interesting phenomena described. The following comments are intended to he of use to those who think this device mav. belo. students to understand oscillations in chemical systems. The system of interest consists of R laree reservoir A filled with water, a smaller container B containing a denser concentrated salt solution, and a restricted connection C between the two solutions. That connection may consist of a lengthof capillary as inFigure 1of the preceding paper ( I ) or merely a small hole in the bottom of the container as in Figure 4 (1). The essential feature is that a fluid of higher density lies above one of lower density with very restricted access between the two fluids. The ultimate state of eouilibrium will consist of fluid of uniform composition everywhere. Even if noorher processes occurred. that euuilibrium would ultim~telvhe attained hv diffusion is so slow thatif there were nb diffusion. currents within the solution then i t would take months if not years for even this small laboratory system to approach equilibrium. If a dense fluid in a gravitational field lies on top of a lighter one, the interface generates an instability that can he relieved by the dense fluid flowing downward and the light fluid flowing upward. If the interfacial area between the two fluids is large, such a flow will be initiated by fluctuations,
-
ow ever,
and "fingers" of salt water will descend until the distribution of the layers has been inverted. Convection arising from thermal gradients will then cause the system with a large interface to approach uniformity much more rapidly than it would by diffusion alone. However, when the connection C is a small capillary or a pinhole, interfacial tension effects are important enough that two-way flow will not take place. If such a constraint exists, then when hydrostatic forces are not in exact balance there will be a unidirectional flow consisting of fresh water moving u p or of salt solution flowing aownward. As Yoshikawa et al. (1) point out, the directions of that flow will repeatedly reverses; thecomposition of thesysem moves in the direction of the still distant equilibrium. Osclllallons wlih a Capillary The system where C is a fine capillary comes closest to resembling a chemical oscillator. Let us assume that the capillary is sufficiently long and of small enough diameter that anv flow throueh the ca~illarvis alwavs quite slow. Then ~ i g u r e s1 an$ 2 illustrate two possible stationary states. Those figures are identical with ones presented by Martin (2) in his original paper about this system and by Strong (3)in a discussion of Martin's discovery. The oscillatory behavior consists of repeated transitions between these two stationary states. Figure 1 illustrates stationary state 1in which the capillary is full of salt solution. Let d, be the density of water and d. be that of salt solution. Let a, be the distance from the s;rface of the reservoir A to the bottom of the capillary,let bl be the height of salt solution in container B, and let c be the
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Figure 1. Stationary state wllh capillary full of salt solution from 6, which Is 25% more dense than water in A.
Flgure 2. Statlonary state for the same system except capillary is full of water from resewolr.
length of capillary C. The balance of pressures is described
ate Dosition in the caoillaw and with the level in B such that pressures precisely balanced at the mouth of the capillary. However, such an intermediate stationary state would he unstable to fluctuations in either direction.. Any fluctuation would cause the boundary to move to one end or the other of the capillary, and flow through that capillary would then cause the system as a whole to evolve either toward state 1or state 2. I t should not he necessary t o point out that this system is not a oeroetual motion machine. Everv time solution flows from B to A during approach tu state i, d, increases. Every time the flow is from A to B during approach to state 2, d, decreases. Free energy is decreasing monotonirally regardlessof thedirection ofsuch flow, and the final state is that of uniform compoiition everywhere. Although the analogy is not exact, this salt-water oscillator witha lenethof narrow caoillarvexhibits features~imilar to those t h a t a r e responsible for Lhemical oscillators. The Belousov-Zhabotinskv oscillatine reaction involves oxidation of an organic substrate like malonic acid by acidic bromate catalyzed by a redox couple such as Ce(III)/Ce(IV). The system exists temporarily in either an oxidized or in a reduced oseudo-steadv state and switches rapidlv from one to the other. The concentration of bromide-ion-in the reduced state is orders of magnitude greater than that in the oxidized state. Reactions in the reduced state consume bromide, and those in the oxidized state produce it; therefore, reactions in either state tend to create conditions that destroy the persistence of that state. At certain critical situations, the system jumps almost discontinuously between oxidized and reduced states. The mechanism has been presented in a review article (4), and many further details are presented in a recent book (5). However, the analogies are not exact. The chemical system can exist in one or the other of two dynamic hut pseudosteadv states, each of which either creates or destroys bromideion until that state becomes unstable with respect to the other one; then there is an almost discontinuous transi-
o,d, = b,d,
+ ed.
(1)
The capillary is full of fresh water in stationary state 2 in Figure 2. The balance of pressures is now described by equation 2. a,d, = b,d.
+ cd,
(2)
If the exposed surface of A is much larger than that of B, then al and a2 will he almost equal and bz will he larger than b,. In other words. the level of the fluid in B will be hieher when the capillary' is full of water from the reservoir than it will be when the caoillarv is full of the denser salt solution. Either of the twb stationary states could persist indefinitely if there were no fluctuations and if the extremely slow diffusion of salt across the mouth of the capillary could be neglected. If the system were started with fluid at about the same level in A and in B, the dense salt solution would flow through the capillary until state 1was attained. Then nothing more would happen in the absence of fluctuations. However, if even a small amount of fluid from A were to enter the mouth of the canillarv. the oressure in B and C would no longer be able tobalance that a t the same level in A. and water from the reservoir would flow uo the canillarv with an ever-increasing driving force. Once the capilla.ry wai full of water instead of salt solution, flow would persist until the level in B had risen to stationary state 2.1f the capillary were long enough and narrow enough that the flow generated negligibik momentum effects, theapproach to that stationary state would be monotonic. Stationary state 2 is also unstable to fluctuations. If alittle salt solution enters the top of the capillary from B, the increased oressure will cause an acceleratine flow until the capillary has been filled with salt solution. F ~ O Wfrom B will then continue until state 1has been attained azain. In principle, a stationary state could a ~ s o k x i s twith a boundary between water and salt solution at an intermedi208
Journal'of Chemical Education
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tion based on deterministic equations. The salt-water oscillator with a long and narrow capillary can exist in one or the other of two dynamic states depending upon whether the capillary is full of fresh water or of salt water. Either of those dvnamic states will evolve monotonicallv toward a state of ~~" true hydrostatic balance that could perkst indefinitely in the absence of anv fluctuations. However. fluctuations will cause the cornpoiition of the capillary td change and will initiate a move toward the other stationary state. ~~
~
~
~~
~
~
~
Osclllatlons wlthout a Capillary Figure 4 in the preceding paper by Yoshikawa e t al. (1) illustrates a modification of the salt-water oscillator that has also been discussed by Walker (6). This modification bears less analogy t o a purely chemical oscillator. The capillary C in our Figures 1and 2 has been replaced by apinhole or short pore in the bottom of container B. For any stationary state, the interface between fresh and salt water must exist in or more probably a t one end or the other of this pore. However, onlv a trivial difference of hvdrostatic Dressure will s e ~ a r a t e stationary states where the poreis filled with fresh water and withsalt water. In soiteofthisrmall difference, the system is a dramatic oscillat&! This oscillator has been discussed in more detail by Yoshikawa (7). Apparently the explanation of the oscillations must invoke persistence of momentum effects during flow through the pore. If the interface between salt and fresh water is inside container B near the bottom, the instability will cause the fresh water to rise and to draw more fresh water up from the reservoir instead of letting salt water creep into the pore behind it. This flow of fresh water upward through the pore will cause a rise of the level in the container B until hydrostatic pressure finally reverses the flow and causes salt water to flow downward through the pore. This dense salt water entering a reservoir of lighter fresh water willsinkinto that reservoir while the flow behind i t will persist until the level in the container B has fallen significantly. The salt-water oscillator based on a short pore in the bottom of container B resembles manv other mechanical oscillators including an almost undamped pendulum. The description of the system a t any time will require specification of both a coordinate and a momentum. Similarly, the descri~tionof the instantaneous state of an electrical oscillator wiil require specification of both a potential and a current. We are used to many examples of systems where description of instantaneous state requires specification of
both the value of a variable and also its simultaneous independent rate of change. Similar requirements arenot necessary for the description of chemical systems. If we know the exact composition of a chemical svstem a t some instant. we do not need anv independent specification of rate of change of compositibn. We believe that rate of chemical chanee is a unioue function of composition and is not independent of that composition. Therefore, the salt-water oscillator with only a short pore in the bottom of the container is not a good analogy of a chemical oscillator. However, the salt-water oscillator can be an excellent device for teaching some of the ways in which purely chemical oscillators far from equilibrium differ from mechanical oscillators. The preceding paper by Yoshikawa et al. also suggests an interesting electrochemical Droblem that I do not recall having seen i i any textbook of'physical chemistry. Oscillations are followed bv the difference in ~otentialof two electrodes each of which is specific t o chloriie concentration. The local environments a t those electrodes probably change only slowly when solution flows between A and B, but the potential undergoes dramatic shifts of 10's of millivolts. Those shifts must be due to changes in the junction potential generated at the interface between dilute and concentrated salt solution. I t is not clear whether the difference arises because the interface is concave or convex or whether some other explanation must be invoked. I t appears that the system described in the preceding paper illustrates some interesting principles of physical chemistry in addition to the oscillations the paper is primarily intended t o illustrate. Acknowledgment I am grateful to Kenichi Yoshikawa, Seelye Martin, and Leonard Soltzberg for very stimulating correspondence that has refined my own understanding of this interesting system. The studies that provided the background for the chemical part of this discussion were supported by the National Science Foundation. Literature Clted Ymhikawa, K.;NaLato,S.; Y a m d e , M.: Wa*i,T. J. Chem. E k . 1989,66,205-207. Martin. S. Oeophya.FiuidDynamira 1970.1,143-160. SVang, C. L. Sci. Am. 1970,225(3). 221-234. Field, R.J.; Novas, R. M. Am. Chem.Re8. 1977,10,214221.273-.280. Field, R. J. In Oaciliatia~and Pouoling Waws in Chemieoi Syatema; Field, R J.: B w w .M.. Eda.: Wiley: New York. 1985: pp55-92. 6. Walker, J. Sci. Am. 1977,237(4), 142150. 7. Yaahibwa. K. D y ~ m i r o Systems i and Applications; Aokl, N. Ed.; World Seienes: Singapore, 1987, pp 205-224.
1. 2. 3. 4, 5.
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