Langmuir 1992,8, 2567-2571
2567
Oscillations of Electrical Potential Differences in the Salt-Water Oscillator S. Upadhyay, A. K. Das, V. Agarwala, and R. C. Srivastava’ Department of Chemistry, Banaras Hindu University, Varanasi 221005, India Received March 2,1992. In Final Form: May 28, 1992
The electricalpotential oscillationsobserved recentlyin the salt-water oscillatorhave been investigated. The data suggest that the electricalpotential oscillations may be due to oscillating streaming potentials. Bistable nature of the system has also been demonstrated.
Introduction Yoshikawa et al.1 based on Martin’s observation2 designed a salt-water oscillator with didactic intention of bringing home some of the concepta of nonlinear dynamics in a far from equilibrium condition. The experimental setup used was simple.’ It consisted of an open glass tube with a capillary attached at one end. To conduct the experiment an aqueous solution of sodium chloride was filled in the tube which was partially submerged in a bigger vessel containing distilled water such that the level of the liquids in the inner tube and in the outer vessel was the same. Due to the imbalance of the hydrostatic pressures, the salt solution begins to flow downwardwhich terminates after some time and then the upward flow of water from the outer vessel to the inner one through the capillary seta in. After some time the upward flow of water terminates and the downward flow of the salt solution begins again and so on. In addition to these oscillations i.e. flow of the fluid up and down which one can see with naked eye, the electrical potential difference across the AgJAgC1 electrodes introduced in the inner tube and in the outer vessel was also shown to oscillate with time. The duration of the oscillations depends on the concentration of salt solution taken in the inner tube. Noyee3while commenting on the oscillationsof electrical potential differences reported by Yoshikawa et al.l has remarked that “it suggesta an interesting electrochemical problem that I do not recall having seen in any text book of physical chemietry. The local environmentof AgJAgC1 electrodes changes only slowly as the liquids flow up and down between the inner and the outer vessels where.= the electrical potential shiftsdramatically”. Noyes3suggested that “these shifta in electrical potentials must be due to changes in junction potentials generated a t the interface between dilute and concentrated salt solution”. Noyes3 has further observed that “it is not clear whether the difference arisesbecause the interface is concave or convex or whether some other explanation must be invoked”. The investigations reported in the present communication which were prompted by the suggestions and comments made by Noyes draw attention toward another poeeibility. The data suggestthat the observed oscillations in electrical potential differences could be due to oscillations in streaming potential differences. Data have also been obtained to gain information on the bistable nature of the system.
* To whom correclpondence should be addreaeed.
(1) Ywhikawa,K.,Nhta,S.;Yamanaka,M.;Waki,T. J. Chem.Educ. 1989,66,206-207. ( 2 ) Martin, S . Geophye. Fluid Dyn. 1970,1, 143-160. (3)Noyea, R. M.J . Chem. Educ. 1989,66, 207-209.
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Figure 1. Schematic representation of the salt-water oscillator.
Experimental Section The electricalpotential oscillationswere monitored usingmore or less the same setup as used by Yoshikawa et al.’ except for a minor modification. The modification was only in having a narrow side tube C attached to the inner tube B. The setup is depicted in Figure 1. Aqueous solutions of salts of desired concentration were filled in the inner tube B through the side tube C. When the inner tube was completely fiied with the aqueous solution to the end of the capillary D, the side tube was sealed off with a stretched rubber membrane so that the aqueoue solution stays in the inner tube and does not flow out through the capillary. The inner tube filled with the aqueoussaltsolution was then hung into a bigger glass vessel, A, containing distilled water such that the level of the liquids in the inner tube and in the outer vessel was the same. The rubber membrane seal over the side tube C was then ruptured and the electrical potential difference acrossthe electrodes in the inner tube and in the outer vessel was recorded with time using an x-t recorder (Digital Electronics Model Omniscribe series 5OOO). Data on the bistable nature of the system were obtained using a specially designed glass cell shown in Figure 2. The volume flow J, induced by the pressure difference AP was measured in the presence of a constant density difference between the liquids in the inner tube B and in the outer vessel A. The bottom of the outer vessel which was made from a B-40socket was f i t removed. The inner tube B was then filled with the salt solution of desired concentration, and the stop cock S was closed so that the solution stands in the inner tube. The outer vessel whose bottom was then restored was filled with distilled water. Known pressure differences were applied using the pressure head attached to the
0743-7463/92/2408-2567$03.00/00 1992 American Chemical Society
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Capillary (dia = l m m )
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Figure 2. Glass cell used for bistability studies. cell (Figure 2) and consequent volume flow was measured by noting the rate of advancement of liquid miniscus in the capillary LIL2. The positions of the pressure head and that of the liquid meniscusin the capillaryLlL2were measuredwith acathetometer reading to 0.001 cm. Time was measured using a stopwatch reading to 0.1 s. After each run the cell was filled with fresh samples of the salt solution in the inner tube and water in the outer vessel to enforce the condition of constant density difference. All chemicals used in this study were of Anal& grade. Deionized water distilled twice in an all-Pyrex glass still was used for preparing solutions. The Ag/AgCl electrodes and the platinum electrodes used in the experimentawere obtained from M/s Elico, Ltd., Hyderabad. All experiments were performed at constant temperature using an air thermostat set at 30 f 0.2 O C .
Results and Discussion In this study the oscillations in the direction of the flow of the liquids through the capillary, i.e. up and down, are observed concomitant with the oscillations in electrical potential differences across the electrodes in the inner and the outer tube. The traces of electrical potential differences against time, shown particularly in Figures 4 and 5, are square waves which change between vertical and horizontal segmenta. If we start from the top, the horizontal segment occurs when the flow is taking place and the next vertical segment occurs when the direction of the flow is reversed, and so on. This is in agreement with the directions indicated by Yoshikawa et aL4in their more recent paper. There are two distinct questionsarising out of these observations. These are (i) why does the flow of liquid in the capillary oscillate up and down and (ii) why does the potential difference across the electrodes in the inner and the outer tube oscillate? Martin tried2 to explain the mechanism of the saltwater oscillator using a theory based on the Navier-Stokes equation. In a more recent paper Yoshikawa et al.? starting with the Navier-Stokes equation, have conducted a detailed study of the saline oscillator and shown, using numerical simulation based on a simple nonlinear differential equation, that it can serve as an example of a simple nonlinear dynamical system exhibiting various nonlinear characteristics such as limit cycle, bifurcation, and entrainment. YoshikawasSehas theoretically simulated the (4) Yoehikawa, K.; Oyama, N.; Shoji, M.; Nakata, S. Am. J. Phys. 1991,59,137-141. (5) Yoehikawa, K. Dynamical Systems and Applications, Aoki, N., Ed.;World Scientific: Singapore, 1987; pp 205-224. (6) Yoshikawa, K. Chem. Today (Gendai Kagaku) 1988,205,56-61.
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Figure 3. Inner tube of the oscillatorwith a U-shaped capillary.
oscillatory flow making use of the buoyant force due to density difference of the liquids in the inner tube and in the outer vessel. It has been shownH that the main driving force of the oscillations is not the osmotic pressure but the gravitational force due to density difference. To check this point further, experimentswere repeated with the inner tube whose capillaries were U-shaped (Figure3). Two such inner tubes were used-one in which the tip of the capillary was at the same level as the lower end of the inner tube and the other in which it was well below the lower end of the inner tube. Using both these tubes, experiments were conducted (i) when the level of the salt solution in the inner tube was the same as that of water in the outer tube so that the flow was from the inner tube to the outer and (ii) when it was much lower in the inner tube such that the flow was from the outer tube to the inner one. In none of these experiments were oscillationsobserved-neither the up and down movement of liquids nor oscillations in the electrical potential differences. Let us now examine the question of oscillations in electrical potential differences and the suggestions made by Noyes3 in this context. If as suggestedby Noyes3the shiftsin electrical potential differences, in the experiments of Yoshikawa et all were due to changes in liquid-liquid junction potentials generated at the interface between dilute and the concentrated salt solution, the effect should either not be observed in the case of potassium chloride or ita magnitude should be very small, because the transport numbers of potassium ion and chloride ion are very close to each other (-0.5). Further if the shifts in electricalpotential differences arise because the interface is concave or convex, then replacement of water in the outer vessel by an aqueoussurfactant solution of concentration equal to its critical micelle concentration should result either in cessation of the effect or in the amplitude of the electrical potential oscillations reducing considerably. The data obtained (Figures 4 and 5) do not corroborate the above expectations. The system with potassium chloride (1M) does show oscillationsof electricalpotential differences (Figure 4, curve a). Also in the experiments with sodium chloride (1 M) in the inner tube and the aqueoussolution of a surfactant,cetylpyridinium chloride in the present case, of concentration equal to its critical micelle concentration, in the outer vessel, oscillations of electrical potential differences were obtained. The amplitude of the oscillations when cetylpyridinium chloride solution was used in the outer vessel was comparable with those when water was used (Figure 4 curve b, Figure 5, curve a).
Electrical Potential Oscillations
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Figure 4. Traces of the oscillations of the electrical potential differences: (curve a) data using 1M KCl in the inner tube and bright platinum electrodes; (curve b) data using 1M NaCl in the inner tube and the surfactant (cetylpyridinium chloride) solution of concentration equal to ita critical micelle concentration (0.9 mM) in the outer vessel and Ag/AgCl electrodes; (curve c) data using 3 M NaCl in the inner tube and water in the outer, the Ag/AgCl electrode in the inner tube farthest away from the capillary mouth (just dipping into the solution); (curve d) data using 3 M NaCl in the inner tube and water in the outer, the inner Ag/AgCl electrode at the capillary mouth; (curve e) data using 3 M urea in the inner tube and water in the outer, and platinum electrodes.
However, we fully concur with Noyes that the differences in potentials of the two Ag/AgCl electrodes (Figure 1)are not because of the changes in chloride ion concentration in the neighborhood of the electrodes. To substantiate this, electrical potential differences were monitored when the Ag/AgCl electrode in the inner tube was placed very close to the mouth of the capillary and also when it was placed farthest away from the capillary mouth, i.e. when it was just dipping into the electrolyte solution in the inner tube. Although, the local ionic environment is expected to change more rapidly in the former situation than in the latter, the amplitudesof the electricalpotential oscillation were not much different in the two situations (Figure 4, curves c and d). In view of these observationswe make another proposal. We postulate that these oscillating electrical potentials are due to streaming potentials. The double layer is formed in the capillary. When liquids flow up and down, the mobile phase of the double layer is also carried along causing charge separation. The direction of the charge separation when the liquid moves upward would be opposite to that when the liquid moves downward and,
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Figure 5. Traces of electrical potential oscillationsusing sodium, barium, and aluminum chlorides: (curve a) data using 1M NaCl in the inner tube and water in the outer vessel and Ag/AgCl electrodes; (curve b) data using 1M BaC12 in the inner tube and water in the outer vessel and Ag/AgCl electrodes; (curve c) data using 1 M AlCls in the inner tube and water in the outer vessel and Ag/AgCl electrodes.
hence, oscillates. The following observations indicate favorably toward this surmise. Experiments similar to the salt-water oscillator were performed using benzene, cyclohexane, and bright platinum electrodes. The denser liquid benzene was put in the inner tube and the lighter liquid cyclohexane in the outer vessel. No electrical potential oscillations were observed, although one could see with the naked eye the flow of liquids up and down as in the case of the salt-water oscillator. This observation is consistent with the streaming potential hypothesisfor the occurrence of the electrical potential oscillations in the salt-water oscillator. With nonpolar substances like benzene and cyclohexane, formation of an electrical double layer in the glass capillary is not expected. In fact electro-osmosis or streaming potential effects with benzene/glass membrane or cyclohexane/glass membrane systems are not documented in literature. It may be mentioned that when the lighter liquid cyclohexanewas taken in the inner tube and benzene in the outer vessel, even the up and down movement of the liquids was not observed. This observation is consistent with the fact that the main driving force of the oscillations in the direction of the fluid (up and down movement) is the gravitational instability due to density difference.
Upadhyay et al.
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Figure6. Traces of electrical potential oscillationusing different concentrations of sodium chloride: (curve a) data using 2 M NaCl in the inner tube and water in the outer and platinum electrodes; (curve b) data using 1M NaCl in the inner tube and water in the outer and platinum electrode, (b') a portion of the curve obtained when liquid in the outer tube was stirred; (curve c) data using 0.5 M NaCl in the inner tube and water in the outer and platinum electrode; (curve d) data using 0.1 M NaCl in the inner tube and water in the outer and platinum electrode. Table I. Variation of Time Period of Electrical Potential Oscillations with Diameter of the Capillary. diameter of time diameter of time caoillarv (mm) Deriod (min) capillary (mm) period (min) 0.5 69.93 1.0 6.41 0.7
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Table 11. Variation of Time Period of Electrical Potential Oscillations with Length of the Capillary. length of time length of time capillary (cm) period (min) capillary (cm) period (min) 6.0 3.20 9.0 5.62 7.0 8.0
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4 Diameter of the capillary = 1 mm. Concentration of sodium chloride in the inner tube = 1 M. Experiments with aqueous urea (3M)in the inner tube and distilled water in the outer vessel also showed oscillations (Figure 4, curve e) in electrical potential
difference acrose the bright platinum electrodes inserted in the inner tube and the outer vessel. In the case of experimentswith urea solution, formation of an electrical double layer in the glass capillary is a real possibility. Experimentswere also performed with aluminum chloride and barium chloride in addition to sodium chloride. Amplitudes of the electrical potential oscillations were
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Figure 7. Plot of volume flow (4) against pressure difference AP in the presence of constant density difference: (a) 1M NaCl in the inner tube and water in the outer; (b) 0.05 M NaCl in the inner tube and water in the outer. found to be in the order (Figure 5 curves a, b and c)
aluminum chloride > barium chloride > sodium chloride, which is consistent with the proposed streaming potential hypothesis of the phenomenon based on the existence of an electrical double layer in the glaas capillary.' Stirringthe liquid in the outer vessel should impede the up and down movement of the liquids through the capillary. If the oscillations in the electrical potential difference are due to up and down displacement of the mobile phase of the double layer, stirring should considerably reduce the amplitude of the oscillations. This is what was actually observed (Figure 6, see portion b' of curve b). (7)Sheludko, A. Colloid Chemietry; Elsevier: Amsterdam, 1966.
Langmuit, Vol. 8, No. 10, 1992 2571
Electrical Potential Oscillations
Amplitude of the electrical potential oscillations did not show any significant variation with the length and diameter of the capillary. This observation is consistent with the expression for streaming potential S derived on the basis of a simple Helmholtz double layer in a single capillary. The expression reads as8
where P is the pressure difference, is the zeta potential, and D, 7,and K~ are respectively the dielectric constant, coefficient of viscosity, and specific conductance of the medium. If the electrical potential oscillations are due to oscillating streaming potentials, it is obvious from eq 1 that the amplitude of the oscillations should depend neither on the length nor on the diameter of the capillary. The time period of the oscillations, however, showed variations with both diameter and length of the capillary. The time period decreased with increase in the diameter of the capillary (Table I). This trend, which is in agreement with the observation of Yoshikawa et al.,l can be understood in terms of displacement of the mobile phase of the double layer. Since narrower capillaries offer more resistance to the flow of the liquids, longer time is required for the complete displacement of the mobile phase of the double layer. With increase in the length of the capillary, however, the time period showed an increasing trend (Table 11). This trend can also be understood in terms of displacement of the mobile phase of the double layer. Although the observations described above indicate favorably that the oscillations in electrical potential differences could be due to oscillatingstreaming potentials consequent to the oscillating up and down movement of the liquids, further studies, particularly on nonelectrolytic systems, are called for to finally decipher the issue. Bistable Nature of the System. The amplitude of the electricalpotential oscillations showed a decrease with the decrease in the concentration of the salt solution in the inner tube, and for sodium chloride it was found that (8) Glasstone, S . A n Introduction to Electrochemistry; Noetrand Company: New York, 1965; Chapter XVI, p 530.
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at concentrations equal to or lower than 0.1 M, no oscillations were observed (Figure 6 curves a, b, c, and d). The present system has two possible stationary states, one in which the capillary is filled with the salt solution and the other in which water fills the capillary.3 The oscillatory behavior consists of repeated transitions between these two stationary states. The data on volume flow J, induced by pressure difference AP in the presence of a constant density difference are plotted in Figure 7. Figure 7a represents the data for the case when the inner tube was filled with 1 M sodium chloride solution, the concentration at which oscillations are observed, whereas the curve in Figure 7b represents the data when the inner tube (Figure 2) was filled with 0.05 M sodium chloride solution, the concentration at which no oscillations are observed. Let us now consider the curve in Figure 7a. Segments AB and CD represent the stable states. Along AB the capillary (Figure 2) is filled with water and along CD it is filled with a solution of sodium chloride. Segment BC shown by dotted lines represents unstable states of the system which are inaccessible to experimental determinations. It can be seen that the state corresponding to J, = 0 lies in the unstable region represented by the segment BC. Even the slightest fluctuations would lead to the system switchingover to one of the stable states and, hence, oscillations. The nature of curve in Figure 7b for 0.05 M sodium chloride solution is similar to that of the curve in Figure 7a except that the state correspondingto J , = 0 lies on the stable segment A’B’ and hence no oscillations.
Acknowledgment. Thanks are due to the Council of Scientific and Industrial Research, New Delhi, for support. We are grateful to Professor R. P. Rastogi for bringing the very interesting work of Yoshikawa et al.’ to our notice and for encouragementand to Professor R. M. Noyes whose commenta3motivated us to undertake this study. Thanks are also due to anonymous reviewers for constructive criticism. Registry No. KC1,7447-40-7;NaCl, 7647-14-5;BaC12.1036137-2;A1C13,7446-70-0; cetylpyridinium chloride, 123-03-5;urea, 57-13-6.
