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Electrochemical methods in the study of the hydrodynamic drag reduction by high polymer additives
Elwbochimicr Acta, 1975, Vol. 20. pp. W-911.
Pergamon Press Printed in Great Britain
SHORT COMMUNICATION ELECTROCHEMICAL METHODS IN THE STUDY OF THE HYDRODYNAMIC DRAG REDUCTION BY HIGH POLYMER ADDITIVES* C. DESLOUIS,I. EPELBOIN,B. TRIBOLLETand L. Vnr
Groupe de Recherche no 4 du C.N.R.S. “‘Physique des Liquides et Electrochimie”, associe ci I’Universite Paris VI Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris Cedex 05, France (Received 8 December 1974)
It is now well-known in hydrodynamics that the injection into a turbulent flow of certain compounds having very high molecular weights gives rise to a damping of turbulence near the wall and to a hydrodynamic drag reduction which can reach 70 per cent in most favorable cases[l]. This effect, known as the Toms effect, is of high importance in chemical engineering and in ship-building, but it still remains rather unexplained. This is due in particular to the non-Newtonian behaviour of most polymer solutions which are used for drag reduction. For a Newtonian fluid, the shearing stress cXI where p the dynais d&ed by the relation T,~ = @“ay mic viscosity of liquid depends only on the temperature, and 8pJay is the shear rate. For a non-Newtonian solution of the Ostwald type, rXI depends on two rheological parameters K the fluid consistency and n the viscosity index and obeys the following power-law:
The polymer chosen for this study, the polyoxyethylene (polyox WSR 301-Union Carbide) is one of the most effective non-ionic polymers for drag reduction due to a long straight chain and a mean molecular weight of about 4 x 106. Studying the drag reduction by high polymer additives one meets with additional difficulties due to the fact that the coefficients K and n depend not only on the nature and concentration of polymer, but also on the antecedents of the solution in particular on the preparation conditions (temperature and stirring), mechanical stress imposed to the liquid and conservation time. For aqueous polyox solutions, we noted a trend with time towards a Newtonian behaviour after about 100 days[2]. Generally speaking, measurements by conventional hydrodynamic methods (Pitot tube, hot wire anemometer, laser velocimeter etc.) do not permit to measure the local drag at the wall. We have shown that it is possible, by using electrochemical methods to measure the local hydrodynamic drag at the wall without introducing a probe in the Row. and thereby to study very accurately the drag reduction effect of polymer additives[2,3]. This was possible thanks to the analogy which exists between the momentum transfer within the hydrodynamic boundary layer and the mass transport by convective diffusion within the limiting diffusion layer at the same wa11[4]. In order to control * Communication presented at the 25th Meeting of the SIE, Brighton, September 1974.
the hydrodynamic flow we used a rotating smooth platinum disc or ring electrode whose speed was measured by a stroboscope to nearly 1 percent. However the supporting electrolyte and the diffusing electroactive ions must allow the polymer to dissolve without chemical degradation. It is not convenient to use in that case a solution of high pH, as there has however been done by Hanratty et aI[S],Butson and Glass[6] to study the fluctuating mass transport coefficient in turbulent flow in presence of polymer additives, since polyethylene oxide is almost insoluble in alkaline media at room temperature. That is why we chose the reduction at 25 &- O,i”C of 10e3 M potassium ferricyanide in presence of equimolecular fcrrocyanide in a 1 N potassium chloride solution, deaerated by argon bubbling. This reaction is known to be fast on platinum electrode[7J It is worth noting that the polyox WSR 301 solutions in 1 N KC1 at room temperature are much more stable than aqueous solutions. There is indeed no change in the rheological parameters K and n at 25°C within the experimental errors, after several months for such a polymer, electrolyte solution prepared and kept at room temperature. This stability is doubtless due to a salt effect in electrolyte solution which decreases the dimensions of the aggregates in solution and therefore makes the molecular chains stronger. The current-potential curves were recorded by using a potentiostatic device. Besides, the electrode impedance was measured by means of a digital transfer function analyser under galvanostatic conditions[S]. The general shape of the current-potential curve for the ferricyanide ions reduction on rotating platinum disc electrode is not altered, when polyox WSR 301 is added[2]. However we have shown that the diision properties can be modified, according to the polymer concentration and the hydrodynamic conditions[2,3]. In fact the drag reduction can be observed for polymer concentrations lower than 40-50 w.ppm. which do not alter the limiting diffusion current in laminar flow i,. At these polymer concentrations the solution behaves as a Newtonian one, the kinematic viscosity Y and the molecular diffusion coefficient D keeping the same values mea. sured in the absence of polymer. In order to study the drag reduction produced by high polymer additives, we used a platinum rotating ring electrode, so that the whole electrode area were in turbulent flow. The width of the ring (4R = 01 mm) was very small in comparison with its mean diameter 2 Ro. With this electrode the thickness of the diffusion layer is much lower than with the disc at the same rotation speed, and the
SHORT
910
CQMMUNICATI~N
A 20wppm 0 40wppm
Fig. 1. Dimensionless diffusibn flux Sh = (J(R,)R,)/ (CJS) us Re = nR$v for a ring electrode (R,, = 40 mm, AR = C-l mm), for several WSR 301 polyox concentrations, in laminar and turbulent flows.
ditision current is characteristic of the phenomena occurring very near the surface. For such a ring, transport by axial convection is negligible in comparison with transport by radial convective diffusion. In addition, the influence of tangential convection is cancelled out. It has been shown that the diision flux J (R,) at the surface of such a thin ring is proportional to the cube root of the radial component F, of the hydrodynamic drag at the surface[9): 3 (27g 1 J(R,)=-p--2 (9/p l-(4/3)
c p/3 ,QU3p/3 m
where r is the gamma function and C, the bulk concentration with F, = &W’,/8y)R, 2n R,, AR, and t,,? = .~((aV,/ay) is the radial component of the shearing stress at the ring surface. As an example the Fig. 1 presents the limiting diffusion flux, expressed in terms of the dimensionless Sherwood number Sh = [.l(R,)R,]/[C,mDS] us the Reynolds number Re = @R,‘)/(v), for a ring for which R,, = 40mm, AR = 0.1 mm and for low polymer concentrations (<4@ 50 w.ppm). In laminar flow (Re < 2.5 x 105), the diffusion flux is not altered for such low polymer concentrations and follows the Levich law. On the other hand, in turbulent flow (RE > 2.5 x IO’) the addition of polyox, even at very low concentrations, markedly decreases the limiting diffusion current. This one is then proportional to Rex, where X is an exponent depending on polymer concentration. This exponent X, as calculated by a least squares method, decreases from 0.73 to 06~@6&0.56 and 0.53 when the polymer concentration increases from 0 to 5, 10, 20 and 40 w.ppm respectively. The value X = 0.73 obtained in 1 N KC1 solution without polymer is somewhat higher than the value X = 0.60 theoretically found in the expression of the diflusion flux in turbulent flow for a thin ring[9]. This difference can be due to a small contribution of turbulent diffusion in absence of polymer to the measured diffusion flux, which is not taken into account in the theory for a thin ring. These experiments under steady state conditions show that at some polyox WSR 301 concentration, close to 4G 50 w.ppm, the limiting diffusion current in turbulent flow is the same as that it would be, if the laminar flow was maintained beyond the critical Reynolds number Rq, which marks the transition from laminar to turbulent flow in absence of polymer. The variation of the exponent X shows that the flow in the diffusion boundary layer is progressively changed
from turbulent to nearly laminar flow, when the polymer concentration increases from 0 to 40 w.ppm, this effect decreasing by the same way the contribution of the residual turbulent diffusion to the diffusion flux. The value of the limiting diffusion current can give an estimation of the average thickness of the Nernst molecular diffusion layer at the wall. For example, at Re = I@, and for a polyox concentration of 40 w.ppm this thickness is about @6 x 10-j mm[Z]. The VISCOUS sublayer thickness is perhaps hundred times larger. Such low values for the boundary-layer thickness in presence of polymer, explain why it is not possible to measure the drag reduction at such a distance from the wall, by introducing a classical probe which perturbs the flow near the wall. From the values of the ditfusion current in turbulent flow, we can so deduce in first approximation the radial component ~2;:: of the local drag for a polyox concentration C, m. The high sensitivity of this electrochemical method allows the measurement of the local drag reduction at very low polymer concentrations. As an example, the Fig. 2 shows the variation of the local friction co&cient
with the Reynolds number for a thin ring (R~I = 40 mm, AR = 0.1 mm), and for 1 and 0.5 weight ppm polyox WSR 301. To our knowledge, no ofher method ever allowed one to measure the variation of the local drag in external turbulent flow, at such low polymer concentrations. We have also plotted the impedance diagram at the halfwave potential for the redox system 10e3 M ferri-ferrocyanide in 1 N potassium chloride at 25”C, using a platinum ring electrode (R, = 34 mm, AR = O-l mm)[3]. In laminar flow, (here Re = 2.6 x 1O4),the general shape of the impedance diagram is not altered by the addition of IO ppm polyox, except for a slight shift of the experimental points towards low frequencies. Consequently the diffusion conditions are not modiied. The shape of the diagram at high frequencies indicates that the reaction rate remains very high with respect to convective diffusion. The Fig. 3 shows that on the contrary in turbulent flow, (here Re = 5 x 105), the impedance diagram is markedly altered by the addition of some ppm of polymer. The intercept of the diagram with the real axis at low frequencies is the more shifted as the polymer concentration increases. This confirms that the presence of polymer modiies the diffusion conditions in the boundary layer in turbulent flow. Here again there is a shift of the experimental points towards low frequencies as the polymer concentration increases. ” owppm 0 05wppm 0 lwppm
Fig. 2. Friction coefficient on a thin ring (Ro = 4Onun, AR = O-l mm) vs the Reynolds number, for very low polyox WSR 301 concentrations.
SHORT COMMUNICATION
911
o40wppm Swppm f Owppm
l
R mm.
Fig. 3. Impedance diagrams of a platinum thin ring electrode (Ro = 34mm, AR = 0.1 mm) located inturbulentflow(Re = nR$v = 5.1 x 1O5).Recordedattbehalf-wavepotentialoftheredoxsystem IOm3M potassium Ferri-Ferrocyanide in 1 N potassium chloride at 25°C for a polyox WSR 301 concentration C = 0. 5, 40ppm.
These two Impedance diagrams are quite in agreement with diffusion current measurements performed under steady state conditions. These two methods show up that there is a difference between the behaviours of the diffusion layer in laminar and in turbulent flow in the presence of polymer. This difference is not only due to a variation of the di@usion layer thickness with the flow velocity, but must very likely be related to the mechanism of the hydrodynamic drag reduction itself. Certain authors assume in fact that polymer molecules in solution can form aggregates at zero and at low velocity gradients, but take chain configurations at very high velocity gradients in turbulent flow[1&12]. To conclude, we may hope that further quantitative study of impedance diagrams for a disc or a ring electrode will certainly allow us to determine whether there is an adsorption of polymer at the interface, and thereby provide new information on the mechanism of drag reduction in turbulent flow.
RE,FERENCES 1. J. W. Hoyt, J. bas. Engng. Trans. ASME, serie D, 94. 258, 1972.
2. C. Deslouis, I. Epelboin, B. Tribollet and L. Vie< Colloque Inr. CNRS “poly&rrs et lubrzjkation” Brest, May 1974. 3. C. Deslouis, I. Epelboin, B. Tribollet and L. Viet, C.r. h&d. .%a~. Acad. Sci, Paris T. 277-S&e C-353, 1973. 4. V. Levich. Pltysicochemicaf Hydrodynamics. Prentice Hall, N.J. 1962. 5. G. Fortuna and J. Hanratty, J. Fluid Mech. 53. 575, 1972. 6. J. Butson and D. H. Glass, rnt. Confi on drag reduction BHRA. Cambridge, 1974. 7. J. Kuta and E. Yeager, Extended abstract 198 Congris CITCE p. 116 Dttroit 1968. 8. C. Gabrielli, Th&e d’8tat Paris (1973) M&ux, corrosion industrie no. 573, 574, 577, 578, 1973. 9. C. Deslouis and M. Keddam, int. J. Heat Mass Transj& 16, 1763, 1973. IO. J. H. Hand and M. C. Williams, Nature 227, 5256, 369, July 25 1970. Symposium Series Drag Reduction 67 6. 111, 1971. 11. Ph. Grammain and Ph. Philippides, Colloque Int. CNRS PolymPres et Lubrijication May 1974 Brest (in press). 12. E. J. Hincb Colloqur Int. CNRS Polymkes et Lube@carion May 1974 Brest (in press).
Pergamon Press Printed in Great Britain
SHORT COMMUNICATION ELECTROCHEMICAL METHODS IN THE STUDY OF THE HYDRODYNAMIC DRAG REDUCTION BY HIGH POLYMER ADDITIVES* C. DESLOUIS,I. EPELBOIN,B. TRIBOLLETand L. Vnr
Groupe de Recherche no 4 du C.N.R.S. “‘Physique des Liquides et Electrochimie”, associe ci I’Universite Paris VI Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris Cedex 05, France (Received 8 December 1974)
It is now well-known in hydrodynamics that the injection into a turbulent flow of certain compounds having very high molecular weights gives rise to a damping of turbulence near the wall and to a hydrodynamic drag reduction which can reach 70 per cent in most favorable cases[l]. This effect, known as the Toms effect, is of high importance in chemical engineering and in ship-building, but it still remains rather unexplained. This is due in particular to the non-Newtonian behaviour of most polymer solutions which are used for drag reduction. For a Newtonian fluid, the shearing stress cXI where p the dynais d&ed by the relation T,~ = @“ay mic viscosity of liquid depends only on the temperature, and 8pJay is the shear rate. For a non-Newtonian solution of the Ostwald type, rXI depends on two rheological parameters K the fluid consistency and n the viscosity index and obeys the following power-law:
The polymer chosen for this study, the polyoxyethylene (polyox WSR 301-Union Carbide) is one of the most effective non-ionic polymers for drag reduction due to a long straight chain and a mean molecular weight of about 4 x 106. Studying the drag reduction by high polymer additives one meets with additional difficulties due to the fact that the coefficients K and n depend not only on the nature and concentration of polymer, but also on the antecedents of the solution in particular on the preparation conditions (temperature and stirring), mechanical stress imposed to the liquid and conservation time. For aqueous polyox solutions, we noted a trend with time towards a Newtonian behaviour after about 100 days[2]. Generally speaking, measurements by conventional hydrodynamic methods (Pitot tube, hot wire anemometer, laser velocimeter etc.) do not permit to measure the local drag at the wall. We have shown that it is possible, by using electrochemical methods to measure the local hydrodynamic drag at the wall without introducing a probe in the Row. and thereby to study very accurately the drag reduction effect of polymer additives[2,3]. This was possible thanks to the analogy which exists between the momentum transfer within the hydrodynamic boundary layer and the mass transport by convective diffusion within the limiting diffusion layer at the same wa11[4]. In order to control * Communication presented at the 25th Meeting of the SIE, Brighton, September 1974.
the hydrodynamic flow we used a rotating smooth platinum disc or ring electrode whose speed was measured by a stroboscope to nearly 1 percent. However the supporting electrolyte and the diffusing electroactive ions must allow the polymer to dissolve without chemical degradation. It is not convenient to use in that case a solution of high pH, as there has however been done by Hanratty et aI[S],Butson and Glass[6] to study the fluctuating mass transport coefficient in turbulent flow in presence of polymer additives, since polyethylene oxide is almost insoluble in alkaline media at room temperature. That is why we chose the reduction at 25 &- O,i”C of 10e3 M potassium ferricyanide in presence of equimolecular fcrrocyanide in a 1 N potassium chloride solution, deaerated by argon bubbling. This reaction is known to be fast on platinum electrode[7J It is worth noting that the polyox WSR 301 solutions in 1 N KC1 at room temperature are much more stable than aqueous solutions. There is indeed no change in the rheological parameters K and n at 25°C within the experimental errors, after several months for such a polymer, electrolyte solution prepared and kept at room temperature. This stability is doubtless due to a salt effect in electrolyte solution which decreases the dimensions of the aggregates in solution and therefore makes the molecular chains stronger. The current-potential curves were recorded by using a potentiostatic device. Besides, the electrode impedance was measured by means of a digital transfer function analyser under galvanostatic conditions[S]. The general shape of the current-potential curve for the ferricyanide ions reduction on rotating platinum disc electrode is not altered, when polyox WSR 301 is added[2]. However we have shown that the diision properties can be modified, according to the polymer concentration and the hydrodynamic conditions[2,3]. In fact the drag reduction can be observed for polymer concentrations lower than 40-50 w.ppm. which do not alter the limiting diffusion current in laminar flow i,. At these polymer concentrations the solution behaves as a Newtonian one, the kinematic viscosity Y and the molecular diffusion coefficient D keeping the same values mea. sured in the absence of polymer. In order to study the drag reduction produced by high polymer additives, we used a platinum rotating ring electrode, so that the whole electrode area were in turbulent flow. The width of the ring (4R = 01 mm) was very small in comparison with its mean diameter 2 Ro. With this electrode the thickness of the diffusion layer is much lower than with the disc at the same rotation speed, and the
SHORT
910
CQMMUNICATI~N
A 20wppm 0 40wppm
Fig. 1. Dimensionless diffusibn flux Sh = (J(R,)R,)/ (CJS) us Re = nR$v for a ring electrode (R,, = 40 mm, AR = C-l mm), for several WSR 301 polyox concentrations, in laminar and turbulent flows.
ditision current is characteristic of the phenomena occurring very near the surface. For such a ring, transport by axial convection is negligible in comparison with transport by radial convective diffusion. In addition, the influence of tangential convection is cancelled out. It has been shown that the diision flux J (R,) at the surface of such a thin ring is proportional to the cube root of the radial component F, of the hydrodynamic drag at the surface[9): 3 (27g 1 J(R,)=-p--2 (9/p l-(4/3)
c p/3 ,QU3p/3 m
where r is the gamma function and C, the bulk concentration with F, = &W’,/8y)R, 2n R,, AR, and t,,? = .~((aV,/ay) is the radial component of the shearing stress at the ring surface. As an example the Fig. 1 presents the limiting diffusion flux, expressed in terms of the dimensionless Sherwood number Sh = [.l(R,)R,]/[C,mDS] us the Reynolds number Re = @R,‘)/(v), for a ring for which R,, = 40mm, AR = 0.1 mm and for low polymer concentrations (<4@ 50 w.ppm). In laminar flow (Re < 2.5 x 105), the diffusion flux is not altered for such low polymer concentrations and follows the Levich law. On the other hand, in turbulent flow (RE > 2.5 x IO’) the addition of polyox, even at very low concentrations, markedly decreases the limiting diffusion current. This one is then proportional to Rex, where X is an exponent depending on polymer concentration. This exponent X, as calculated by a least squares method, decreases from 0.73 to 06~@6&0.56 and 0.53 when the polymer concentration increases from 0 to 5, 10, 20 and 40 w.ppm respectively. The value X = 0.73 obtained in 1 N KC1 solution without polymer is somewhat higher than the value X = 0.60 theoretically found in the expression of the diflusion flux in turbulent flow for a thin ring[9]. This difference can be due to a small contribution of turbulent diffusion in absence of polymer to the measured diffusion flux, which is not taken into account in the theory for a thin ring. These experiments under steady state conditions show that at some polyox WSR 301 concentration, close to 4G 50 w.ppm, the limiting diffusion current in turbulent flow is the same as that it would be, if the laminar flow was maintained beyond the critical Reynolds number Rq, which marks the transition from laminar to turbulent flow in absence of polymer. The variation of the exponent X shows that the flow in the diffusion boundary layer is progressively changed
from turbulent to nearly laminar flow, when the polymer concentration increases from 0 to 40 w.ppm, this effect decreasing by the same way the contribution of the residual turbulent diffusion to the diffusion flux. The value of the limiting diffusion current can give an estimation of the average thickness of the Nernst molecular diffusion layer at the wall. For example, at Re = I@, and for a polyox concentration of 40 w.ppm this thickness is about @6 x 10-j mm[Z]. The VISCOUS sublayer thickness is perhaps hundred times larger. Such low values for the boundary-layer thickness in presence of polymer, explain why it is not possible to measure the drag reduction at such a distance from the wall, by introducing a classical probe which perturbs the flow near the wall. From the values of the ditfusion current in turbulent flow, we can so deduce in first approximation the radial component ~2;:: of the local drag for a polyox concentration C, m. The high sensitivity of this electrochemical method allows the measurement of the local drag reduction at very low polymer concentrations. As an example, the Fig. 2 shows the variation of the local friction co&cient
with the Reynolds number for a thin ring (R~I = 40 mm, AR = 0.1 mm), and for 1 and 0.5 weight ppm polyox WSR 301. To our knowledge, no ofher method ever allowed one to measure the variation of the local drag in external turbulent flow, at such low polymer concentrations. We have also plotted the impedance diagram at the halfwave potential for the redox system 10e3 M ferri-ferrocyanide in 1 N potassium chloride at 25”C, using a platinum ring electrode (R, = 34 mm, AR = O-l mm)[3]. In laminar flow, (here Re = 2.6 x 1O4),the general shape of the impedance diagram is not altered by the addition of IO ppm polyox, except for a slight shift of the experimental points towards low frequencies. Consequently the diffusion conditions are not modiied. The shape of the diagram at high frequencies indicates that the reaction rate remains very high with respect to convective diffusion. The Fig. 3 shows that on the contrary in turbulent flow, (here Re = 5 x 105), the impedance diagram is markedly altered by the addition of some ppm of polymer. The intercept of the diagram with the real axis at low frequencies is the more shifted as the polymer concentration increases. This confirms that the presence of polymer modiies the diffusion conditions in the boundary layer in turbulent flow. Here again there is a shift of the experimental points towards low frequencies as the polymer concentration increases. ” owppm 0 05wppm 0 lwppm
Fig. 2. Friction coefficient on a thin ring (Ro = 4Onun, AR = O-l mm) vs the Reynolds number, for very low polyox WSR 301 concentrations.
SHORT COMMUNICATION
911
o40wppm Swppm f Owppm
l
R mm.
Fig. 3. Impedance diagrams of a platinum thin ring electrode (Ro = 34mm, AR = 0.1 mm) located inturbulentflow(Re = nR$v = 5.1 x 1O5).Recordedattbehalf-wavepotentialoftheredoxsystem IOm3M potassium Ferri-Ferrocyanide in 1 N potassium chloride at 25°C for a polyox WSR 301 concentration C = 0. 5, 40ppm.
These two Impedance diagrams are quite in agreement with diffusion current measurements performed under steady state conditions. These two methods show up that there is a difference between the behaviours of the diffusion layer in laminar and in turbulent flow in the presence of polymer. This difference is not only due to a variation of the di@usion layer thickness with the flow velocity, but must very likely be related to the mechanism of the hydrodynamic drag reduction itself. Certain authors assume in fact that polymer molecules in solution can form aggregates at zero and at low velocity gradients, but take chain configurations at very high velocity gradients in turbulent flow[1&12]. To conclude, we may hope that further quantitative study of impedance diagrams for a disc or a ring electrode will certainly allow us to determine whether there is an adsorption of polymer at the interface, and thereby provide new information on the mechanism of drag reduction in turbulent flow.
RE,FERENCES 1. J. W. Hoyt, J. bas. Engng. Trans. ASME, serie D, 94. 258, 1972.
2. C. Deslouis, I. Epelboin, B. Tribollet and L. Vie< Colloque Inr. CNRS “poly&rrs et lubrzjkation” Brest, May 1974. 3. C. Deslouis, I. Epelboin, B. Tribollet and L. Viet, C.r. h&d. .%a~. Acad. Sci, Paris T. 277-S&e C-353, 1973. 4. V. Levich. Pltysicochemicaf Hydrodynamics. Prentice Hall, N.J. 1962. 5. G. Fortuna and J. Hanratty, J. Fluid Mech. 53. 575, 1972. 6. J. Butson and D. H. Glass, rnt. Confi on drag reduction BHRA. Cambridge, 1974. 7. J. Kuta and E. Yeager, Extended abstract 198 Congris CITCE p. 116 Dttroit 1968. 8. C. Gabrielli, Th&e d’8tat Paris (1973) M&ux, corrosion industrie no. 573, 574, 577, 578, 1973. 9. C. Deslouis and M. Keddam, int. J. Heat Mass Transj& 16, 1763, 1973. IO. J. H. Hand and M. C. Williams, Nature 227, 5256, 369, July 25 1970. Symposium Series Drag Reduction 67 6. 111, 1971. 11. Ph. Grammain and Ph. Philippides, Colloque Int. CNRS PolymPres et Lubrijication May 1974 Brest (in press). 12. E. J. Hincb Colloqur Int. CNRS Polymkes et Lube@carion May 1974 Brest (in press).