968 Analyst, September, 1978, Vol. 103,pp. 968-972

Assessment of Mixing Efficiency Using the Oxidation of Iodide by Hydrogen Peroxide

T. J. N. Carter and B. R. Stanbridge Wol f son Research Laboratories, Queen Elizabeth Medical Centre, Edgbaston, Birmingham, B 16 2TH

-4 method of assessing mixing efficiency in spectrophotometric cells is described. The rate a t which iodide is oxidised by hydrogen peroxide, indicated by the time taken to consume a finite amount of thiosulphate, was found to be dependent on mixing efficiency in a system in which force of injection was the sole mixing mode. In the system studied it was shown that mixing to a total volume of 1 ml by injecting less than 0.5 ml is inadequate.

Keywords : iWixing e f ic iency ; iodide oxidat ion ; hydrogen peroxide ; reaction vate

Efficient mixing of the reactants in analytical processes is one of the most important require- ments for ensuring that acceptable accuracy and precision are obtained yet, as far as is known, no experimental data are available to illustrate the efficiency of mixing processes nor, hitherto, has any method of assessment been advanced. Most published mixing te~hnologyl-~ is specific for industrial applications in which relatively large volumes are involved.

In this laboratory, a requirement arose that high-speed mixing of two aqueous solutions in a spectrophotometric cuvette should be reliably achieved. Because of analytical con- straints, it was not possible to use conventional means such as physical shaking, rotating paddles or vibrating probes and, as mixing had to be achieved virtually instantaneously, mixing by force of injection was the only practicable solution. This paper describes an experimental approach to the quantitation of this form of mixing, which is often employed when using analytical equipment, notably in clinical chemistry.

The mechanisms of mixing in turbulent fields have been well discussed by B r ~ d k e y . ~ In essence, the principal process taking place, and the one that is primarily enhanced by mixing techniques, is dispersion, in which the ingredients are intermingled in as fine a blend as possible. The aggregates in this blend are, however, considerably larger than those at the molecular level. The other process involved, upon which reaction velocity ultimately depends, is molecular diffusion on the sub-microscopic scale, which is generally too slow to ensure maximum reaction rates unless the dispersion process, i.e., mixing, can create very fine blends upon which diffusion can act efficiently.

Thus, as mixing efficiency improves, the reaction rate will increase towards a maximum value, corresponding to nearly perfectly mixed reactants and beyond which improvements in mixing efficiency will have no further effect. It should therefore be possible to measure mixing efficiency by determining the time taken for a specified reaction to reach completion.

A suitable reaction for the assessment of mixing by force of injection is the thiosulphate- retarded oxidation of iodide by hydrogen peroxide. This reaction was chosen because the conditions can be arranged so as to give a sharp, easily measurable end-point as a simple quantitation of reaction rate.

Experimental Reagents

All reagents were of analytical-reagent grade.

Oxidation of Iodide by Hydrogen Peroxide Principle

The concentration of free iodine produced by the acid oxidation of excess of iodide with hydrogen peroxide [reaction (l)] is maintained at very low levels by reduction with a limited amount of thiosulphate until the latter is totally consumed [reaction (2)]. At this point, the

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CARTER AND STANBRIDGE 969

concentration of iodine increases rapidly, which is indicated by the formation of a blue complex with soluble starch [reaction (3)]. The time taken for the total consumption of thiosulphate will be dependent on the efficacy of dispersion of the reactants, i e . , of the mixing procedure.

21- + H,O, + 2H+ -+ I, + 2H,O . . .. - . (1)

41, + S,0,2- + 6H,O -+ 81- + 2SO,,- + 10H+ . . - (2)

I, + Soluble starch 3 Blue complex . . .. .. - - (3)

Procedure A plastic cuvette (10 x 10 mm) contained reagents as detailed in Table I to a total volume

of A ml. For the assessment of mixing efficiency these reagents were mixed, as described below, with B ml of the appropriate hydrogen peroxide solution, giving a final hydrogen peroxide concentration of 0.5% m/m. Volumes A and B ml were simultaneously and inversely varied in steps of 0.1 ml.

TABLE I DETAILS OF REAGENTS

In cuvette: 0.01 ml of 0.1 moll-l K,S,O,; 0.02 ml of 0.1 mol 1-1 KI; 0.02 ml of H,O; 0.05 ml of 1% m/m soluble starch; + 0.1 mol 1-1 H,SO, to a total volume of A ml.

Mixed volumes : Volume in cuvette Volume of H202 in Concentration of H,O, in

( A ) Iml syringe (B)/ml 0.1 moll-1 H,SO,, % m/m 0.9 0.1 5.00 0.8 0.2 2.50 0.7 0.3 1.67 0.6 0.4 1.25 0.5 0.5 1 .oo 0.4 0.6 0.83 0.3 0.7 0.71 0.2 0.8 0.63 0.1 0.9 0.55

Assessment of Mixing Efficiency EquiPment

The experimental arrangement, shown in Fig. 1, includes a “custom-built” powered syringe unit (Fig. 2). This utilised a disposable plastic syringe (1 or 2 ml; Gillette Industries Ltd., Isleworth, Middlesex), the plunger of which was driven between two adjustable stops (the “in” and “out” sensors) by a d.c. motor and lead-screw assembly, delivering a pre- determined volume of liquid. The precision of delivery was approximately 0.2% (coefficient of variation, C.V.) at 1 ml and 0.5% (C.V.) a t 0.1 ml. The rate of travel could be varied by means of a control unit and the time of travel between the sensors was measured with a Model 5302A Universal Counter (Hewlett-Packard, Santa Clara, Calif., USA). Hydrogen peroxide solution was stored in a reagent reservoir and the syringe was re-filled via a three- way valve. Liquid was ejected into the cuvette through a 0.7 mm i.d. stainless-steel injection tube, the tip of which was 10 mm from the cuvette base. A light-emitting diode (LED, Type MLED 850; Motorola Ltd., Wembley, Middlesex) and a photomultiplier tube (PMT, Type 9601B ; E M 1 Electronics Ltd., Electron Tube Division, Hayes, Middlesex! arranged on either side of the cuvette were used to monitor the absorbance of the solution. The PMT was supplied with high voltage by a Model 415B high-voltage supply (Fluke Mfg. Inc., Seattle, Wash., USA) and the resultant signal was amplified by a 741 operational amplifier (Texas Instruments Ltd., Bedford) and displayed on a potentiometric chart recorder.

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970 CARTER AND STANBRIDGE : ASSESSMENT OF MIXING EFFICIENCY AnaZyst, Vol. 103

3-Way valve

15-0-1 5-V power supply

L

- Fig. 1. Experimental arrangement. LED, light-emitting diode ; PMT, photomultiplier tube.

Procedure Before each run the syringe was calibrated, by mass, to deliver the required volume

(B ml, Table I) and iodide, thiosulphate, starch and sulphuric acid solutions were added to the cuvette ( A ml, Table I). The syringe was primed with the correct concentration of hydrogen peroxide and the speed of delivery set. The high voltage to the PMT was switched on and the LED current adjusted until the recorder pen was on the scale. The chart recorder (range 0-10 V, speed 10 mm s-l) was then started, injection initiated and the injection time displayed on the timer. After completion of the reaction, the time between initiation of the injection and the increase in absorbance were measured from the recorder chart. The range of injection velocities available was limited at the lower end by the inability of the motor, when running at low speeds, to overcome the syringe friction and at the higher end

Fig. 2. Powered syringe unit, showing syringe (A), lead screw (B) and follower (C), adjustable “in” (D) and “out” (E) sensors, flag (F) and motor (G).

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September, 1978 USING THE OXIDATION OF IODIDE BY HYDROGEN PEROXIDE 971 by its maximum torque. In practice, except a t very low injection volumes (less than 0.4 ml), the highest injection velocities were unsatisfactory owing to splashing of reagents out of the cuvet te .

Results The effect of injection velocity on mixing, as evidenced by reaction time, is shown in

Fig. 3 for injected volumes from 0.1 to 0.5 ml (using a l-ml syringe) and for volumes from 0.5 to 0.9ml (using a 2-ml syringe). In order to aid comparison, all reaction times for a particular injection volume have been expressed relative to the mean of the values a t the slowest injection speed for that volume. Three results for reaction time were obtained a t each injection velocity, but in the interests of clarity individual experimental results have been omitted and the curves represent the best line between the means.

Typical reproducibility is illustrated in Fig. 4, which shows three of these curves (for injected volumes of 0.2, 0.6 and 0.7 m1) together with the experimental points. As can be seen, poor agreement between triplicate values occurred occasionally, especially with injected volumes of less than 0.5 ml.

A plateau in reaction time, indicating good mixing, was achieved only for injected volumes greater than 0.5 ml. In most curves a discontinuity appeared at high injection speeds, corresponding to the point a t which splashing of the cuvette contents occurred. For injected volumes of 0.4 and 0.5 ml, splashing of the cuvette contents occurred before a plateau was reached. For all injected volumes greater than 0.3 ml, splashing occurred at high injection speeds and this generally occurred more readily a t higher injected volumes.

I I I I

0 1 2 3 4 -10'

Injection veIocity/mI s-'

Fig. 3. Effect of injection velocity on reaction time using a l-ml syringe (1-5) and a 2-ml syringe (6-10). Volumes injected: 1, 0.1; 2, 0.2; 3, 0.3; 4, 0.4; 5, 0.5; 6, 0.5; 7,0.6; 8, 0.7; 9, 0.8; and 10, 0.9 ml. In each instance the final volume was 1.0 ml.

Discussion In the system studied, it was shown that mixing to a total volume of 1 ml by injecting less

Above this volume the repeatability of results allowed adequate than 0.5 ml is inadequate.

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972 CARTER AND STANBRIDGE

+1 A

-IIt

A A

-10 I 1 I I 1

0 1 2 3 4

Injection veiocity/mi s-”

Fig. 4. Reproducibility of results. Curves 2, 7 and 8 from Fig. 3, together with individual experimental observations.

discrimination between curves for different injected volumes and hence a range of injection velocities can be deduced that give good mixing without splashing of the contents of the cuvette. The discontinuity in the curve shape at high injection velocity, corresponding to splashing, was unexpected, but allows the choice of injection velocity to be made more precisely. Splashing might be reduced by re-designing or re-positioning the injection nozzle; this method is, of course, applicable to the assessment of such effects on mixing efficiency.

While the general principle of assessing mixing efficiency from measurements of reaction rate may be considered to have been proved, its use as described was designed specifically for the development and evaluation of analytical equipment in clinical chemistry. It is possible that this method might have more general application in the investigation of mixing but it should be emphasised that no evaluation has been undertaken in any other system. Similarly, as the method was designed essentially as a practical method of assessing mixing, no theoretical treatment has been attempted, but this should not detract from the general validity or utility of conclusions that might be drawn from the method.

Mr. R. A. Bunce is thanked for the design and fabrication of the mechanical components used, and Professors T. P. Whitehead and R. Belcher for their advice and encouragement.

References 1. 2. 3. 4. 5.

Simpson, L. L., “Turbulence in Mixing Operations,” Academic Press, New York, 1973, p. 277. Toor, H. L., Ind. Engng Chem. Fundamentals, 1969, 8, 655. O’Brien, E. E., Phys. Fluids, 1971, 14, 1326. Corrsin, S., Phys. Fluids, 1964, 7, 1156. Brodkey, R. S., “Turbulence in Mixing Operations,” Academic Press, New York, 1973, p. 47.

Received December 14th, 1977 Accepted March 9th, 1978

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