Measurement of Small Volumetn'c Flow Rates in Small-Scale Chemostats INTRODUCTION Besides the working volume V in a chemostat, the influx of the nutrient medium V * into the bioreactor (also called the flow rate F) is crucial to quantitative analysis of the nutrient-controlled changes in the multiplying cell population.' The dilution rate D (the ratio of V' to V) connects these two values. Among other things, the constant influx V* is a prerequisite of steady-state chemostat conditions. But a constant V* often requires an additional measurement and control of the flow rate.* In research the analysis of unsteady-state conditions, such as shifts in the dilution rate: is also interesting. Here measurement and control of the flow rate are indispensable. In this paper two measuring devices for very low flow rates based on volumetric principles are introduced. The more simple device (method A) is sufficient for the condition of constant flow rate, whereas the more complicated device (method B) also meets the requirements for transient processes. MEASURING PRINCIPLES For normal requirements there are many ways of measuring the volumetric flow rate. But many of them are not suitable with small-scale chemostats, where all of the parts that are in contact with the medium have to be sterilized, and the flow rate is very low. Because of very small volumetric flow rates, the physical effects generated by the flowing fluid (e.g., pressure drop, drag force, induction, change of heat transfer coefficient, vortex shedding, etc.) are undetectably small and therefore unsuitable as measuring principles. Only two principles meet these requirements to a certain degree: the rotameter and the volumetric principle. Measurement of the Volumetric Flow Rate The rotameter is frequently used where great accuracy is not required, as it is a simple and robust instrument. There are important disadvantages compared with a volumetric design: the relation between the volumetric flow rate V" and the position of the float is nonlinear, and the position of the float depends on the density, pressure, temperature, and viscosity of the medium. Remote indication of the measuring value by a displacement transducer is complicated and difficult because additional correcting elements are necessary. Measurement of the Volumetric Flow Rate by Volumetric Principles In order to avoid the disadvantages of the rotameter, two methods according to the volumetric principles have been developed. The volume V of fixed measuring chambers (calibrated measuring tubes) and the time interval At, to fill or empty them, can be measured very accurately. Additionally we have a linear relationship between the time interval At and the volumetric flow rate V* and the result does not depend on density, pressure, temperature, and viscosity. Choosing a suitable measuring volume, small volume flows can be detected (down to V* = 10 mm3/sec). The main disadvantage is that continuous measurement is not possible. However, this disadvantage can be overlooked in many applications. Biotechnology and Bioengineering, Vol. XXII, Pp. 655-659 ( 1980) @ 1980 John Wiley & Sons, Inc. ooo6-3592/80/0022-0655$0 1.OO
656 BIOTECHNOLOGY AND BIOENGINEERING VOL. XXII (1980) Method A [Fig. l(a)] By a control device (CD) and a magnetic valve (MV) the volume V (= A.l) of the measuring chamber can be filled and emptied by a pump running at a constant speed. With the aid of two optical sensors (0s) and a float (F), the time At to empty can be measured exactly by a counter. Thus, the momentary mean volumetric flow rate V* can be determined in the calculating element C V* = V/At. It is obvious that this measurement is not a continuous one; the measuring value only appears at certain discrete times: meanwhile it has to be held in a sample- and hold-element (SH) and displayed at the meter (M), until a new value occurs. This measuring design is very accurate and can be easily realized by a small expense (e.g., in relay technique) in every laboratory. It suits stationary processes very well where disturbances are seldom and slow. For nonstationary processes, however, a new measuring value can appear too late to compensate for disturbances by the aid of a closedloop control system; the error would become too large. (b) Fig. 1. rates V. Two flow-rate measuring systems suitable for very low volumetric flow
COMMUNICATIONS TO THE EDITOR 657 A
658 BIOTECHNOLOGY AND BIOENGINEERING VOL. XXII (1980) Method B [Fig. l(b)] The disadvantage of method A-slow detection of changes in the volumetric flow rate-can be avoided if one measures the speed u (t) of the descending level of the fluid in the measuring volume V, since V*(t) = A.u(t). This is possible by the aid of an optical servo system (0s). where the speed n of the driving motor is proportional to the velocity u of the float; n can be measured accurately (SM). Calculation of the result V* is realized simular to method A. One obtains the true momentary volumetric flow rate V*(t), so this method can be applied to nonstationary processes. There is still some dead-time with this method during the filling of the measuring tube. Figure 2 is a signal flow diagram of this apparatus. showing that the feedback path is able to cause instabilities due to unsuitable design especially of the driving system D (hysteresis or looseness). Method B is costly but widely applicable. Both methods use optical servo systems with alternating infrared light. The influence of daylight can therefore be eliminated. Systematic measuring error is kept as low as 1%. CONCLUSION Method A (measurement of time to empty a definite volume) has been used in our laboratory for three years and has been found to be accurate and reliable to maintain a constant flow rate. But to perform defined shifts in the flow rate the deviaton times were too long. For this reason the measuring principle was improved by method B (measurement of the float speed). This device also meets the requirements of transient processes. It must be noted that for better control of the dilution rate (D) the control of the working volume (V) has to be improved. The classical syphon system is unsatisfactory due to its dependence on flow rate, gas hold-up, stirrer speed, foam, etc. Work is being performed at present in our laboratories to develop such a device for a better control of the working volume. Nomenclature A I, A1 n t, At U U V V* v* V*(t) area (m2) length, difference of length (m) speed (rpm) time, difference of time (sec) voltage (v) velocity (m/sec) volume ( m3) volumetric flow rate (m3/sec).volumetric mean flow rate (m3/sec) volumetric instantaneous fl~w rate (m3/sec) The authors wish to thank Dr. A. Fiechter and Dr. P. Profos for providing facilities in their laboratories and Dr. A. Einsele for helpful discussions. This work was supported by grants from the Swiss Federal Institute of Technology, Zurich. References 1. 1. Malek and Z. Fencl, Throrrticul und Methodologicul Basis of Continuous Culture (Academic Press. New York. 1966).
COMMUNICATIONS TO THE EDITOR 659 2. G. Platon, Methods in Microbiology, J. R. Morris and D. W. Ribbons, Eds. (Adacemic, New York, 1970). Vol. 2, pp. 229-241. 3. H. J. Kuhn, "Einfluss der Temperatur auf das Wachstum von Bacillus caldotrnax," Thesis, ETH No. 6435. Zurich, 1979. Department of Measurement and Control Chair of Microbiology Swiss Federal Institute of Technology CH 8 02 Zurich, Switzerland Accepted for Publication September 24, 1979 K. RUHM H. J. KUHN