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medium 1b fed Into the culture vessel at a steady flow rate (F)

and culture emerges from It at the ease rate, an overflow device keeping the volume (V) of culture In the veeeel constant. A continuous-flow culture is therefore characterised "by its fractional rate of medium replacement or its dilution rate (D) which has the units of reciprocal time (h~^)i

D “ v (l.*.)

The reciprocal of D is the mean residence time which is defined as the average time an organism remains in the culture vessel. As the doubling time (tj) becomes longer there is a greater chance that an organism will be washed out of the chemoetat before it divides. The washout rate, that is, the rate at which organisms initially present in the culture vessel would be removed if growth

ceased but the flow continued, is described

by

dx

- 3T - »*

(1.5.)

l.tf.l.

3

In the culture vessel organisms are growing at a rate described

by equation (1.1.) and simultaneously being washed away at a rate

determined by equation (1.5«) so the net change in x with time is the sum of the growth and output of the cells*

increase ■ growth - output dx dt \tX - Dx Substituting equation (1.2.) f o rpt

a£ "x[F»ax(f ^ r ) ■ D]

(1.6.)

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is positive and the concentration of organises will Increase or if D > p , then A x / A t is negative and the concentration of organisms will decrease and will eventually washout. However, when p ■D, then A x / A t - 0 and x is constant so a steady state culture is obtained with the rate of new biomass production (growth) exactly balanced by the rate of biomass removal (washout).

l.it.l.h. C h a n g e s i n s u b s t r a t e c o n c e n t r a t i o n A s i m i l a r b a l a n c e e q u a t i o n c a n b e f o r m u l a t e d f o r t h e s u b s t r a t e c o n c e n t r a t i o n , s. A s s u m i n g t h a t t h e g r o w t h - l i m i t i n g s u b s t r a t e i s e n t e r i n g t h e c u l t u r e v e s s e l a t a c o n c e n t r a t i o n S R , b e i n g c o n s u m e d b y t h e o r g a n i s m s a n d f l o w i n g o u t a t a c o n c e n t r a t i o n s, t h e n e t r a t e o f c h a n g e o f s u b s t r a t e c o n c e n t r a t i o n 1st i n c r e a s e " i n p u t - o u t p u t - c o n s u m p t i o n H - DSR- D. - E (1.8.) Substituting equation (1.2) for pt

f t - » < V > - ^ < K ^ > (1.9.)

From equation (1.8.) it can be seen that if |OD, thends/dt is negative and the growth-limiting substrate concentration will decrease or if D > p , than ds/dt is positive and the growth-limiting substrate concentration will increase. However, when p-D, then ds/dt-0 and the growth-limiting substrate concentration is constant reaching a steady state value at the same time as the biomass concentration.

l.k.1.5* Substrate and organism concentrations under steady state conditions

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critical value (designated Dcrlt, see below),then unique values of x and s exist as the system will he in a steady state. Under these conditions dx/dt-0 and ds/dt-0 and the simultaneous equations (1.7.) and (1.9.) can be solved with steady state values of x and s being designated x and s respectively!

x - Y ( S r-£) (1.10.) • - ' . V B-D> (l.U.) “max Substituting s’ in equation (1.10. )* x - Y rsn-K./ D v~l (1.12.) From these equations it is possible to predict steady state organism and substrate concentrations in the chemostat for any value of D and concentration of inflowing substrate, provided that the values of the growth constants u _, K and Y are known. It

1 max s

can be seen that the chemostat has a self-adjusting capacity because D determines s (equation 1.11.) which itself determines p(equation 1.2.) so when D- psteady state conditions are restored. This self-

ad jtisting property results in stable growth conditions.

It is clear that D cannot be greater than Hmax so there is an

upper limit for D, which is nearly equal to designated

(the critical dilution rate). W h e n D O D ^ ^ non-steady state conditions are obtained and an exponential washout of the organisms occurs.

1.^.2. Departures from theory

The kinetics discussed above can usually account far the behaviour of chemostat cultures but exact agreement tends to be infrequent as the model is oversimplified and, therefore, must be modified in certain cases. For example, the yield factor (assumed by Monod

to be constant and independent of growth rate) say, in fact, vary with growth rate due to, for example, maintenance energy requirements, change of cell composition or change in efficiency of substrate

utilisation. Another variance may result from the effect of population densities due to the excretion of growth stimulatory or growth inhibitory substances. Deviations will also occur if, for example, the growth-limiting substrate is toxic at high D

values, if there is imperfect mixing or wall growth in the fermenter or if not all the organisms in a culture are viable.