Niveles de glucemia

A chem ostat f i t t e d w ith some d e v ic e to in c re a s e th e biomass c o n c e n tra tio n above v a lu e s p o s s ib le in th e sim p le chem ostat, t h a t is Y ( S r - S ) , is term ed a chem ostat w ith feedback o f biom ass, H e rb e rt^ ® ; P i r t &

Kurowski .

A ccording to P ir t ^ ^ , th e c o n c e n tra tio n o f

biomass may be ach ieved in v a rio u s ways ( see F i g . 1 .2 .4 ;

( a ) , ( b ) , ( c ) , (d ) ) .

In system (a ) a c e l l - f r e e o r d i lu t e biomass stream is removed by f i l t r a t i o n and th e re is a ls o an o u t le t f o r th e c o n c e n tra te d biomass suspension. In system (b ) th e c u ltu r e is d iv id e d in to two zones, an a g ita te d homogeneous zone a t th e base where th e grow th occurs and, above th e b a f f le p la te , a s e d im e n ta tio n zone, v i r t u a l l y w ith o u t g ro w th , in which th e biomass can sedim ent and

re tu rn to th e a g ita t e d zone. Thus a c e l l - f r e e o r d i lu t e stream o f biomass le a v e s th e to p o f th e fe rm e n te r and th e c o n c e n tra te d biomass suspension lea ves from an o u t le t in t e grow th zone.

In th e "monostream" system (c ) i t is assumed t h a t th e biomass is c o n c e n tra te d by f i l t a t i o n o r s e d im e n ta tio n in th e o u t le t stream and th e r is no o u t le t f o r th e c o n c e n tra te d biom ass.

In system (d ) th e biomass is c o n c e n tra te d o u ts id e th e fe rm e n te r and th e c u ltu r e is s e p a ra te d in to two stream s o f biomass one d i lu t e and one c o n c e n tra te d ; a p a r t o f c o n c e n tra te d stream is fe d back to th e fe rm e n te r.

The systems ( a ) , (b ) and (c ) a re re p re s e n te d by in te r n a l feedback model and system (d ) by th e e x te rn a l feedback m odel. We w i l l c o n s id e r th e model d e p ic te d in F ig . 1 .2 .4 (d ) due to i t s d ir e c t r e la t io n s h ip w ith our work.

In system (d ) th e e f f lu e n t c u ltu r e is passed through a s e p a ra to r, f o r exam ple a c e n tr ifu g e , which c o n c e n tra te s th e biomass and produces both d i lu t e and c o n c e n tra te d stream s o f biom ass. P a rt o f th e c o n c e n tra te d stream is fe d back to th e c u ltu r e v e s s e l. The o v e r a ll d ilu t io n r a te is g iven by F/V = D where V is th e c u ltu r e volum e. The c u ltu r e o u tflo w r a te is g iven by th e e q u a tio n below , where a is th e f r a c t io n o f th e o u tflo w liq u id stream which is fe d b a c k .

F g = F + a F g (2 1 )

From e q u a tio n (2 1 ) i t fo llo w s th a t

h x s (1-c ) F (a) /fX Sedimentation zone Baffle plate Growth zone I---1 I--- - T c F %=0 Stirrer X (b) /?x Separator Stirrer (c) s ffx (d)

FIG 1 .2 .4 - V a rio u s systems f o r feedb ack o f biomass 1n a chem ostat: ( a ) In te r n a l f i l t r a t i o n ; (b ) In te r n a l s e d im e n ta tio n ; ( c ) monostream feed b ack; (d ) e x te rn a l fe e d b a c k . Symbols: F and Fg a re flo w r a te s ; x Is biomass c o n c e n tra tio n ; s and s^ a re grow th - lim it in g s u b s tra te c o n c e n tra tio n s and c , g and h a re c o n s ta n ts d1m ensionless.

The s e p a ra to r c o n c e n tra te s th e biomass by th e fa c to r g and s in c e th e amount o f biomass fe d back is agFg, i t can be seen t h a t ag is th e fr a c t io n o f biomass le a v in g th e fe rm e n te r, which is fe d back. The biomass balan ce f o r th e c u ltu r e is g iv e n by

N et grow th = grow th - o u tp u t + feedback which f o r th e whole c u ltu r e w i l l be

V .dx = V jux.dt - F g X .d t + a F g g x .d t (2 2 )

s u b s t itu tin g f o r Fg ( E q .2 1a ) and d iv id in g through by V .d t , e q u a tio n (2 2 ) becomes

d x /d t = AJX - D x /( 1 -a ) + ag D x/( 1 -a ) (2 3 ) and in s te a d y -s ta te when d x /d t = 0 we have

( AJ - pD )x = 0 (2 4 )

where p = ( 1-ag ) / ( 1 -a )

The f a c t o r p is a p o s it iv e f r a c t io n because 1 > ag > a .

I f ag = 1, i t would mean th a t a l l th e biomass is fe d back and th e re co uld no t be a s t e a d y -s ta te . In th e s te a d y -s ta te , ju = p o , th us ju < D.

S u b s titu tin g ju = P m ax'® /( s + K@ ) we o b ta in

s = pO Ks/( )Umax ~ PD ) (2 5 )

For th e g r o w th -lim itin g s u b s tra te b alan ce we have

n e t r a te = in p u t + feedback - o u tp u t - s u b s tra te

o f in c re a s e r a te r a te r a te u t i l i z e d

f o r grow th t h a t is , p er u n it o f volume

d s /d t =DSp + a D s /(1 - a ) - D s /( 1 -a ) - jUx/Y (2 6 ) w hich reduces to th e e q u a tio n f o r d s /d t in th e sim p le chem ostat th a t i s , d s /d t = D( s^ - s ) - Jjx/Y .

S u b s titu tin g ju = pD in t h a t e q u a tio n we o b ta in f o r th e s te a d y -s ta te o f x ;

s = ( Sp - s )Y /p (2 7 )