INTERACTION OF CR (VI) WITH GREEN MICROALGAE GROWTH: A COMPARATIVE STUDY - Biochemical Engineering - page 260

dn

= μ × n

(1)

dt

where μ is the specific growth rate of biomass (h -1 ), characteristic of each organism and
culture medium, and is primarily governed by the growth capacity of the organism and the
environmental conditions [8, 25]. This model assumes unlimited exponential growth.
However, in batch systems every population is limited either by lack of nutrients or
accumulation of toxic metabolites and then some allowance must be made to restrict the
growth [25]. Verhulst derived the logistic equation of population growth, sometimes called
Verhulst model, in 1845 [24], which is frequently presented as the initial form of a Riccati
equation:

dn ⎛ 1 ⎞

= μ × n × 1 − × n

⎝ ⎠

(2)

dt K

This equation can be easily integrated to obtain the logistic curve:

1

n = (3)

⎛ ⎞

1 1 1

−μ t

⎜ ⎟

− e +

n K K

⎝ ⎠

0

where n 0 is the initial biomass concentration (mg l -1 ) and K the maximum biomass
concentration (mg l -1 ). The logistic curve is sigmoidal and leads to a stationary population of
size K , i.e., for t =∞ , n = K .
The logistic equation perfectly describes the exponential and stationary growth phases,
but it does not include the initial lag phase and the decline phase. According to Krebs [27],
there are two ways of viewing the logistic curve. One is to view it as an empirical description
of how populations tend to grow in number when conditions are initially favourable. This is
the more general, more flexible viewpoint. The other way is to view the logistic model as an
implicit strict theory of population growth, as a “law” of population growth. This last one is,
perhaps, the one that interests us most.

3. Materials and Methods

3.1. Microalgae

Samples of Chlorella fusca ACOI 621, Chlorella vulgaris ACOI 879, Scenedesmus
acutus ACOI 538 and Scededesmus obliquus ACOI 550 strains, all chlorophyceae, were
obtained from stock cultures maintained by the Algal Culture Collection ACOI, Department
of Botany, University of Coimbra, Portugal. The genera Chlorella and Scenedesmus belong to
the order Chlorellales [22]. All species are unicellular green algae, without motion capacity.
Species from the Chlorella gender are spherical or ellipsoidal, exhibiting a simple life cycle