impeller agitation rate, and include rotational speed (N) and impeller tip speed (πND).
Kobayashi et al. (1993) successfully used an impeller speed of 30 rpm in a train of 3
vessels, ranging in volume from 10 L to 500 L, for the cultivation of Aralia cordata
suspensions. Assuming geometric similarity between all three vessels, this corresponds to
almost a 4-fold increase in tip speed, moving from the smallest to the largest vessel.
Scragg et al. (1988) found cultures of C.roseus and Helianthus annus to be largely
resistant to tip speeds of up to 3.8 m s−^1 , for exposure times of up to 5 hours in a 3 L STR,
with negligible loss of viability on subsequent regrowth. However, suspensions of
Cinchona robusta and Tabernaemontana divaricata were growth-impaired at tip speeds
in excess of 0.6 m s−^1 , in a similar bioreactor (Meijer, 1989). Wu and Zhong (1999)
present evidence that ginseng suspensions can be cultivated without any loss of
productivity in a 2 L STR, equipped with a marine impeller, at tip speeds of 0.65 and 2.5
m s−^1. While appropriate for comparison purposes in a single vessel, neither impeller
rotational speed nor tip speed is suitable for characterising flow conditions across
different reactor/impeller geometries. As a scale-up parameter, it also should be noted
that, for geometrically similar vessels and assuming comparable aeration conditions,
constant impeller tip speed can be achieved only by a reduction in specific power input,
with consequent reductions in mass transfer coefficients. Moreover, examination of the
available data reveals that a comparatively narrow range of impeller tip speeds is
typically employed in pilot-and production-scale STRs (Table 14.4). Time-averaged
shear rates in a STR are frequently assumed to be proportional to N, although this simple
relationship does not hold under turbulent conditions. Relevant, system specific
expressions, for average and maximum shear rates are summarised by Chisti (1999) and
Thomas (1990). In ALRs, average shear rates ( ) are usually correlated with superficial
gas velocity (us), using expressions of the form:
(2)although values of K vary widely and the general applicability of the relationship may be
questionable. Characterisation of the intensity of the flow field in which plant cells are
suspended has also been undertaken in terms of both the time-averaged shear stresses,
and the so-called Reynolds stresses, associated with the very rapid fluctuations in
turbulent flow (e.g. Meijer, 1989; Dunlop et al., 1994). The Kolmogoroff length scale
approach has been usefully applied to mammalian cell systems (e.g. Croughan et al.,
1989) and, to a lesser extent, to plant cell suspensions (Dunlop et al., 1994; Huang et al.,
1998), but the larger dimensions of plant cells suggest that they may be more susceptible
to eddies in the inertial subrange.
Considering agitation alone, energy dissipation rates in a STR can be calculated as:
(3)where (P/V) is the specific power impeller input (W m−^3 ), based on an appropriate
volume, V, N is the impeller rational speed (s−^1 ), D is the impeller diameter (m) and Np is
the power number for the relevant impeller, at the prevailing Reynolds number. In the
high shear region surrounding the impeller, local turbulent energy dissipation rates may
Bioreactor design for plant cell suspension cultures 429