Biomedical Engineering Reference
In-Depth Information
14.1.2 Review of Literature
In 1911, Wager studied movement patterns of the flagellate
Euglena viridis
,
among others, and showed that the tendency to swim against gravity was nec-
essary for pattern formation among live organisms. In 1961, Platt coined the
name bioconvection for this hydrodynamic phenomenon, and noted for the
first time the analogy between thermoconvection (Benard convection) and
bioconvection. In 1970, Keller and Segel focused attention on this analogy in
analyzing the aggregation process of
Amoebae,
as well as the instability prob-
lems in homogeneous mechanical systems subject to two or more forces of
different types described by Chandrasekhar (1961). In the same year, Roberts
suggested that the principal cause for geotaxis in ciliates such as
Paramecium
is a hydrodynamic interaction between the microorganisms and the medium,
the magnitude of which is determined by the size and shape of the microor-
ganisms. He developed a general mathematical theory of geotaxis to describe
the motion of these organisms under gravity, and the predictions of the the-
ory were compared with measurements in suspensions of
Paramecia
in long,
vertical columns (Roberts 1970). In a later study, Roberts and Deacon (2002)
examined in more details the movement of gravitactic ciliates such as
Parame-
cium
(Roberts and Deacon 2002). They found that the shape-dependent ori-
entation plays an important role in the gravitactic responses of
Paramecium
.
The first bioconvective model of pattern formation was developed by Plesset
and Winet (1974) and Plesset and Whipple (1974) who explained the onset of
bioconvection by applying the theory of Rayleigh-Taylor instability, in which
the organism-rich sublayer is seen as a layer of dense fluid overlying a less
dense, deeper layer of fluid. They found that the wavelength of the most
rapidly growing mode agreed with the observed scale of the convection pat-
terns. They concluded that the Rayleigh-Taylor instability is the mechanism
for the observed bioconvection in
Tetrahymena pyriformis
culture (Figure
14.1) and may also explain the sedimentation patterns
(positive geotaxis)
in
other microorganism swarms in so far as they are not disturbed by surface
wind or by thermal gradients. In the Rayleigh-Taylor instability, the preferred
horizontal wavenumber is basically predicted by the upper layer thickness and
density difference regardless of the total depth of the container. The weak-
ness of this model is due to neglecting cell diffusion between two layers with
the result that the proposed basic state is not a solution of the governing
equations. In the same year, Winet and Jahn (1974) proposed the gravity-
propulsion theory of negative geotaxis of
T. pyriformis (hereafter referred to
as TP)
, suggesting that the negative geotactic orientation was a physical con-
sequence of the gyrational torque produced by geometrical asymmetry of the
microorganisms.
Childress et al. (1975) and Levandowsky et al. (1975) developed the
model of pattern formation of gravitactic microorganisms, based on the
Navier-Stokes equation and a diffusion-convection equation for motile
microorganisms, showing a remarkable analogy with Benard convection. They
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