MATERIALS AND METHODS
2.1 Microorganisms and culture
methods
The industrial DHA producing strains Schizochytrium sp.,Aurantiochytrium sp., and Thraustochytrium sp. were used
in this study and were obtained from the China Center for Type Culture
Collection, stored at -80 oC with 20% (v/v) glycerol.
The media and culture conditions were the same as in our previous
studies. The seed medium was artificial seawater supplemented with
glucose (50 g/L) and yeast extract (0.4 g/L). The fermentation medium
was artificial seawater containing 70 g/L glucose, 1 g/L yeast extract,
and 30 g/L glutamate [1].
Culture experiments in the laboratory were performed in 96-well plates.
The strains were inoculated in conventional microtiter plates and novel
bioreactors. The specific dimensions of the novel microplate are shown
in Figure 1 . The conventional 96-well plates are square or
circular cross-sectional microtiter plates commonly used in
laboratories.
2.2 Rheological measurement and Staining of
cells
To ensure the accuracy of the simulation, it is necessary to make
precise measurements of the rheological parameters of the liquid phase
[31-32]. Therefore, it is necessary to determine the density,
viscosity and surface tension of the fermentation broth ofSchizochytrium sp. The density was measured using the
density meter DM40, the viscosity was determined using the viscometer
ROTAVISC lo-vi, and the surface tension was analyzed using the tensile
meter k11. Because the biomass of microorganisms varies at different
stages of growth, rheological measurements of the organism are required
at each time point to obtain accurate rheological properties.
The staining of bacterial species was performed using Nile red staining
for intracellular lipid. 1 mg Nile red (MACKLIN) was dissolved in 10 mL
of acetone and stored away from light. A certain amount of culture
solution was mixed with dimethyl sulfoxide, then Nile red solution was
added and stained in the dark. The fluorescence intensity was measured
using a multifunctional microplate reader.
2.3 CFD simulation
All simulations were performed using ANSYS FLUENT software (ANSYS, USA).
ANSYS ICEM software was used to create the mesh and refine the model
boundaries to improve the accuracy of computer numerical calculations.
The medium was modeled as a Newtonian fluid with density and viscosity
based on the actual fermentation broth.
2.3.1 Model Settings
Two phases, liquid and gas, exist inside the microtiter plate and have a
clear distinct interface. In this study, the Volume of Fluid (VOF) model
was used to track the gas-liquid interface. This classic multiphase flow
model simulates non-mixing and distinct interfaces and has been used in
many studies to simulate the motion of vibrating bioreactors, proving to
be an effective method for fluid evaluation [33-34]. The rotational
motion of the microtiter plate drives the internal liquid to rotate,
leading to a gas-liquid interface with high strain rate and high
distortion. The RNG k-ε turbulent transport model is suitable for
describing the turbulent motion.
In order to improve the accuracy of the calculation process, such as the
influence of the model mesh number on the solution results, the mesh
size was established as 5.5×106 computational units.
Three interfacial compression levels were tested simultaneously to
simulate the air-liquid interface more realistically. The solver was set
to run for at least 5 seconds, and the average turbulent energy
dissipation rate was monitored to ensure that the simulation could reach
quasi-steady state.
2.3.2 Microtiter plate motion
model
The movement of the microplate is usually a rotary movement driven by
the device. In order to calculate the distribution of liquid in the case
of rotary motion, Buchs et al. described the movement of liquid as a
superposition of two motion processes: on the one hand, the liquid moves
in a circular motion with a certain radius; on the other hand, the
liquid rotates around the center of the microplate. These two movements
work together to make the liquid move periodically in a fixed direction.
Many studies used the dynamic grid method to simulate this movement, but
the dynamic grid requires mesh reconstruction at each step of the
calculation, resulting in a large amount of resource consumption and low
efficiency.
This paper used another way to simulate this motion process. The
movement of microtiter plates is mainly subjected to two forces: gravity
and centrifugal force. The movement of the microplate generates
centrifugal force, which drives the liquid to move, thus forming a
gas-liquid interface. Therefore, it can be assumed that the microplate
is stationary and the liquid rotates under a combination of periodic
centrifugal force and a gravitational force. Periodic centrifugal force
can be described in the following two equations [35]:
\begin{equation}
\begin{matrix}\text{\ \ F}_{x}=\omega^{2}\text{rcos}\left(\text{ωt}\right)\#\left(1\right)\\
\end{matrix}\nonumber \\
\end{equation}\begin{equation}
\begin{matrix}F_{y}=\omega^{2}\text{rsin}\left(\text{ωt}\right)\#\left(2\right)\\
\end{matrix}\nonumber \\
\end{equation}where ω is the angular velocity of the microplate rotation (rad/s), r is
the radius of rotation, which is 3mm, and t is the running duration (s).
2.3.3 Oxygen mass transfer
model
\begin{equation}
\begin{matrix}a=\frac{A}{V}\#\left(3\right)\\
\end{matrix}\nonumber \\
\end{equation}where A is the gas-liquid interface area (m2), V is
the volume of liquid (m3). There are many theories in
the literature for the calculation of the transfer coefficient
KL, and this paper used the minimum eddy model proposed
by Lamont and Scott [37]:
\begin{equation}
\begin{matrix}K_{L}=K\sqrt{D_{L}}\left(\frac{\varepsilon}{\vartheta}\right)\#\left(4\right)\\
\end{matrix}\nonumber \\
\end{equation}where K=0.4 is the model constant. DL is the diffusion
coefficient of oxygen at 25°C, and \(\vartheta\) is the kinematic
viscosity of the liquid. When oxygen mass transfer in the microplate
occurs at the gas-liquid interface, as oxygen mass transfer occurs at
the interface, the local averaged energy dissipation\(\varepsilon\ \)shows better agreement with reported experimental data
than volumetric averaged energy dissipation. So here, \(\varepsilon\) is
the face average energy dissipation rate at the gas-liquid interface.
2.2.4 Mixing model
Volume power input and average energy dissipation are key parameters for
microscale bioreactor mixing performance and fluid dynamics engineering
[38]. The average energy dissipation rate ε can be represented by
the following equation [39]:
\begin{equation}
\begin{matrix}\varepsilon=\frac{\mu\Phi\nu}{\rho}\#\left(5\right)\\
\end{matrix}\nonumber \\
\end{equation}Volumetric power consumption is based on the energy expended by fluid
motion and is expressed by the following equation [39]:
\begin{equation}
\begin{matrix}\frac{P}{V}=\frac{\int_{\vartheta}\mu\Phi_{v}\text{dV}}{V}\#\left(6\right)\\
\end{matrix}\nonumber \\
\end{equation}The μ in the above two equations is the kinematic viscosity of the
fluid, and Φν is the viscous dissipation function, which can be
expressed in the study using the shear rate [39]:
\begin{equation}
\Phi_{\nu}=2\left[\left(\frac{\partial\mu}{\partial x}\right)^{2}+\left(\frac{\partial v}{\partial y}\right)^{2}+\left(\frac{\partial w}{\partial z}\right)^{2}\right]\nonumber \\
\end{equation}\begin{equation}
\begin{matrix}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\left(\frac{\partial\mu}{\partial y}+\frac{\partial v}{\partial x}\right)^{2}+\left(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y}\right)^{2}+\left(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x}\right)^{2}\#\left(7\right)\\
\end{matrix}\nonumber \\
\end{equation}The above equation can be transiently followed by parameters such as
volumetric power input, interface area, oxygen mass transfer, etc.,
through which various indicators of microtiter plate vibration in the
orbit can be monitored in real-time.