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.