Table 1.
Declaration of the variables used in the equations.
Fig 1.
Schematic illustration of the working principles of the centrifuge (left), clinostat (middle) and Random Positioning Machine (RPM, right).
Centrifuges are used for hypergravity experiments. Thereby, the sample (red dot) is rotated around a vertical axis within a certain radius from the axis. Clinostats and RPMs are used for simulated microgravity experiments. Whereas the clinostat rotates the samples around one horizontal axis, the RPM rotates the samples around two perpendicular axes.
Fig 2.
Velocity profile during one period on the RPM.
Both frames rotate with constant and equal velocity; the flask is placed at the center of rotation. The rotational velocity is 60 deg/s. The time interval between the illustrations is 1 second (top left: 0 s; top middle: 1 s; top right: 2 s; bottom left: 3 s; bottom middle: 4 s; bottom right: 5 s).
Fig 3.
Shear stresses along the walls during one period on the RPM.
Both frames rotate with constant and equal velocity; the flask is placed at the center of rotation. The rotational velocity is 60 deg/s. The time interval between the illustrations is 1 second (top left: 0 s; top middle: 1 s; top right: 2 s; bottom left: 3 s; bottom middle: 4 s; bottom right: 5 s).
Fig 4.
Velocity of the fluid in the flask during three periods on the RPM for three different rotational velocities (40, 60 and 90 deg/s).
Both frames rotate with constant and equal velocity, and the flask is placed at the center of rotation. Top: Volume average of the velocity plotted over time. Bottom: Fastest velocity plotted over time.
Fig 5.
Shear stresses in the flask during three periods on the RPM for three different rotational velocities (40, 60 and 90 deg/s).
Both frames rotate with constant and equal velocity, and the flask is placed at the center of rotation. Top: Volume average of the shear stresses in the “bulk volume” over time. The “bulk volume” is 4 mm smaller than the flask and thus has a 2 mm clearance from the flask wall. Middle: Maximum shear stresses in the “bulk volume” over time. Bottom: Maximum shear stresses along the “cultivation surface” (the two largest flask walls).
Fig 6.
The ratio of the “cultivation surface” (the two largest flask walls) exposed to a shear stress larger than a certain threshold.
The thresholds are chosen at 10, 25, 50, 75 and 100 mPa. The time represents three periods on the RPM for three rotational velocities (40, 60 and 90 deg/s). Both frames rotate with constant and equal velocity, and the flask is placed at the center of rotation.
Fig 7.
Convection on the RPM over three periods for three different rotational velocities (top: 40 deg/s; middle: 60 deg/s; bottom: 90 deg/s).
Both frames rotate with constant and equal velocity, and the flask is placed at the center of rotation. The flask was divided into two compartments, denoted as the “y-positive compartment” (for y ≥ 0) and “y-negative compartment” (for y < 0). A virtual variable was placed in the “y-positive compartment” only. Subsequently, the variable was left to mix by convection, and the average concentration in the two compartments was monitored. The rapid fluid motion leads to thorough mixing within two to three periods (arrows).
Table 2.
Effects of shear stresses on various cells.