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ABSTRACT
Detailed numerical analysis is presented for the effect of unsteady natural convection caused by g-jitter on protein crystal growth (PCG) under microgravity. The results show that for step impulse disturbances with the strength of 10−2 g0, the convection can decrease the crystal growth rate, especially for the higher-frequency g-jitter. For sinusoidal impulse disturbance with different amplitudes g*, the effect of convection on PCG is good for g* = 10−4 g0 and it is bad for g* = 10−3 g0. In comparison with the case of crystal at the bottom, the effects of unsteady convection caused by g-jitter for crystal suspended are more obvious due to the larger values of r. However, the crystal suspended in the container can more easily remain regular shaped.
Nomenclature
| C | = | concentration of solution, mol/L |
| Cl | = | concentration of inner crystal surface, mol/L |
| C∞ | = | concentration of container wall, mol/L |
| d | = | diameter of container |
| Ds | = | diffusion coefficient, m2/s |
| f | = | frequency |
| g | = | gravitational acceleration, m/s2 |
| g0 | = | gravity under Earth’s surface, 9.8 m/s2 |
| g* | = | amplitude of gravitational acceleration, 9.8 m/s2 |
| Gr | = | Grashof number |
| L | = | height of container, m |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| R | = | dimensionless radial coordinate |
| r | = | radial coordinate, m |
| r | = | dimensionless number |
| rave | = | average dimensionless number on crystal surface |
| Rc | = | dimensionless radius of protein crystal |
| rc | = | radius of protein crystal |
| Sc | = | Schmidt number |
| t | = | time, s |
| Fo | = | dimensionless time |
| Vmax | = | maximum velocity of solution convection |
| U | = | dimensionless vertical velocity |
| u | = | vertical velocity, m/s |
| UR | = | referenced velocity |
| V | = | dimensionless radial velocity |
| v | = | radial velocity, m/s |
| Vd | = | diffusion velocity of a protein molecule, m/s |
| Vf | = | solution velocity at the center of the protein molecule, m/s |
| Z | = | dimensionless vertical coordinate |
| z | = | vertical coordinate, m |
| ν | = | kinematic viscosity, m2/s |
| Φ | = | dimensionless concentration |
| ΓS | = | nominal diffusion coefficient |
| ρ | = | density, kg/m3 |
| ρ∞ | = | density at the container sidewall, kg/m3 |
| ρl | = | density of crystal interface, kg/m3 |
Nomenclature
| C | = | concentration of solution, mol/L |
| Cl | = | concentration of inner crystal surface, mol/L |
| C∞ | = | concentration of container wall, mol/L |
| d | = | diameter of container |
| Ds | = | diffusion coefficient, m2/s |
| f | = | frequency |
| g | = | gravitational acceleration, m/s2 |
| g0 | = | gravity under Earth’s surface, 9.8 m/s2 |
| g* | = | amplitude of gravitational acceleration, 9.8 m/s2 |
| Gr | = | Grashof number |
| L | = | height of container, m |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| R | = | dimensionless radial coordinate |
| r | = | radial coordinate, m |
| r | = | dimensionless number |
| rave | = | average dimensionless number on crystal surface |
| Rc | = | dimensionless radius of protein crystal |
| rc | = | radius of protein crystal |
| Sc | = | Schmidt number |
| t | = | time, s |
| Fo | = | dimensionless time |
| Vmax | = | maximum velocity of solution convection |
| U | = | dimensionless vertical velocity |
| u | = | vertical velocity, m/s |
| UR | = | referenced velocity |
| V | = | dimensionless radial velocity |
| v | = | radial velocity, m/s |
| Vd | = | diffusion velocity of a protein molecule, m/s |
| Vf | = | solution velocity at the center of the protein molecule, m/s |
| Z | = | dimensionless vertical coordinate |
| z | = | vertical coordinate, m |
| ν | = | kinematic viscosity, m2/s |
| Φ | = | dimensionless concentration |
| ΓS | = | nominal diffusion coefficient |
| ρ | = | density, kg/m3 |
| ρ∞ | = | density at the container sidewall, kg/m3 |
| ρl | = | density of crystal interface, kg/m3 |