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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 8
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Original Articles

Effect of unsteady natural convection mass transfer caused by g-jitter on protein crystal growth under microgravity

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Pages 902-916 | Received 30 Mar 2016, Accepted 23 Jun 2016, Published online: 20 Sep 2016
 

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

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