Bioprocess Engineering

, Volume 5, Issue 2, pp 85–88 | Cite as

Precipitation of protein by ultracentrifuge with angle rotor

Part 1: Model for sedimentation process
  • N. Shiragami
  • T. Kajiuchi


Precipitation of a protein by ultracentrifuge with an angle rotor was simulated by a model for sedimentation process. Assuming that the concentration of solute in an inclined ultracentrifugal tube is given by averaging the concentration in the imaginary horizontal tube, the governing equation describing the concentration in the rectangular-shaped tube with a uniform field of ultracentrifugal force for an inclined tube in an angle rotor was derived. The exact solution to this governing equation was obtained under the condition that the diffusion is absent or present. The dimensionless concentration which is reduced by the initial concentration can be expressed as the function of a dimensionless ultracentrifugal times ω2t in case that the diffusion is absent, and as the function of dimensionless parametersα andt*in case that the diffusion is present. From our first approximated model it is found that the precipitation of a protein by ultracentrifuge with an angle rotor proceeds more rapidly than that with a swing rotor whether diffusion is absent or present.


Precipitation Waste Water Sedimentation Water Management Exact Solution 
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List of Symbols

c kg/m3

concentration of solute

c0 kg/m3

initial concentration of solute

cA kg/m3

concentration of solute for angle rotor

cs kg/m3

concentration of solute for swing rotor

D cm2/s

diffusion coefficient

d cm

diameter of ultracentrifugal tube


dimensionless constant


dimensionless constant

r cm

radial coordinate

r1 cm

minimum radius of ultracentrifugal tube

r2 cm

maximum radius of ultracentrifugal tube

rm cm

mean radius of ultracentrifugal tube


radius from which sedimentation starts

s s

sedimentation constant

t s


z cm

vertical coordinate


dimensionless parameter


dimensionless parameter

θ deg

inclination of ultracentrifugal tube

ω s−1

angular velocity of rotation


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • N. Shiragami
    • 1
  • T. Kajiuchi
    • 2
  1. 1.Department of BioengineeringTokyo Institute of TechnologyTokyo
  2. 2.Department of Environmental Chemistry and EngineeringTokyo Institute of TechnologyYokohamaJapan

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