Advertisement

An Estimation of Thermal Stress Induced by the Freezing Process for Biological Cell Preservation

Part of the Applications of Cryogenic Technology book series (APCT, volume 10)

Abstract

Thermal stresses in a frozen solution, induced by the freezing process, are related to the cryoinjury of biological cells which are suspended inside a physiological medium for the purpose of preservation. Experimental and analytical results indicate that the circumferential compressive stresses inside the frozen solution are much higher than the radial and axial stresses. The maximum circumferential compressive stress is located at the interface position between the frozen and the unfrozen solution.

In this paper, an estimation of the maximum circumferential compressive stress is presented and is based on the one-dimensional experimental freezing model for simulation of cell freezing preservation taking place in a long cylindrical test tube. The result of the analysis indicates that a decrease of the temperature at the outside surface of the tube results in an increase of the maximum thermal stress in the frozen solution. For freezing preservation, a slow freezing process having a relatively high surface temperature has the benefit of reducing the cryoinjury of biological cells caused by the thermal stress.

Keywords

Thermal Stress Dimensionless Time Biological Cell Freezing Process Freeze Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

C, C1, C2

constant

E

Young’s modulus

hLS

latent heat of water freezing

k

thermal conductivity

kR

dimensionless parameter defined in Eq. (8)

K1, K2

constants defined in Eqs. (20) and (21), respectively

L

length of the tube

q

heat transfer rate

r

radial coordinate

Ro

outside radius of the tube

Ri

inside radius of the tube

S

dimensionless interface position between the ice and water, defined in Eq. (6)

t

time

T

temperature

To

outside surface temperature of the tube

Tf

freezing temperature of water

temperature difference (T-Tf)

u

displacement

X

interface position between the ice and water

z

axial coordinate

Greek Symbols

α*

linear thermal expansion coefficient

β

initial strain of the ice

ɛ

strain

ν

Poisson’s ratio

ρ

density

σ

stress

τ

dimensionless time defined in Eq. (7)

Subscripts

1

tube

2

ice

r

radial direction

t

circumferential direction

z

axial direction

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H.T. Meryman, R.J. Williams, and M.St. J. Douglas, Freezing injury from solution effects and its prevention by natural and artificial cryoprotection, Cryobiology, 14: 287–302 (1977).PubMedCrossRefGoogle Scholar
  2. 2.
    P. Mazur, The role of intracellular freezing in the death of cells cooled at supraoptimal rates, Cryobiology, 14: 251–272 (1977).PubMedCrossRefGoogle Scholar
  3. 3.
    D.E. Pegg, M.P. Diaper, H.LEB. Skaer and C.J. Hunt, The effect of cooling and warming rate on the packing effect in human erythrocytes frozen and thawed in the presence of 2M gylcerol, Cryobiology, 21: 491–502 (1984).PubMedCrossRefGoogle Scholar
  4. 4.
    B. Rubinsky, E.G. Cravalho, and B. Mikic, Thermal stresses in frozen organs, Cryobiology, 17: 66–73 (1980).PubMedCrossRefGoogle Scholar
  5. 5.
    S. Lin and D.Y. Gao, Thermal stresses related to cryoinjury of biological cells in freezing preservation, in: “Heat Transfer with Phase Change,” I.S. Habib and R.J. Dallman, ed., HTD-Vol. 114, ASME, New York (1989).Google Scholar
  6. 6.
    A. Higashi, Mechanical properties of ice single crystals, in “Physics of Ice,” N. Riehl, B. Bullemer and H. Engelhardt, ed., Plenum Press, New York (1969).Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Sui Lin
    • 1
  1. 1.Department of Mechanical EngineeringConcordia UniversityMontrealCanada

Personalised recommendations