Assessment of external heat transfer coefficient during oocyte vitrification in liquid and slush nitrogen using numerical simulations to determine cooling rates

Abstract

In oocyte vitrification, plunging directly into liquid nitrogen favor film boiling and strong nitrogen vaporization. A survey of literature values of heat transfer coefficients (h) for film boiling of small metal objects with different geometries plunged in liquid nitrogen revealed values between 125 to 1000 W/(m2 K). These h values were used in a numerical simulation of cooling rates of two oocyte vitrification devices (open-pulled straw and Cryotop®), plunged in liquid and slush nitrogen conditions. Heat conduction equation with convective boundary condition was considered a linear mathematical problem and was solved using the finite element method applying the variational formulation. COMSOL Multiphysics was used to simulate the cooling process of the systems. Predicted cooling rates for OPS and Cryotop when cooled at -196ºC (liquid nitrogen) or -207ºC (average for slush nitrogen) for heat transfer coefficients estimated to be representative of film boiling, indicated lowering the cooling temperature produces only a maximum 10% increase in cooling rates; confirming the main benefit of plunging in slush over liquid nitrogen does not arise from their temperature difference. Numerical simulations also demonstrated that an hypothetical four-fold increase in the cooling rate of vitrification devices when plunging in slush nitrogen would be explained by an increase in heat transfer coefficient. This improvement in heat transfer (i.e., high cooling rates) in slush nitrogen is attributed to less or null film boiling when a sample is placed in slush (mixture of liquid and solid nitrogen)because it first melts the solid nitrogen before causing the liquid to boil and form a film.