Freeze-drying has received renewed interest in connection with biotech
nology, food preservation and chemical industries. Freeze-drying under
reduced pressure causes sublimation to occur. Simultaneous freezing o
f the moisture phase couples the two processes of freezing and sublima
tion and creates a self-driven process without need for any additional
application of external energy other than that required to lower the
surface temperature and pressure initially. A mathematical model consi
sting of coupled diffusion equations describing thermal and mass equil
ibrium in the solid-liquid and solid-vapour regions is solved analytic
ally. The liquid-solid region is included with unknown freezing interf
acial conditions. The effects of various parameters, such as conductiv
ity ratio, latent heats, initial concentration, surface pressure and s
urface temperature, are examined with respect to the freezing and subl
imation rates. The freezing rate is faster than the sublimation rate,
though slower than the corresponding rate for constant freezing temper
ature. The freezing temperature is higher than the sublimation tempera
ture for a constant composition ice pack.