## Lesson 38. CALCULATION OF FREEZE DRYING TIME

Module 4. Freeze dehydration

Lesson 38
CALCULATION OF FREEZE DRYING TIME

38.1 Introduction

Dehydration carried out at low absolute pressures allows the vaporization of water from the solid phase. To Carry out freeze drying successfully, the absolute pressure in the drying chamber must be maintained at a minimum of 620Pa.

Figure 38.1 is a schematic diagram of a freeze drier. The absolute pressure inside the drying chamber is determined by the temperature at which the vapour trap is maintained. This pressure corresponds to the vapour pressure over ice at the vapour trap temperature. The vacuum pump is designed primarily to exhaust the vacuum chamber at the start of the operation and to remove noncondensing gases and whatever air leaked into the system. The volume of vaporized water at the low absolute pressure in freeze drying is very large; therefore, removal of the vapour by the vacuum pump alone requires a very large pump. condensing the vaporized water to ice in the vapour trap is an efficient means of reducing the volume of gases to be removed from the system by the vacuum pump.

Heat must also be supplied to the material being dried to provide the energy of vaporization. This is accomplished by the use of hollow shelves through which a heated liquid is circulated. The temperature of the shelves can be regulated by regulating either the temperature or the supply of the heat transfer medium. The material to be dried rests on top of the heated plates. Heat transfer occurs by conduction from the heated plates, by convection from the air inside the drying chamber to the exposed surfaces, and by radiation.

38.2 Drying Times for Symmetrical Drying

Analysis of freeze drying is different from that of conventional drying in that drying proceeds from the exposed surfaces toward the interior. The outer layers are completely dry as the ice core recedes. Vaporization of water occurs at the surface of the ice core. Heat of sublimation is conducted to the surface of the ice core through the dried outer layer. Vaporized water diffuses through the pores of the dried outer layer before it leaves the solid and goes to the atmosphere in the drying chamber. Symmetrical drying occurs when the rate at which the ice core recedes is equal at both the top and bottom of the material. To simplify the calculations, unidirectional heat transfer is assumed.

38.3 Prediction of Drying Times

Drying of product of 2x thickness between two heating surfaces which dry it from both sides is shown in the figure.

38.4 Example

The density of a sample of beef is 60 lb / ft3 (965 kg / m3). How long will it take to dry a 1 – in. (2.54 – cm) – thick strip of this sample from an initial moisture of 75% to a final moisture content of 4% (wet basis)? Freeze drying is carried out at an absolute pressure of 500 um of mercury. The air in the drying chamber is at 80°F (26.7°C). Assume symmetrical drying. The thermal conductivity of the dried meat is 0.0692 W / (m. K). Estimate the heat transfer coefficient by assuming that a 3-mm-thick layer of vapour (kv of water = 0.0235 W / (m.K)] envelopes the surfaces where dying occurs and that the heat transfer coefficient is equivalent in resistance to the resistance of this vapour film.

From sublimation Fig 38.2, the temperature of ice in equilibrium with a pressure of 66.65 Pa is – 24.5°C. The heat of sublimation Hs = 2.8403 MJ / kg. The final moisture content on a dry basis is : x = 0.04 / 0.96 = 0.0417 kg water / kg dry matter. The initial moisture content on a dry completion of the drying period is X’ = X0 – X / X0 = 3 – 0.0417 / 3.0 = 0.986.

Substituting in equation 7:

38.3 Problems

Example-1

A food product is subjected to freeze drying. The temperature of drying chamber is at 55 oC and temperature of sublimation front is maintained at –20 oC. The half thickness of the product is 7 mm and porosity is 0.85. Take r as 317 kg/m3, kdr as 0.03 W/m K and ls as 2840 X 103 J/kg. Estimate the drying time.