Food Engineering

Lesson 29. DIFFUSION CONTROLLED FALLING RATE PERIOD

Module 3. Food dehydration

Lesson 29

DIFFUSION CONTROLLED FALLING RATE PERIOD

29.1 Introduction

The method used to estimate drying rates and drying times in the falling rate period depends on whether the solid is porous or nonporous. In a nonporous material, once there is no superficial moisture, further drying can occur only at a rate governed by diffusion of internal moisture, and drying may be even take place inside the solid instead of at the surface. One important point to note is that non-hygroscopic foods have a single falling rate period, where as hygroscopic foods have two falling rate periods.

29.2 First Falling Rate Period

The plane of evaporation moves inside the material being dried, and water diffuses through the dry solids to the drying air. It represents a condition whereby the surface is no longer capable of supplying sufficient free moisture to saturate the air in contact with it. Under these conditions, the rate of drying depends very much on the mechanism by which moisture from inside the material is transferred to the surface. This is usually the longest period of a drying operation and in some foods, where the initial moisture content is below the critical moisture content the falling rate period is the only part of the drying curve to be observed.

29.3 Second Falling Rate

At the end of the first falling rate period it may be assumed that the surface is dry and that the plane of separation is moving in to the solid and the vapour reaches the surface by molecular diffusion through the material. The forces controlling the vapour diffusion will determine the final rate of drying, and these will be largely independent of the conditions outside the material. During the falling rate period, the factors that control the rate of drying change. Initially the important factors are similar to those in the constant rate period, but gradually the rate of mass transfer becomes the controlling factor. This depends mostly on the air and the thickness of the food. It is unaffected by the both the relative humidity of the air and the velocity of the air. The air temperature is therefore controlled during the falling rate period, whereas the air velocity and temperature are more important in the constant rate period. In practice foods may differ from these idealized drying curves owing to shrinkage, changes in the temperature and rate of moisture diffusion in different parts of the food and changes in the temperature and humidity of the drying air. The surface temperatures of the food remains close to the wet bulb temperature of the drying air until the end of the constant rate period, due to the cooling effect of the evaporating water. During the falling rate period the amount of water evaporating from the surface gradually decreases but as, the same amount of heat is being supplied by the air the surface temperature rises until it reaches the dry bulb temperature of the drying air. Most heat damage to the food therefore occurs during falling rate period.

Example 29.4

A 50 m diameter droplet of a liquid food is being dried in a spray. Experiments have indicated that the constant rate drying period for this type of situation requires 2 s. If the product entering the spray dryer has 10% total solids and critical moisture content is 35% (wet basis), determine the moisture removal rate during constant rate drying. Assume droplet size does not change during the drying and the product density is 1050 kg / m³

Second method:

w_o = 90 % = 0.9 / 0.1 = 9 kg H₂ O / kg solid.

W_c = 35 % = 0.35/0.65 = 0.5385 kg H₂ O /kg solid.

Drying rate = w_o - w_c / t = 4.23 kg H₂ O / kg solids.