Introduction to Food Process Engineering pp 193-219 | Cite as

# Mass Transfer

## Abstract

Mass transfer is concerned with the movement of material in fluid systems, that is both gases or liquids, under the influence of a concentration gradient. As we saw in Chapter 5, this is analogous to the movement of heat under the influence of a temperature gradient. For example, in drying operations water is removed in vapour form from either a liquid or a solid food into a warm gas stream (usually air). Thus the mass transfer of water occurs because there is a high concentration of water in the food and a lower concentration of water in the air. Most examples of mass transfer in food processes involve the transfer of a given component from one phase across an interface to a second phase. Some examples are listed in Table 8.1

## Keywords

Mass Transfer Mass Transfer Coefficient Sherwood Number Convective Mass Transfer Molar Density## Nomenclature

*a*Coefficient

*b*Index

*c*Index

*C*Molar concentration

- \({C_{{{\textrm{A}}_{\textrm{i}}}}}\)
Concentration of A (liquid phase) at the interface

- \({C_{{{\textrm{A}}_{\textrm{L}}}}}\)
Concentration of A in the bulk liquid

- \(C_{\textrm{A}}^{\textrm{*}}\)
Concentration of A in equilibrium with the bulk gas partial pressure

*d*Diameter

*D*Diffusivity or diffusion coefficient

- \({D_{{\textrm{AB}}}}\)
Diffusivity of A in B

*D*_{G}Diffusivity in the gas phase

*D*_{L}Diffusivity in the liquid phase

*g*Acceleration due to gravity

*Gr*Grashof number

*H*Henry’s constant

*J*_{A}Molar flux of A

*k*_{g}Film gas mass transfer coefficient

*k*_{G}Film gas mass transfer coefficient

*k*_{L}Film liquid mass transfer coefficient

*k*_{x}Film liquid mass transfer coefficient

*k*_{y}Film gas mass transfer coefficient

*K*_{G}Overall gas mass transfer coefficient

*K*_{L}Overall liquid mass transfer coefficient

*L*Characteristic length

*M*_{A}Molecular weight of component A

*N*Molar flux

*N*_{w}Molar flux of water vapour

*p*_{A}Partial pressure of A

- \({p_{{{\textrm{A}}_{\textrm{G}}}}}\)
Partial pressure of A in bulk gas

- \(p_{\textrm{A}}^{\textrm{*}}\)
Partial pressure in equilibrium with bulk liquid concentration

- \({p_{{{\textrm{A}}_{\textrm{i}}}}}\)
Partial pressure of A at interface

*p*_{w}Partial pressure of water vapour

- \({p_{{\textrm{wo}}}}\)
Partial pressure of water vapour at saturation

- \({p_{{{\textrm{B}}_{{\textrm{lm}}}}}}\)
Logarithmic mean partial pressure difference in B

*P*Pressure; permeability

*r*Radius

*R*Universal gas constant

*Re*Reynolds number

*Sc*Schmidt number

*Sh*Sherwood number

*T*Absolute temperature

*x*Mass or mole fraction in liquid phase

*y*Mass or mole fraction in gas phase

- \({y_{{{\textrm{B}}_{{\textrm{lm}}}}}}\)
Logarithmic mean concentration difference in B

*z*Dimension in the

*z*-direction*z*_{G}Thickness of gas film

*z*_{L}Thickness of liquid film

## Greek Symbols

*ΔC*Concentration difference

*Δp*Partial pressure difference

*Δx*Mole fraction difference (liquid phase)

*Δy*Mole fraction difference (gas phase)

*Δρ*Density difference

*μ*Viscosity

*ρ*Mass density

*ρ*_{A}Mass density of A

*ω*Molar rate of evaporation

## Subscripts

- A
Component A

- B
Component B

- w
Water