External Mass Transfer

Uncharged Support

Mathematical Analysis:

Consider an enzyme immobilized to the surface of an uncharged, non-porous particle, the entire surface of which is uniformly accessible. The average flux of substrate (N_s) to the fluid-solid interface may be written as:

where:

k_s: average mass-transfer coefficient

S₀, S^* : Substrate concentrations in the bulk fluid and solid-liquid interface respectively.

At steady state, the enzymatic reaction rate must be equal to the rate of substrate transport to the catalyst surface:

where:

v' : maximum reaction rate per unit surface area of catalyst

In dimensionless form, we rewrite equation (1) as:        

where:

Then we can write :

where:

In the absence of diffusional limitations, we may write equation (2) as:

We introduce an effectiveness factor (external effectiveness factor, h_E):

Therefore:

Hence:

From the definition of h_E we can observe that if h_E << 1, then the system is mass-transfer limited, and if h_E = 1 then the reaction rate is not limited by external mass transfer.

Click here to view an outline of the calculation procedure.

Charged Support

Mathematical Analysis:

Consider a substrate S in a charged medium of ionic strength I is reacting to form a product and is catalyzed by an immobilized enzyme attached to a planar, charged support. The steady state molar flux of a charged substrate to a planar surface that has an electrostatic potential of y₀ is given by:

where:

y(z) : electrostatic potential

T : Temperature

D_s : Molecular diffusivity of substrate

Z : Valence of substrate

F : Faraday’s constant

R : Universal gas constant

N_s is constant at steady state (ie. dN_s/dz = 0). Solving the above equation (9) using the integrating factor [exp(ly(z)/ y₀)/D_s], we get:

where:

Here, l represents the dimensionless potential and M=1 when y(z)=0.

At steady state,

where:

We then define a modified Damkohler number, Da_M, as:

Hence, we get the dimensionless form of equation (11) as:

From equations (6) and (13) and (5) we get an apparent Michaelis constant as:

Thus in this case, intrinsic Michaelis constant is affected by electrostatic interaction and external mass transfer resistance.

Page created by Asif Ladiwala and Shripad Gokhale.

Last modified : 13 December, 2000.