Dimensionless number in mass transfer

Biot Number

Mass transfer biot number is defined as ratio of internal
diffusion resistance to external diffusion resistance. It is used
in case of transient mass transfers.

Bimt = kmL/De >>1
In case of stationary interface (which is generally assumed to
be)with no interface reaction km = Dfluid/δm
Bimt = Mass transfer biot number
δm = thickness of mass transfer boundary layer
km = mass transfer coefficient
L = characteristic length or linear length scale dimension
De = effective diffusivity
Dfluid = Diffusivity of species in fluid

Physical significance

o The boundary layer is the largest it can be in a stagnant
system, and in that case it is approximately the same length
scale as L. (Consider the example of the Sherwood or Nusselt
number for spheres in a stagnant medium.) Thus the ratio L /
δ m is typically greater than one.
o Also, the diffusivity of the species in the fluid is typically
much greater than the effective diffusivity in the particle,
where the species has to navigate the tortuous pore space.
Thus Dfluid / De is also typically much greater than one.
o Biot number is useful in study of reactor limitations.
Whenever we are looking at a reactor where we have bulk
kinetic data, if we find out that we have an external diffusion
limitation, we know that we must also have an internal diffusion limitation. o However, when you have an external limitation, you may be able to predict the reaction rate purely by considering the surface flux. o It is also considered as the ratio of total momentum transferred to the molecular momentum transferred because momentum distribution between the molecules due to higher.