The LDF model has been widely used in various adsorption processes for more than forty years. Since Liaw proposed a parabolic profile within a particle

this profile has been widely accepted as the mathematical and physical basis of the LDF model for twenty years. However

when dimensionless time is very small

this classical parabolic concentration profile would yield a negative profile within a particle

which is physically unrealistic. Although the r 5 profile proposed by Li and Yang can also lead to the LDF model and yield less negative profile than the parabolic profile

it inevitably produces the negative profile at very small time yet. In this paper

a new concentration profile

r n(t) profile

corresponding to the LDF model

is proposed. The exponent n(t) is a function of time

and decreases with time. This profile leads to the LDF model

but does not yield the negative concentration profile at any very small time. Furthermore

it has the volume-average adsorbed amount obtained by integrating this profile which exactly equals to that calculated directly from the LDF model mathematically. When the dimensionless time is smaller than 0.04

the parabolic profiles deviate clearly from the exact profiles

and when the dimensionless time is larger than 0.04

the r 5 profiles deviate from the exact profiles. In contrast to these two kinds of profiles

within the whole time domain

the shape of the r n(t) profiles is much similar and close to the shape of the exact profiles within the particle than the parabolic profile and the r 5 profile. Therefore

the r n(t) profile is the best match for the LDF model.