Abstract: 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.