•Impact of imbibition-profile shape on wettability is investigated thermodynamically.•Wettability is related to change in Helmholtz free energy during spontaneous imbibition process.•Helmholtz free energy is related to area under the curve and slope of imbibition profile.•A modified Lucas-Washburn equation is proposed for co-current imbibition process.•A wettability index is proposed using the calculated Helmholtz free energy values. Spontaneous imbibition profiles are widely used for wettability evaluation of porous media such as rocks. However, mostly the equilibrium imbibed volume is the basis for wettability evaluation. Here, we model the relationship between the shape of imbibition profile and wettability of a medium. We develop a wettability evaluation criterion based on the change in Helmholtz free energy of the system during the imbibition process. The model relates the Helmholtz free energy to the area under the profile, the slope of the imbibition profile, equilibrium imbibed volume, and equilibrium time. We propose a modified form of Lucas-Washburn equation to model the capillary-driven flow of a viscous wetting phase into a porous medium saturated with a viscous non-wetting phase. We introduce a wettability index using the volume-normalized Helmholtz free energy. Finally, the model is tested on imbibition data of eight twin rock samples, and the wettability results show moderate to strong correlations with rock properties. The results show that wettability indices predicted by the proposed technique exhibit more accurate correlations compared with those obtained by the volume-based method.