We present new data on the adsorption of bovine serum albumin (BSA) at the free water interface using an improved setup of the pendant drop method. We show that it is possible to describe quite accurately the surface pressure-time behavior until the surface pressure is about half of its equilibrium value by only taking into account the diffusion of the proteins from the bulk solution to the surface and the thermal convection inside the measurement cell, without invoking the thermodynamics of the adsorption. We believe that this is a first and necessary step for a simpler description of the adsorption dynamics of proteins.