The neutrino production rate strongly depends on the temperature, and a small variation of chemical composition in the central regions can imply a large variation of neutrino flux. For some values of their frequencies and wavenumbers, the internal waves e xcited at the bottom of the solar convective zone are able to propagate until the central region of the star, producing a macroscopic diffusive process (Press 1981, Schatzman & Montalbán 1995). In this paper we analyse the effect of this mixing mechani sm on the neutrino flux production. For that purpose, we introduce some improvements in the treatment of non-adiabatic internal waves in the central region of the Sun. We use the amplitude of these oscillations to determine the macroscopic diffusion coefficient linked to non-adiabatic propagation of gravity waves. We analyse the chemical mixing in the solar center and its effect on the decrease of solar neutrino production. We also study how the diffusion coefficient depends on the source function of internal waves, and we show that the amplitude of the diffusion coefficient in the internal regions is strongly affected by the characteristics of the source function at the boundary convective/stratified regimes.