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This paper investigated the influence of surface internal energy instability caused by the gravitational tilt angle on solutocapillary convection. The results showed that the spatio-temporal evolution of solutocapillary convection in a non-axisymmetric liquid bridge was divided into three stages under different gravitational tilt angles, "the initiating stage near the upper corner", "development to the intermediate height", and "shrinking toward the bottom corner". The non-equilibrium of the left or right interface curvature caused by internal energy instability promotes the distortion of the cell flow structure. The concentration gradient on the far-earth side increases first, due to the gravitational tilt angle. With the increasing gravitational tilt angle, the lateral extension of the cell flow is inhibited. The transverse/longitudinal velocity components are suppressed; however, the velocity gradient near the boundary is increased, and the uniformity of the velocity distribution in the center of the liquid bridge is improved. The axial component of the Bond number decreases in a small range (Bo′ = 1→0.98) with the internal energy instability, however, which has a significant effect on surface flow. Therefore, in the initiation and development stages of solutocapillary convection, the decay rate of the Marangoni number respectively decreases and increases with the increasing Bond number. The axial component of the Bond number decreases in a small range with the internal energy instability, which has a significant effect on the solute Marangoni number (Mac). In the initiation stage of solutocapillary convection, the decay rate of the Mac decreases with the increasing Bond number. Its change law is the opposite in the development stage of solutocapillary convection. [ABSTRACT FROM AUTHOR]