In this paper, the dynamic behavior of a self-propelled droplet along a conical fiber is simulated by using an improved lattice Boltzmann color-gradient method. This method is developed on the basis of our recently developed density ratio model [Zhang et al., Int. Commun. Heat Mass Transfer, 137, 106284 (2022).], but a wetting boundary condition is added to account for the moving contact line on an arbitrary solid surface. First, this method is validated against the analytical droplet shapes and contact angles for droplets surrounded by matrix fluids of different densities on flat and spherical surfaces, and the spontaneous transport of a droplet on a conical fiber. This method is then adopted to systematically study the effects of the Bond number ( ), surface wettability ( ), cone hemi-angle ( ), and droplet volume on the droplet dynamic behavior. In each case, the results show that the droplet climbing velocity first increases and then decreases, and a velocity fluctuation is observed, which is due to that the apparent receding and advancing contact angles do not simultaneously reach the equilibrium contact angle. As droplet volume increases, the equilibrium droplet height monotonically increases. As or increases, the droplet climbing height and the wetting area both decrease. We also found that the equilibrium climbing height first increases and then decreases with , and its maximum is reached around .
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