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Water vapor capture through free surface flows plays a crucial role in various industrial applications, such as liquid desiccant air conditioning systems, water harvesting, and dewatering. This paper studies the dynamics of a silicone liquid sorbent (also known as water-absorbing silicone oil) flowing down a vertical cylindrical fibre while absorbing water vapor. We propose a one-sided thin-film-type model for these dynamics, where the governing equations form a coupled system of nonlinear fourth-order partial differential equations for the liquid film thickness and oil concentration. The model incorporates gravity, surface tension, Marangoni effects induced by concentration gradients, and non-mass-conserving effects due to absorption flux. Interfacial instabilities, driven by the competition between mass-conserving and non-mass-conserving effects, are investigated via stability analysis. We numerically show that water absorption can lead to the formation of irregular wavy patterns and trigger droplet coalescence downstream. Systematic simulations further identify parameter ranges for the Marangoni number and absorption parameter that lead to the onset of droplet coalescence dynamics and regime transitions.