By molecular modeling simulations, we study the dynamics of the rise of a meniscus on the outside of a fiber. We develop methods to measure simultaneously the height of the liquid interface and the contact angle versus time. We observe that in the complete wetting case (with an equilibrium contact angle equal to zero), the dynamic contact angle theta(t) behaves asymptotically as t(-1) contrary to some experimental results where one observes t(-1/2) instead. Using the combined model describing the dynamics of wetting, we predict that there are two different time scale behaviors within this process related to the two dissipation channels: friction between the liquid and the solid, leading to t(-1), and hydrodynamics, leading to t(-1/2). Using this approach, we find that the maximal speed of spreading on a fiber is a nonmonotonic function of the equilibrium contact angle.