This paper starts with an introduction to the Onsager principle of minimum energy dissipation which governs the optimal paths of deviation and restoration to equilibrium. Then there is a review of the variational approach to moving contact line hydrodynamics. To demonstrate the validity of our continuum hydrodynamic model, numerical results from model calculations and molecular dynamics simulations are presented for immiscible Couette and Poiseuille flows past homogeneous solid surfaces, with remarkable overall agreement. Our continuum model is also used to study the contact line motion on surfaces patterned with stripes of different contact angles (i.e. surfaces of varying wettability). Continuum calculations predict the stick-slip motion for contact lines moving along these patterned surfaces, in quantitative agreement with molecular dynamics simulation results. This periodic motion is tunable through pattern period (geometry) and contrast in wetting property (chemistry). The consequence of stick-slip contact line motion on energy dissipation is discussed.

Drop formation and dripping and jetting phenomena occur in an extremely large variety of situation, spanning a broad range of physical length scales. In this paper, we study the dynamics of dripping-to-jetting transition for two immiscible coflowing liquid streams numerically. Two different classes of transition are identified. In both cases, nonlinear dynamical phenomena such as period doubling and chaos are observed between simple dripping and jetting. Extensive numerical calculations show that the first class of dripping-to-jetting transition is determined by the Weber number of the inner fluid W in , and the second class of dripping-to-jetting transition is controlled by capillary number of the outer fluid Cout.