| Dynamic wetting is a process about a fluid on solid wall displaced by another immiscible one.It is a fundamental problem in interfacial fluid dynamics,and is widely encountered in nature and applications.When the moving contact line moves with a low velocity relative to the solid wall,the interface of two-phase flow maintains a stationary meniscus.As the velocity exceeds a threshold,the stationary meniscus cannot be sustained and the wetting transition occurs.After the wetting transition,a liquid or gas film will be deposited on the wall and droplets or bubbles may also be generated.A numerical method based on the diffuse-interface model and lubrication theory were employed to study the wetting transition and liquid film evolution on cylindrical surfaces.The results and conclusions are briefly given as follows:(1)The dip coating of cylinders with various radius was numerically and theoretically studied.It is confirmed that the wetting transition occurs when the apparent contact angle vanishes.The critical velocity decreases with the radius of cylinder.There are four different morphologies of liquid film on the cylinder surface after the wetting transition:a rim connected with the classical Landau-Levich-Derjaguin(LLD)film,two films with different thickness connected by a capillary shock,a thick film with a dimple,and a monotonic film.With the increase of cylinder radius,a thick film will take place of rim owing to the effect of gravity and the rim regime transforms into the capillary shock regime.The steady dimple regime is studied via lubrication theory and a bifurcation diagram about the dimple morphology is obtained.The bifurcation point,corresponds to the critical velocity between dimple and LLD film.As the critical velocity approaches to the one for the onset of film deposition,the dimple regime vanishes.(2)The gas-liquid displacement in a capillary is numerically studied.It is verified that the wetting transition occurs as the apparent contact angle approaches zero.The critical velocity increases with the equilibrium contact angle.After the wetting transition,the contact line collects liquid into a liquid rim,which eventually collapses due to the curvature of the capillary,giving rise to a Taylor bubble.Based on the hydrodynamics of the moving contact line,the bubble formation process was analyzed and a formulation about the bubble length was derived.The theory is consistent with the numerical simulations.(3)The gas-liquid displacement in a vertical tube affected by gravity was numerically studied.The simulations indicate that wetting transition occurs as the apparent contact angle equals to zero and the critical flow rate decreases with the tube radius.We identified two flow regimes based on the interfacial morphologies:the bubble regime in which the rim near the contact line collapses to form a Taylor bubble,the capillary shock regime which is characterized by a capillary shock that connects a thick film and a Landau-Levich-Derjaguin-Bretherton(LLDB)film.From the analysis about the steady thick film,we find that the thick film can exist only when the radius is large enough.The steady capillary shock was studied based on lubrication theory,and a bifurcation diagram on the relation between the position of capillary shock and the flow rate is obtained.The bifurcation point corresponds to the critical flow rate for the transition between bubble regime and capillary shock regime.(4)The movement of a series of Taylor bubbles was numerically investigated.When the distance between bubbles is large enough,the bubble shape and the flow field are similar with that of an isolated bubble.As the bubbles come close,the deformation of the head and tail of bubbles will be suppressed,but the thickness of liquid film between bubble and the wall is not affected;the stagnation ring on the bubble will contract and approaches the stagnation point on the vertex.At large speeds,coalescence of the bubbles occurs,leading to a core-annular flow. |
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