We investigate the dynamic behavior of a two-dimensional droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where one of the phases is viscoelastic represented by a Giesekus model. The Cahn-Hilliard Phase-Field method is used to capture the interface between the two phases. The presence of polymeric molecules alters the viscoelastic drop's deformation over time, categorizing it into two stages before contact line depinning. In the first stage, the viscoelastic droplet deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. The viscous bending of viscoelastic drop is enhanced on the receding side for small De, but it is weakened by further increase in De. On the advancing side, the viscous bending is decreased monotonically for Ca<0.25 with a non-monotonic behavior for Ca=0.25. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening. Finally, when the medium is viscoelastic, the viscoelasticity suppresses the droplet deformation on both receding and advancing sides, and this effect becomes more pronounced with increasing De. Increasing the Giesekus mobility parameter enhances the weakening effect of viscous bending on the advancing side.

Using experiments and numerical simulations, we investigate the spontaneous spread-ing of droplets of aqueous glycerol (Newtonian) and aqueous polymer (shear-thinning) solutions on smooth surfaces. We find that in the first millisecond the spreading of the shear-thinning solutions is identical to the spreading of water, regardless of the polymer concentration. In contrast, aqueous glycerol solutions show a different behavior, namely, a significantly slower spreading rate than water. In the initial rapid spreading phase, the dominating forces that can resist the wetting are inertial forces and contact-line friction. For the glycerol solutions, an increase in glycerol concentration effectively increases the contact-line friction, resulting in increased resistance to wetting. For the polymeric solutions, however, an increase in polymer concentration does not modify contact-line friction. As a consequence, the energy dissipation at the contact line cannot be controlled by varying the amount of additives for shear-thinning fluids. The reduction of the spreading rate of shear-thinning fluids on smooth surfaces in the rapid-wetting regime can only be achieved by increasing solvent viscosity. Our results have implications for phase-change applications where the control of the rapid spreading rate is central, such as anti-icing and soldering.

We present a new and efficient phase-field solver for viscoelastic fluids with moving contact line based on a dual-resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn-Hilliard phase-field model, and the viscoelasticity incorporated into the phase-field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp-interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer-stress constitutive equations. The method is based on second-order finite differences for the discretization of the fully coupled Navier–Stokes, polymeric constitutive, and Cahn–Hilliard equations, and it is implemented in a 2D pencil-like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT-based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual-resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D. 

Self-propelled jumping of two polymeric droplets on superhydrophobic surfaces is investigated by three-dimensional direct numerical simulations. Two identical droplets of a viscoelastic fluid slide, meet and coalesce on a surface with contact angle 180 degrees. The droplets are modelled by the Giesekus constitutive equation, introducing both viscoelasticity and a shear-thinning effects. The Cahn-Hilliard Phase-Field method is used to capture the droplet interface. The simulations capture the spontaneous coalescence and jumping of the droplets. The effect of elasticity and shear-thinning on the coalescence and jumping is investigated at capillary-inertial and viscous regimes. The results reveal that the elasticity of the droplet changes the known capillary-inertial velocity scaling of the Newtonian drops at large Ohnesorge numbers; the resulting viscoelastic droplet jumps from the surface at larger Ohnesorge numbers than a Newtonian drop, when elasticity amplifies visible shape oscillations of the merged droplet. The numerical results show that polymer chains are stretched during the coalescence and prior to the departure of two drops, and the resulting elastic stresses at the interface induce the jumping of the liquid out of the surface. This study shows that viscoelasticity, typical of many biological and industrial applications, affects the droplet behaviour on superhydrophobic and self-cleaning surfaces.

We investigate the dynamic behaviour of a two-dimensional (2D) droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where either the droplet is viscoelastic (V/N) or the surrounding medium (N/V). The fluid viscoelasticity has been modeled by the Giesekus constitutive equation, and the Cahn–Hilliard Phase-Field method is used to capture the interface between two phases. The contact angle hysteresis is represented by an advancing contact angle and a receding contact angle . The results reveal that the deformation of the viscoelastic drop over time is changed due to the presence of polymeric molecules, and it can be categorized in two stages prior to depinning of the contact lines. In the first stage, the viscoelastic droplet speeds up and deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. In the V/N case, the viscous bending is enhanced on the receding side for small De, but it is weakened by further increase in De, and this non-monotonic behavior brings about an increase in the receding contact line velocity at small De and a decrease at large De. On the advancing side, the viscous bending is decreased monotonically, and hence the advancing contact line velocity is decreased with increasing De. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening due to the presence of dominant extensional flow on the advancing side. Finally, in the N/V system, the viscoelasticity of the medium suppresses the droplet deformation on both receding and advancing sides, and this effect is more pronounced with increasing De; the weakening effect of viscous bending is enhanced significantly at the advancing side by increasing the Giesekus mobility parameter in the N/V system. These results give a thorough understanding of viscoelastic effect on both drop deformation and depinning of both contact lines over a surface with contact angle hysteresis.