Influence of viscosity on the impingement of laminar liquid jets

• We study the collision of viscous liquid jets solving the full Navier–Stokes system.
• The impact pressure is directly proportional to the viscosity of the jets.
• Sheet thickness decreases logarithmically with the distance from the impact point.
• Increasing viscosity increases the thickness and uniformity of the fluid sheet.

The impingement of low-viscosity liquid jets has been studied extensively for over a century due to their fundamental scientific interest and their practical importance in spray and atomization technologies. However, the role of the fluid viscosity in the impingement dynamics is largely unknown despite the fact that viscous liquids are common in spray and atomization processes ranging from spray drying in the food industry to the atomization of gelled propellants in rocket engines. Here, we report direct numerical simulations that enable a detailed analysis of the influence of viscosity on the impingement dynamics. The simulations solve the complete Navier–Stokes system governing the free-surface dynamics, and so fully account for the interplay of inertia, viscous and capillary forces. Results show that the liquid viscosity profoundly affects the impingement dynamics. The collision of viscous liquid jets generates a fluid sheet that thins at a rate r−1r−1 with the distance r   from the impact point at intermediate viscosities, in contrast to the inertial case in which the sheet thins at a faster rate r−2r−2. As the viscosity increases, the fluid sheets become thicker and more uniform, and contrary to the inertial case, the velocity of the sheets is lower than the velocity of the jets. Results further reveal that due to viscous stresses the impact pressure generated by the collision of viscous liquid jets scales as Re−1Re−1, where ReRe is the jet Reynolds number.