Dependence of the Drag Over Super Hydrophobic and Liquid Infused Surfaces on the Textured Surface and Weber Number

Abstract

Direct Numerical Simulations of a turbulent channel flow have been performed. The lower wall of the channel is made of staggered cubes with a second fluid locked in the cavities. Two viscosity ratios have been considered, m = µ 1 /µ 2 = 0.02 and 0.4 (the subscript 1 indicates the fluid in the cavity and 2 the overlying fluid) representing superhydrophobic surfaces (SHS) and liquid infused surfaces (LIS) respectively. A first set of simulations with a slippery interface has been performed and results agree well with those in literature for perfect slip conditions and Stokes approximations. To assess how the dynamics of the interface affects the drag, a second set of DNS has been carried out at W e = 100 and 1, 000 corresponding to W e + ≃ 10 −3 and 10 −2. The deformation of the interface is fully coupled to the Navier-Stokes equation and tracked in time using a Level Set Method. Two gas fractions, GF = 0.5 and 0.875, have been considered to assess how the spacing between the cubes affects the deformation of the interface and therefore the drag. For the dimensions of the substrate here considered, under the ideal assumption of flat interface, staggered cubes with GF = 0.875 provide about 20% drag reduction. However, a rapid degradation of the performances is observed when the dynamics of the interface is considered, and the same This work was supported under ONR MURI Grants N00014-12-0875 and N00014-12-1-0962, Program Manager Dr. Ki-Han Kim. Numerical simulations were performed on the Texas Advanced Computer Center.

Comparison between super-hydrophobic, liquid infused and rough surfaces: a direct numerical simulation study

“…In this case, depending on the Weber number, and how the deformation of the interface is correlated with streamwise velocity fluctuations, the momentum transfer inside the texture may be only partially reduced with a consequent detrimental effect on the drag. The amount of drag reduction is less than that obtained with a flat and slippery interface as shown by García-Cartagena et al (2018). In addition, more studies are needed to optimize the morphology of the texture and size of the cavities to avoid the depletion of the fluid and increase durability.…”

“…In reality the interface is deformable and not slippery as assumed in the present model. García-Cartagena et al (2018) and Seo et al (2018) showed that when the interface deforms the amount of drag reduction is drastically reduced. Though exploring the role of interfacial deflections will be important to understanding many of these slippery surfaces, such an exploration is beyond the scope of this manuscript.…”

A theory for the slip and drag of superhydrophobic surfaces with surfactant

“…The second key assumption made in our scaling model is that the surfactant-induced Marangoni shear rate along the interface is approximately uniform. This is related to having a uniform concentration gradient, following the linearised coupling condition (19). From the broad range of parameters tested, see table 1 and figure 8, appendix A, we find that this assumption is invalid only in the partial stagnant cap (SC) regime, where the concentration gradient presents an abrupt increase at some point along the interface, separating the no-shear and no-slip regions.…”

Heat transfer in a turbulent channel flow with super-hydrophobic or liquid-infused walls

“…The numerical implementation of the level-set method (2.7) is detailed in García Cartagena et al. (2018).…”

“…2017; Van Buren & Smits 2017), at least if the two-fluid interface remains flat (García Cartagena et al. 2018). Heat transfer over these surfaces has not received as much attention.…”