Thermocapillary flow on superhydrophobic surfaces

Abstract

A liquid in Cassie-Baxter state above a structured superhydrophobic surface is ideally suited for surface driven transport due to its large free surface fraction in close contact to a solid. We investigate thermal Marangoni flow over a superhydrophobic array of fins oriented parallel or perpendicular to an applied temperature gradient. In the Stokes limit we derive an analytical expression for the bulk flow velocity above the surface and compare it with numerical solutions of the Navier-Stokes equation. Even for moderate temperature gradients comparatively large flow velocities are induced, suggesting to utilize this principle for microfluidic pumping.Introduction -Microtextured surfaces have mainly received attention due to their wetting properties [1]. A liquid drop placed on a suitably structured hydrophobic surface will only be in contact with the material on protruding tips, while gas is trapped in the valleys in between. In this so called Cassie-Baxter state nearly perfect hydrophobicity can be obtained, reflected in contact angles close to 180• . Recently, such surfaces have gained interest with respect to their ability for drag reduction [2,3] and surface induced transport [4,5], in particular electroosmotic and diffusioosmotic flow.In this letter we analyze temperature induced Marangoni convection as a driving force for fluid transport along microtextured surfaces. In particular, we focus on finned surfaces as sketched in figure 1, with a temperature gradient along or perpendicular to the fins, and the liquid being in the Cassie-Baxter state. We use an integral relation for the Stokes equation to derive an analytical formula for the macroscopic flow velocity observed at some distance above the surface. Both situations are further investigated by numerical solutions of the Navier-Stokes equation and compared to the analytical formula. Our analysis focuses on substrates of high thermal conductivity, such as silicon.Fluid actuation and transport are core functionalities in many microfluidic systems. The most prominent examples for the corresponding driving mechanisms are pressuredriven and electroosmotic flow. Our analysis shows that moderate temperature gradients of the order of 10 K/cm can lead to fluid velocities of several mm/s for water based systems on superhydrophobic surfaces. Thermocapillary convection may thus add to the portfolio of actuation principles in microfluidic settings and may even enable larger flow velocities than typically achieved with electroosmosis.Marangoni flows -The stress on a liquid-gas interface due to a gradient in surface tension is [6]

Temperature Jump Coefficient for Superhydrophobic Surfaces

“…Transactions of the ASME t{x,y,z) = n=l (19) where To, A", B^, C"", are undetermined coefficients, and…”

“…As a result, heat convection near the surface is entirely ignored in the present analysis. Thermocapillary arising from temperature gradient on the liquid-gas interface [19] is also ignored.…”

Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

“…Thermocapillary stress for flow over ridged surfaces has been considered by Baier et al (2010) and recently by Hodes et al (2015a), and evaporation/condenstaion investigated by Hodes et al (2015b). However, all previous work on heat transfer (including that mentioned in the previous paragraph) has assumed a flat meniscus.…”

Electro-osmotic flow along superhydrophobic surfaces with embedded electrodes

“…Taking into account the symmetries of the problem, integration of the Lorentz reciprocity theorem (2) analogously to [7,19] yields a relation between the electro-osmotic velocity far from the surface and the flow field at the surface in the shear-driven case. Here, we model the velocityû as a superposition of a Couette flow and flow over patches with infinite local slip length within a no-slip wall:…”

“…Equation (19) exhibits a stable branch, corresponding to the energy minima, and an unstable branch, corresponding to the maxima. The system follows the stable branch until, at the point of instability, it meets the unstable branch.…”