Evaporative cooling of sessile water microdrops measured with atomic force microscope cantilevers

Abstract

We monitored the evaporation kinetics of drops from solid surfaces and the resulting cooling of the surfaces. To do this we deposited water drops with diameters smaller than 100 µm onto atomic force microscope (AFM) cantilevers. Due to the surface tension of the liquid, the Laplace pressure inside the drop, the change of the interfacial stress at the solid-liquid boundary and evaporative cooling, the cantilevers are deflected by typically some hundred nanometers. We used pure silicon and gold-coated silicon cantilevers in order to be able to separate and quantify the cooling effect from that due to the surface tension. We measured the bending of the cantilevers along their longitudinal axis versus time with an AFM-like setup, and monitored the contact angle and radius of the evaporating drops with video microscopy. We developed a FEM model for the bending of a cantilever as a result of surface forces and evaporative cooling. Experimental results are reproduced by FEM simulations.

Formation of liquid menisci in flexible nanochannels

“…with A the area of the liquid-air interface, q the average heat flux (∼2 kJ/s m 2 ), ρ the density of the fluid and H ν the vaporization enthalpy (2.27 × 10 6 J/kg and 8.41 × 10 5 J/kg for water and ethanol, respectively) [35][36][37], and take a meniscus length along the channel of about l = 5 μm. For the characteristic time τ for displacement of the meniscus over its length one finds then: τ = lρ · H ν /q ≈ 5 s and 2 s for water and ethanol, respectively.…”

“…Further, we consider situations in which the length of the meniscus along the channel is smaller than, or in the order of the channel width w, which is the case in our experiments. Then the deflection in the elasticity problem is virtually independent of z and we are left with a quasi one-dimensional problem, the so-called cylindrical bending of a long rectangular plate [35]. It reads −κ∂ 4…”

Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet

“…During the latest years, Bonaccurso et al have made some studies on the transverse effect of a sessile droplet on the bending of a flexible microcantilever [36][37][38][39]. Recently, they studied the surface deformation of several tens micrometers-thick PDMS membrane with very low modulus induced by a sessile droplet using laser scanning confocal microscopy and estimated that the breadth of surface layer is approximately 16.0 nm by comparison between their experimental data and Rusanov's theoretical solution [17].…”

Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney–Rivlin and linear elastic constitutive models

“…10. First, we suppose the droplet is ideally cylindrical [37] and the contact angle is θ . The wetted area is A = 2wa = 2wr sin θ , where r is the curvature radius of the water droplet.…”

“…Some researchers studied the influence of nanobubbles on the bending of MCLs [35,36]. Recently, Bonaccurso et al developed a FEM model for the bending of a cantilever and measured the bending versus time [37]. Zheng et al used the energy method to study the directional movement of liquid droplets on a microbeam with a varying or gradient stiffness and found that the droplet will move to the softer end of the beam [38].…”