Investigation of Thermo-Capillary Flow Inside an Evaporating Pinned Water Droplet

Abstract

International audienceThermo-capillary flow inside an evaporating water drop on heated or non-heated substrate is investigated. The modeling of the internal flow inside the drop takes into account the effects of the privileged evaporation near the contact line as well as thermo-capillarity. Heat transport equations by convection-diffusion in the drop, conduction in both solid and gas phases, and vapor diffusion in the surrounding air are solved numerically in a quasi-steady state. Results showed that the temperature profile at the drop surface rules the patterns of the thermo-capillary flow which is mainly dominant except near the contact line and toward the evaporation end. It is highlighted that the substrate temperature and its thermal conductivity have a great impact on the flow inside the drop. For instance, a multi-cellular pattern is induced within a heated drop for contact angles between 11 and 20. and the thermo-capillary flow could be reversed for contact angles less than 11. under certain conditions of the substrate thermal conductivity. Furthermore, the evaporation rate of the heated drop may be considerably influenced by thermo-capillarity at high contact angles

Characterization of interface properties of fluids by evaporation of a capillary bridge

“…We thus do not expect strong Marangoni flow in our experiment. This was also pointed out by Xiao et al [26] and Bouchenna et al [24], who found the influence of the thermo-capillary effect on the evaporation of a sessile droplet negligible at ambient temperatures.…”

“…The importance of those flows can be estimated by the Marangoni Ma number [24],Ma=(normal∂γ/normal∂T)ΔThμαT,where γ is the surface tension, Δ T the temperature difference, h the characteristic length, μ the dynamic viscosity of the liquid and α T the thermal diffusivity of the liquid. For pure water, ∂ γ /∂ T = 1.56 × 10 −4 kg s −2 K −1 [25], Δ T ≃ 0.1 K, μ = 1.0 × 10 −3 kg −1 m −1 s −1 and α T = 1.43 × 10 −7 m 2 s −1 and a bridge in contact between two walls, h = z 1 /2 ≃ 0.75 10 −3 m, the Marangoni number is Ma ≃ 80.…”

A Numerical Study of Particle Transport in an Evaporating Colloidal Sessile Droplet

“…The mathematical formulation based on conservation equations, i.e., mass, momentum, energy, and particles concentration is written in a general form (Ait Saada et al, 2010, 2013Bouchenna et al, 2015). The flow inside the droplet is governed by the Navier-Stokes equations; it is induced by the strong evaporation rate at the contact line, the thermo-capillarity, and the thermal buoyancy.…”

“…The associated dimensionless boundary conditions are indicated in Fig. 1 and the dimensionless conditions at interfaces are written as (Bouchenna et al, 2015):…”

Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis

“…The efficient numerical technique is a more reliable tool for simulating the droplet evaporation process owing to its capability to consider the fully coupled mechanisms, like heat and mass transfer, thermal effects of substrate, evaporative cooling and thermocapillary convection [14,15]. In the present work, the effects of the substrate on Marangoni flow with respect to the influential parameters (thermal conductivity, thickness and substrate temperature) in a wide range are investigated.…”