Dynamics of Leidenfrost droplets on microtextured substrates

Abstract

A liquid droplet placed on a heated substrate at temperatures significantly higher than the saturation temperature of the liquid levitates over a thin film of vapor and is termed as a Leidenfrost (LF) droplet. Leidenfrost state of droplets compromises heat dissipation in cooling applications because of the intervening insulating vapor layer. In this thesis, we study the dependence of Leidenfrost temperature of liquid droplets on substrate microtextures and associated dynamics of the droplet and vapor layer. In the initial part of the thesis, we report on the dependence of the Leidenfrost temperature (LFT) of a deionized water droplet on the morphology of micropillared substrates and propose a pressure-based model to explain the associated droplet dynamics. We observe that the LFT increases with the height of micropillars and spacing between them. The LFT increases by ~ 1.8 times compared to a smooth silicon substrate and reaches ~ 507 °C for a silicon micropillar array with an interpillar spacing of 100 μm and height of 63 μm. The wall heat flux at the Leidenfrost state varies between 13 ± 1.8 W cm-2 and 52 ± 7 W cm-2 depending on the substrate morphology of the microtextured surfaces. We show that irrespective of the height of the textures, the effect of surface roughness diminishes beyond a certain critical interpillar spacing (~ 200 μm). We develop a semi- analytical model to show that the excess vapor gap between the top of the pillars and the base of the droplet is dependent on the permeability of the substrate and influences the vapor pressure under the droplet. The excess vapor gap is shown to play a crucial role in determining the range of temperatures that sustain transition boiling and affects the rate of evaporation of the droplet in Leidenfrost state on textured substrates. Further, we present a framework for modelling the evaporation of Leidenfrost droplets on microtextured surfaces. We present a theoretical model to determine the total heat transfer to a Leidenfrost droplet on microtextured substrates. The rate of evaporation is shown to be dependent on the shape of the liquid-vapor interface beneath the Leidenfrost droplet on a microtextured substrate. The maximum and the minimum vapor gap beneath a LF droplet is determined to be dependent on the volume of droplet, the surface temperature, and micropillar geometry. The excess vapor gap between the top of the pillars and the base of the droplet, for a substrate with high substrate permeability, predicted by the curved interface model is an order of magnitude higher than that predicted by flat interface model. The convective heat transfer from the ambient air to the top surface of the droplet is shown to contribute significantly to the rate of evaporation of the Leidenfrost droplet. We determine the total evaporation time of a Leidenfrost droplet over a microtextured with and without considering the curvature of the liquid-vapor interface beneath the droplet and compare with that obtained from experiments. The overprediction of the average rate of evaporation of a Leidenfrost droplet by the flat interface model ranges from ~59% for tall and sparse pillars (marked by high substrate permeability) to ~ 29% for short pillars (with low substrate permeability). We show that the average rate of evaporation of a LF droplet obtained using the curved interface model agrees reasonably (within 9%-23%) with that observed in the experiments. Leidenfrost droplets have been shown to exhibit strong internal convection. Here, we investigate the role of surface micropillars on the internal convection in Leidenfrost droplets using particle image velocimetry. The flow field inside a LF droplet with size less than the capillary length is shown to be asymmetric resembling solid-body rotation. We observe that the internal flow velocity is higher on smooth substrates and on short and dense pillars compared to that on tall and sparse pillars. In addition, the convective flow velocity increases with an increase in substrate temperature. We attribute the internal flow within the LF droplet to the vapor flow beneath the droplet and the resulting shear stress acting at the liquid-vapor interface. The permeability of the microtextured surface and the substrate temperature influences the excess vapor height beneath a LF droplet. We develop a model to show the impact of substrate flow permeability and substrate temperature on the vapor shear stress at the liquid-vapor interface beneath the droplet. On tall and sparse pillars, the higher flow permeability decreases the excess vapor gap and subsequently reduces the shear stress and resulting flow velocity inside the droplet. We observe that a threefold increase in the substrate permeability on tall and sparse pillars as compared to smooth substrate leads to a 70% reduction in the internal flow velocity. Additionally, on superhydrophobic silicon nanograss substrate and substrates with high permeability, for a 100 ℃ increase in substrate superheat, the internal velocity increases by 1.5 times. The proposed model offers insights into the combined effects of surface microtextures and substrate temperature on vapor shear stress, leading to variations in the excess vapor gap and, consequently, influencing induced internal convection velocity within levitating droplets. We experimentally observe an increase in the angular velocity of the internal convection of a LF droplet as it reduces size due to evaporation on a smooth substrate. We use interferometric technique to show that this increase in the angular velocity is accompanied by an increase in the asymmetry in the vapor gap beneath the droplet. We demonstrate that the tilt in the vapor gap increases as the size reduces resulting in an increase in the angular velocity inside the LF droplet. This finding further confirms the role of vapor gap in inducing the internal asymmetric flow in LF droplets