Heating analysis of a droplet on stretchable hydrophilic surface

Highlights

• Stretching of elastomer sample causes extension of the droplet axisymmetric at same rate.

• Stretching alters the wetting area and height of the droplet.

• The size and orientation of circulation structures alter in droplet fluid with stretching.

• Maximum flow velocity reduces inside droplet as stretching progresses.

• Nusselt and Bond numbers with stretching of elastomer sample.

Abstract

Heating of a droplet on a stretchable hydrophilic surface is investigated and fluid dynamics in the droplet under the heating load is assessed. Elastomer wafers are considered as the sample material and the fixture is designed and manufactured to assure uniform stretching of the droplet located elastomer surface. Droplet adhesion and possible slipping/sliding of the droplet are evaluated during stretching of the sample surface. Numerical simulations are carried out to predict thermal and flow response of the droplet fluid before and after stretching. The effect of droplet volume on heating enhancement is also included in the numerical simulations. Experiments are carried out using a high-speed recording system towards comparing the flow predictions. Findings reveal that predictions are in agreement with their counterparts of experiments. Stretching of sample surface increases wetting area and lowers height of the droplet while influencing thermal flow structures in the fluid. The Nusselt and the Bond numbers increase with enlarging stretching, which becomes more visible for large droplet volume (80 µl). Hence, stretching corresponding to 80% extension of elastomer surface gives rise to 60% improvement in the Nusselt number.

Introduction

Liquid droplet heating/cooling is important for various applications in biomedicine, fuel cells, combustions, aerospace, and similar technologies. Droplet heating on a surface generates convection currents in the fluid, which contributes to the heating rates from surface to fluid (Al-Sharafi et al., 2016a). The flow structure in the droplet depends on many influences, which may include wetting state, liquid volume and properties, ambient temperature, pressure, and humidity. Particularly, the wetting state of the surface changes the droplet characteristics from hydrophilic to hydrophobic and flow behavior in the droplet fluid changes significantly (Al-Sharafi et al., 2016c). As the surface texture composes of hierarchical distributed micro/nano pillars and nano-whiskers like structures, surface becomes hydrophobic with low hysteresis because of the Lotus influence generated by the nano-whiskers like structures in the texture (Yamamoto et al., 2015). As the surface texture possesses few micro-pillars with large spacings or possesses perfectly smooth texture, the Wenzel state reveals and surface demonstrates hydrophilic wetting. The state of the contact angle hysteresis greatly influence the droplet dynamics whether droplet slides/ or pins on the surface. Droplet pinning on hydrophilic surface changes the heat transfer rates because of large wetting area with low droplet height. In general, flow stability in liquid is attributed to the diffusion time, which is the square of the droplet diameter (D) over the liquid thermal diffusivity (${\alpha }_T$). This becomes larger than unity for the stable thermal motion ($\frac{D^2}{{\alpha }_T}>1$) (Tam et al., 2009), i.e. as the heating time becomes greater than one, the flow field mostly settles in the liquid (Al-Sharafi et al., 2018a). Two flow currents are mainly dominant in the droplet as it is heated at temperatures well below the evaporation temperature of the droplet liquid. These include Marangoni and buoyancy currents. The velocities of flow currents in the droplet also play a role on the droplet behavior. The ratio of velocities due to flow currents can be expressed as: $\frac{\frac{\partial \gamma }{\partial T}\mathrm{\Delta }T}{\beta \rho g{D}^2}$ $\frac{\frac{\partial \sigma }{\partial \mathrm{T}}\mathrm{\Delta }\mathrm{T}}{\beta \rho \mathrm{g}{\mathrm{L}}_{\mathrm{c}}^2}$where the dominator represents the Marangoni influence while denominator corresponds to the buoyancy influence. For the water droplet diameter (D) less than 2 mm results in velocities ratio less than unity and the droplet can roll on the surface (Al-Sharafi et al., 2016b. Moreover, elastomeric materials (rubber) are stretchable and the wettability of the elastomer surface can change with the amount of stretching. In general, surface contact angle of rubber changes within 50°–105° (Yilbas et al., 2019). The flow developed in a droplet at low contact angle surfaces (hydrophilic surfaces), the heating is attributed to thermal diffusion and the convection current influence on the heating becomes less important (Al-Sharafi et al., 2016c). Increasing droplet wetting area provides large area of contact between the liquid and the heated surface, i.e. lowering the contact angle towards increased hydrophilicity enhances the heat transfer rates from the hydrophilic surface. The wetting area of the droplet can be increased on the elastomer surface trough mechanical stretching. Hence, examination of the droplet heating on the stretchable elastomer surface becomes essential.

The pinning of the liquid droplet on the hydrophilic surfaces creates a sessile droplet and the size of the wetted area on the surface becomes important for heating applications, particularly heating from the interfacial-contacted surface to the fluid. The droplet pinning under a large hysteresis allows the droplet stretching as the solid surface stretches. This causes changing of the droplet contact on the surface. This becomes particularly true for the droplet that is formed on the thin liquid film. Hence, the heat transfer rates changes considerably because of the thin liquid film behavior (Wenzel et al., 2016). Moreover, to observe the flow behavior in spherical liquid droplets, optical refractometry technique can possibly be used; the measurements has several limitations such as optical beam size and beam waist position, which should be in certain ranges for the proper measurements (Zhou et al., 2019). Using a laser induced fluorescence technique can also provide insight diagnoses of evaporating droplet characteristics (Volkov and Strizhak, 2017). Temperature measurement of surrounding air in the close region of the droplet can provide the rate of vaporization from surfaces (Kuznetsov et al., 2017). As the droplet heating time increases at high fluxes, evaporation from the droplet surface cannot be avoided. Several model studies are introduced to formulate and predict the evaporation rates from the droplet surfaces, particularly adopting the gas phase model (Sazhin et al., 2006). In formulating the droplet evaporation, incorporating convection and radiation losses from the droplet surface together with droplet internal fluidity remain essential (Jin et al., 2019, Sazhin et al., 2005a). Utilization of effective thermal conductivity model in the droplet heat transfer can provide improved formulation of the heating situations, which is essentially important as the model study is extended to fuel droplets (Sazhin, 2006). The correct formulation of the droplet evaporation is vital for the multiple mixture fluids. Emulsion and droplet formation, due to collapsing of multi-small droplets into a large size droplet, are affected by the heating conditions. As the fluid mixture atomized by the fuel spraying system, the droplet heating and evaporation influences the level of atomization, which alters the mixture properties (Shen et al., 2020). Hence, the multi-component modeling of fuel droplets incorporating the interaction between the surrounding fluid and the droplet in terms of energy exchange becomes favorable predicting the correct thermal state of the droplet (Al Qubeissi et al., 2017, Poulton et al., 2020). The model and experimental studies differ considerably as the ignition for combustion or the explosion of the droplet are mutually considered (Antonov et al., 2020, Sazhin et al., 2005b).

Heating enhancement pertinent to liquid droplets on the hydrophilic surfaces can be achieved through extension of the wetting diameter of the droplet. This can be achieved through stretching of the hydrophilic surfaces. Hence, utilization of stretchable hydrophilic surface becomes essential to increase the droplet wetting diameter without causing significant alteration of the droplet characteristics such pinning. The droplet pinning occurs on the hydrophilic surface because of large hysteresis and the elastomer surfaces can provide the large hysteresis while enabling the droplet residing on the surface during the stretching. Although the droplet heating on the reversible hydrophobic surfaces (Al-Sharafi et al., 2019, Yilbas et al., 2019) are studied earlier, thermal response of the droplet on hydrophilic stretchable surfaces remains a future study. Rolling droplet interaction with the dust particles on stretchable hydrophobic surfaces was studied earlier (Yilbas et al, 2019). Stretching of the hydrophobic surface was found to alter the surface wetting, which influence the dust mitigation rates. However, heat transfer analysis during dust mitigation was not considered. The droplet heat transfer on a inclined and solid hydrophobic surface was studied previously (Al-Sharafi et al. 2018a). Although the influence of inclination angle of the non-stretching surface on droplet heat transfer (Al-Sharafi et al. 2018a) was presented, the effect of wetted are at solid-liquid interface was not accommodated in the analysis. In addition, several studies were conducted on the droplet heat transfer (Al-Sharafi et al., 2018b, Al-Sharafi and Yilbas, 2019b, Al-Sharafi and Yilbas, 2019c); however, most of the studies were focused on heat transfer enhancement through radiative heating (Al-Sharafi et al. 2018b), introducing extended surfaces inside droplet fluid, such as fin (Al-Sharafi et al. 2019b), and droplet in between hydrophobic plates (Al-Sharafi et al. 2019c). Heat transfer enhancement through droplet wetting area change on the stretchable hydrophobic surfaces were left for future study. Moreover, hydrophobic droplet heating and influence of wetting area at solid-liquid interface becomes critical for heat transfer enhancement. Through stretching, increasing the droplet wetting diameter changes the droplet height as the droplet volume is kept constant on the stretched surface. This alters the strength of flow current in the fluid and modifies convective heating inside the fluid. It is worth to mention that droplet height reduction increases the droplet ovality and changes the surface tension gradient, which directly influences the Marangoni current. Consequently, increasing the droplet wetted area can cause a dual effect on the droplet thermal state. These include: i) heat conduction enhancement in the droplet fluid in the close region of wetted surface, and ii) suppressing Marangoni current via reducing the Marangoni current intensity because of reduced surface tension gradient ($\frac{d\gamma }{\mathit{dT}}$, where γ is surface tension and T is temperature). Hence, in the present study, the droplet heating incorporating the stretchable surface is simulated and the influence of wetting diameter (stretching length) and droplet volume on the thermal state and flow structures in the droplet are examined. Experiments are carried out and the predicted flow fields are compared with those obtained from the experiments.