Electrowetting-based enhancement of droplet growth dynamics and heat transfer during humid air condensation

Highlights

• Electrowetting (EW) accelerates coalescence and growth of condensed droplets.

• Magnitude, frequency of applied AC fields influences droplet growth dynamics.

• EW alters droplet size distributions to favor condensate removal via roll-off.

• >30% enhancement in condensation rate resulting from EW fields.

• Analytical model to predict EW-enhanced condensation of humid air.

Abstract

Condensation heat transfer can be significantly enhanced by condensing vapor as droplets (instead of a film), which rapidly roll-off. This work studies the use of electrowetting to enhance coalescence, growth and roll-off dynamics of condensed droplets, thereby enhancing the condensation rate and associated heat transfer. This enhancement depends on the nature of fluid motion (translation of droplets, oscillations of the three phase line), which in turn depends on the magnitude and frequency of the applied electrical actuation waveform. Experiments are conducted to study early-stage droplet growth dynamics, as well as steady state condensation under the influence of an electric field. It is seen that droplet growth is enhanced as the voltage and frequency of AC electric fields is increased, with AC electric fields seen to be more effective than DC electric fields. Roll-off dynamics also depends on the frequency of the AC field. Overall, electric fields alter the droplet size distribution and move the condensate to more favorable states for removal from the surface. The condensation rate depends on the roll-off diameter of the droplet, frequency of roll-off events, and on the interactions of the rolled-off droplets with the remainder of the droplets. An analytical heat transfer model is utilized to relate the measured condensation rate with condensation heat transfer. It is noted that this study deals with condensation of humid air, and not pure steam. Overall, this study reports more than 30% enhancement in condensation rate resulting from the applied electric field, which highlights the attractiveness of electrowetting for condensation heat transfer enhancement.

Introduction

Condensation of water is the basis of many applications including atmospheric water harvesting [1], [2], [3], power generation [4] and desalination [5], [6]. The condensation rate and associated heat transfer is limited [7] by a condensate film on the surface; this occurs in most applications since metallic condenser surfaces are hydrophilic. Heat transfer is significantly enhanced if water condenses as drops which then roll-off [8], thereby exposing the surface to fresh vapor for re-nucleation. Dropwise condensation (DWC) [7] is observed on hydrophobic and superhydrophobic surfaces, which offer lower resistance to roll-off. Eliminating the thermal resistance of the film increases heat transfer coefficients by 5–10X [7] as compared to filmwise condensation.

DWC has been widely studied [7], [9], [10] from the objective of developing surfaces which enhance condensation heat transfer (CHT). There are three stages that a condensing fluid finds itself in during DWC [11], [12]. Firstly, droplets nucleate and grow by direct vapor condensation on the surface. In the second stage, droplets grow rapidly by coalescence of neighboring droplets, which widens the droplet size distribution. In the third stage, sufficiently large droplets roll-off under gravity, and capture additional condensate droplets on their way down. Condensation dynamics and droplet size distributions have been studied on surfaces with a variety of textures and chemistry [9], [13], [14], [15], [16]. A majority of experimental studies on DWC have involved condensation of steam or saturated vapor; there exist fewer studies on condensation in the presence of non-condensable gases (NCGs), [14]. On the theoretical front, recent studies [8], [17], [18] have used measured droplet size distributions to estimate CHT using single droplet-based thermal resistance models.

In addition to surface engineering-based approaches, the use of an electric field to promote condensation heat transfer has generated significant recent interest [19], [20], [21], [22]. Miljkovic et al. [23] used an electric field to prevent droplets jumping from the surface (due to the energy released via coalescence) from returning back; a 50% enhancement in heat transfer was measured. There also exist studies on the use of an electric field [24], [25] to alter the surface tension of the condensing surface and condensed droplets, as a tool for enhancing DWC.

This work presents a study of the influence of electrowetting (EW) on condensation heat transfer enhancement. EW is a well-studied [26], [27], [28], [29] fluid handling technique to control the wettability of droplets and enable microfluidic operations like the movement, splitting and merging of droplets. EW is based on the application of an electrical potential difference across a dielectric layer underlying the droplet (electrically conducting) to modulate wettability, and to actuate the droplet. The classical Young-Lippman’s equation [26], [30] predicts the voltage-dependent contact angle as:

$$\cos \theta =\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_{\mathit{eq}}+\frac{C}{2\gamma }{V}^2$$

where ${\theta }_{\mathit{eq}}$ is the equilibrium contact angle (no voltage), $\gamma$ is the liquid-vapor interfacial tension, $V$ is the applied voltage and $C$ is the capacitance per unit area of the dielectric layer. The dielectric layer is a critical component of EW systems, with high dielectric constant, high electrical breakdown field and low surface energy being favorable attributes. Additionally, the dielectric material needs to be pin-hole free to prevent current flow.

The role of the frequency of the AC waveform used in EW actuation has been examined in prior studies. For context, a study of the influence of the AC frequency on condensation is a key aspect of the present work. For DC and low frequency AC waveforms, the droplet can be considered electrically conducting and equipotential (no electric field exists inside the liquid). However, at frequencies higher than the one corresponding to the charge relaxation time, the electric field begins to penetrate the droplet. The role of AC frequency is best understood by examining the expression for complex permittivity [26] of the droplet, ${\epsilon }^{\ast }=k{\epsilon }_0-j\frac{\sigma }{\omega }$. Here $k$ is the dielectric constant, $\sigma$ is electrical conductivity and $\omega$ is the AC frequency. The first term represents the capacitance, and the second term represents the resistance. As the frequency increases, the relative influence of the electrical conductivity is reduced and the droplet behaves more as an insulator. In practice, low frequency AC fields are used in many EW applications, since contact angle hysteresis is lower for AC fields as compared to DC fields [26], [28], [30]. Under an AC field the contact line is continuously perturbed by the oscillating voltage; de-pinning becomes easier [26], [30], which reduces hysteresis as compared to DC fields.

A significant number of studies on EW analyze EW-induced droplet motion, which is the key to the present study on EW-assisted droplet coalescence. The most commonly used configuration for EW-induced actuation of droplets consist of flat parallel plates separated by a fixed spacing. Arrays of individually addressable electrodes are fabricated on the bottom plate; the top plate acts as a common ground electrode to bias the droplet. The electrodes are covered with the EW dielectric layer and a hydrophobic topcoat to reduce the resistance to motion. When an electrode (on the bottom plate) adjacent to the droplet is turned on, electrostatic forces propel the droplet towards the center of the actuated electrode (which is the minimum energy position for that configuration). The actuation force that drives droplet motion depends on the change of the droplet area in contact with the actuated electrodes. For DC electric fields the EW force can be approximated as [27], [28]:

$$F_{\mathit{EW}}=\frac{1}{2}{V}^2\frac{\mathit{dA}}{\mathit{dx}}\left(\frac{k_d{\epsilon }_0}{d}\right)$$

where $k_d$ is the dielectric constant of the dielectric layer, $d$ is the thickness of the dielectric layer and $\frac{\mathit{dA}}{\mathit{dx}}$ is the change in area of the droplet in contact with the actuated electrode. The above equation estimates the force as the gradient of the electrostatic energy distribution. Also, droplet motion is opposed by contact line friction, viscous drag and wall shear forces [27]. In the present experiments, the electrodes have a co-planar geometry where the positive and ground electrodes are in the same plane, separated by a non-conducting gap. In this case, the field lines form an arc from the high voltage electrode to the ground [24], [31].

There exist five studies on the use of EW for condensation enhancement. The first study on EW and condensation was by Kim et al. [25], wherein an EW voltage was used to reduce the critical inclination angle for droplet roll-off. Experiments were first conducted using single droplets [25]; a later study involved removing condensate from evaporator fins [32]. In a more recent study, Baratian et al. [24] studied the coalescence of droplets condensing under the influence of a 1 kHz AC EW field. Energy-minimization considerations were used to explain condensation patterns and droplet size distributions. Another study from the same group showed that certain EW electrode configurations reduce droplet shedding radii and achieve faster roll-off, while other configurations trap droplets and hinder roll-off [33]. Yan et al. [34] showed that application of a DC electric field increased water shedding by inducing roll-off. However, this study involved condensation of mist droplets from a commercial water mister and cannot be directly compared with other studies on condensation which strictly involve condensation via phase change.

This manuscript details a fundamental study on EW-accelerated droplet growth dynamics and condensation heat transfer. Importantly, all experiments involve condensation of humid air (with significant non-condensables) unlike steam condensation which is the focus of a majority of existing studies. The influence of the applied voltage and frequency of the AC EW field on droplet growth and coalescence is experimentally characterized, and the underlying physical mechanisms are discussed. The influence of EW fields on condensation dynamics is studied both in the pre-droplet shedding phase, and in the droplet shedding phase. The CHT enhancement resulting from the EW fields is estimated by measuring the water condensation rate, which feeds into an analytical thermal resistance-based heat transfer model.