Impact of substrate elasticity on contact angle saturation in electrowetting

The electrostatically assisted wettability enhancement of dielectric solid surfaces, commonly termed as electrowetting-on-dielectric (EWOD), facilitates many microfluidic applications due to simplicity and energy efficiency. The application of a voltage difference between a conductive droplet and an insulated electrode substrate, where the droplet sits, is enough for realizing a considerable contact angle change. The contact angle modification is fast and almost reversible; however it is limited by the well-known saturation phenomenon which sets in at sufficiently high voltages. In this work, we experimentally show and computationally support the effect of elasticity and thickness of the dielectric on the onset of contact angle saturation. We found that the effect of elasticity is important especially for dielectric thickness smaller than 10 μm and becomes negligible for thickness above 20 μm. We attribute our findings on the effect of the dielectric thickness on the electric field, as well as on the induced electric stresses distribution, in the vicinity of the three phase contact line. Electric field and electric stresses distribution are numerically computed and support our findings which are of significant importance for the design of soft materials based microfluidic devices.


Sample characterization
Before conducting electrowetting experiments, the samples were characterized by their static contact angle and contact angle hysteresis as described in "Experimental setup & methods". The measurements were carried out on the commercial goniometer/tensiometer ramé-hart (model 100) mounted with an automated dispensing system. The contact angle hysteresis was estimated by the method of adding/removing volume. In particular, a droplet of 7 μl was deposited via the micro syringe of the dispensing system and rested on the sample for 20 s. With the micro syringe immersed in the drop, its volume was then increased in steps of 0.1 μL/s. The advancing contact angle was measured after each volume increment as the volume increased up to 12 μL. At this point, the droplet was kept at constant volume for further 20 s. By decreasing the volume of the droplet with the same rate to a final volume of 2 μL, the receding contact angle was obtained. At the final volume of 2 μL, the contact angle was measured for another 20 s.  The higher apparent contact angles and contact angle hysteresis observed on samples with a lower Young's modulus is solely an effect of substrate viscoelasticity. The surface chemistry is hardly affected by mixing of the two components of the Sylgard 184 kit. The first one, the "monomer", is actually a linear poly(dimethyl siloxane) molecule, vinyl-terminated. One can find the structure here [3]. The curing agent cross-links with these linear PDMS chains. The exact composition is proprietary, but according to the Material Safety Datasheet (MSDS) the curing agent contains: (i) Dimethyl, Methylhydrogen Siloxane, Trimethylsiloxy-terminated, (ii) Dimethyl Siloxane, Dimethylvinylsiloxy-terminated, (iii) Dimethylvinylated and trimethylated silica nanoparticles, (iv) <1% of solvent. Thus, the first two components (>70% of total mass) are siloxanes and have very similar structure to the linear PDMS "monomer" and the silica nanoparticles also have a similar surface coating. So, the surface chemistry is not affected by adding the curing agent, which was anyway less than 10% in all cases. What changes between samples is the number of methylene "bridges" between the linear PDMS molecules that affect bulk viscoelastic properties [4]. The crosslinking reaction can be found here [5]. The final product is a PDMS network. The varying mixing ratio has otherwise a minimal effect on density, well below 1%, so the surface tension is expected to change at most by this amount, which cannot have any measurable effects.
Many previous experimental studies [6][7] have reported that the contact angle of milimetresized droplets on soft substrates increases with decreasing elastic modulus. The deposition of a liquid droplet on a solid surface that is deformable, results in the formation of a wetting ridge in the vicinity of the three-phase contact line (TPCL). The water surface essentially "pulls" upward the soft substrate. The apparent contact angle that is measured from the horizontal plane may, thus, differ from the Young's angle [8].
The height and aspect ratio of the ridge increase with decreasing elastomer modulus. The socalled static contact angle is usually very close to the advancing contact angle of the liquid. So, according to the Gibbs relation (see, e.g., [9]) the apparent contact angle (measured from the horizontal plane) increases, because the PDMS-air interface to the right of the ridge has a negative slope. This slope increases, in absolute value, with decreasing modulus, so the apparent contact angle increases.

Electrowetting experiments
In this section, the data obtained from the electrowetting experiments are once again presented. In order to identify the effect of thickness on samples of the same elasticity, the apparent contact angle with respect to the applied voltage and the corresponding electrowetting number were plotted. The measurements are summarized in Figures 3 and 4.  We perform numerical simulations to study the wetting behavior of a 2D axisymmetric droplet on a rigid flat dielectric layer with thickness, , when applying an electric potential, (see figure 5). The dynamics of the liquid droplet are governed by the Navier-Stokes equations, which describe the conservation of mass and momentum, and are given by: where is the fluid velocity field, denotes the gravitation field and the total stress tensor. The droplet is considered to be an incompressible and conductive Newtonian fluid, with density, , viscosity, and surface tension, (liquid-ambient interfacial tension). In accordance to your previous work, we treat the liquid-gas and liquid-solid interfaces in a unified manner that form the liquid-ambient interface around the droplet. Therefore, the solution of the Navier-Stokes equations is determined by imposing a single boundary condition along the liquid-ambient interface.
where is the local curvature. The above equation represents the normal stress component and includes the liquid-solid and electrostatic interactions. The liquid-solid interactions are lumped in a disjoining (Derjaguin) pressure term, : where is the initial radius of the droplet, are parameters in the potential, is 0 , , 1 , 2 ( , ) the Euclidean distance of the droplet from the nearest wall and is the depth of the potential, which sets the Young's contact angle implicitly according to Dupré's approach [10]. The distance, is the electric field magnitude, represents the contribution of the electric potential to the wetting state of the droplet. The electric field, is calculated by solving Gauss' law: where the relative permittivity, , is assumed to have a value of 1 for the ambient phase (air) and 2.4 for the solid dielectric.
Finally, the moving interface is captured by imposing the following kinematic boundary condition along the liquid-ambient interface: The 2D axisymmetric model is implemented using the COMSOL Multiphysics ® software package.