[Paper Review] A partially wetting film of water and surfactant under the influence of a propagating MHz surface acoustic wave

Gennady Altshuler, Ofer Manor|arXiv (Cornell University)|Nov 4, 2015

Fluid Dynamics and Thin Films56 references17 citations

TL;DR

This study investigates the dynamic wetting and dewetting of thin, partially wetting films of water-surfactant mixtures under a MHz Rayleigh surface acoustic wave (SAW), where the dominant mechanism is Schlichting boundary layer flow due to direct SAW-liquid coupling. The key finding is that capillary stress and mass drift balance determines film behavior: weak capillary effects lead to spreading, while strong capillary effects induce synchronized front-rear motion and capillary wave trains, with experimental data collapsing onto a theoretical scaling law based on the $ heta^3/ ext{We}$ parameter.

ABSTRACT

We use both theory and experiment to study the response of {\it partially wetting} films of water and surfactant solutions to a propagating MHz vibration in the solid substrate in the form of a Rayleigh surface acoustic wave (SAW). The SAW invokes a drift of mass in the liquid film, which is associated with the Schlichting boundary layer flow (also known as the Schlichting streaming). We study thin films that are governed by a balance between the drift and capillary stress alone. We demonstrate weak capillary contributions, such as for silicon oil films, support dynamic wetting and lead to the spreading of the liquid over the solid substrate along the path of the SAW. Strong capillary contributions, such as for water films, support however a concurrent dynamic wetting and dewetting along the path of the SAW, such that the film displace along the solid substrate. In addition, such films may support the formation of a capillary train-wave that propagate along the the same path. We further note the mechanism for film dynamics we discuss here is different to the more familiar Eckart streaming mechanism, which is associated with a film thickness that is greater than the wavelength of the sound leakage off the SAW and usually observed to support the motion of drops. The thickness of the films we discuss here is small in respect to the wavelength of the sound leakage, rendering contributions from the Eckart streaming, acoustic radiation pressure, and the attenuation of the SAW small.

Motivation & Objective

• To understand the dynamic wetting and dewetting of thin, partially wetting water-surfactant films under MHz surface acoustic waves (SAWs).
• To isolate and analyze the role of Schlichting boundary layer flow (Schlichting streaming) as the dominant mass transport mechanism in films too thin to support acoustic wave accumulation.
• To differentiate the film dynamics from Eckart streaming by studying systems where sound wave leakage does not accumulate in the film, rendering Eckart streaming negligible.
• To establish a theoretical framework linking the balance between mass drift and capillary stress to observable film morphology and velocity, validated by experimental collapse onto a scaling law.

Proposed method

• Theoretical modeling of film dynamics based on a balance between viscous-driven mass drift (Schlichting streaming) and capillary stress, derived from the Navier-Stokes equations under lubrication approximation.
• Use of the non-dimensional parameter $ heta^3/ ext{We}$ to quantify the relative importance of mass drift (via Reynolds number Re) and capillary stress (via Weber number We).
• Experimental setup using a MHz SAW on a piezoelectric substrate to generate periodic surface motion, inducing viscous flow in thin liquid films.
• Film thickness $h \ll \lambda$, where $\lambda$ is the wavelength of sound leakage, ensuring negligible acoustic radiation pressure, Eckart streaming, and SAW attenuation.
• High-speed imaging to measure front and rear velocities of the film, with normalization to extract dimensionless scaling behavior.
• Comparison of experimental data collapse with theoretical prediction based on modified capillary velocity $ (\theta\epsilon)^3 \gamma / \mu $, where $\theta$ is contact angle, $\epsilon$ is film aspect ratio, $\gamma$ is surface tension, and $\mu$ is viscosity.

Experimental results

Research questions

• RQ1 How does the balance between Schlichting streaming-induced mass drift and capillary stress govern the dynamic wetting behavior of thin, partially wetting films under a MHz SAW?
• RQ2 What distinguishes the film dynamics in thin films ($h \ll \lambda$) from those in thicker films ($h \approx \lambda$) where Eckart streaming and acoustic radiation pressure are significant?
• RQ3 Can the experimental velocity data of film fronts and rears be collapsed onto a single theoretical scaling law, indicating the correct underlying physics?
• RQ4 To what extent do secondary effects like evaporation and surfactant convection contribute to film dynamics in the observed parameter range?
• RQ5 Why do partially wetting water-surfactant films exhibit synchronized front-rear motion and capillary wave train formation, unlike fully wetting silicon oil films?

Key findings

• For thin films with $h \ll \lambda$, Eckart streaming, acoustic radiation pressure, and SAW attenuation are negligible, confirming that Schlichting streaming is the dominant mechanism for mass transport.
• In films with weak capillary stress (e.g., silicon oil), the front of the film advances with the drift velocity $\text{Re}U$, while the rear remains nearly stationary, leading to continuous area increase.
• In films with strong capillary stress (e.g., water-surfactant), the front and rear move synchronously at a velocity scaled by the modified capillary velocity $ (\theta\epsilon)^3 \gamma / \mu $, indicating a constrained free surface.
• Experimental data for front and rear velocities collapse onto a single curve when normalized by the theoretical capillary velocity, validating the proposed scaling law.
• The monotonous trend in normalized velocity data across varying $\theta^3/\text{We}$ values indicates that contributions from evaporation and Marangoni effects are minor in the studied parameter range.
• Capillary wave trains are observed to propagate along the SAW path in partially wetting films, resulting from the interplay between mass drift and capillary stress when $\theta^3/\text{We} > 1$.