Contact angle-based predictive model for slip at the solid–liquid interface of a transverse-shear mode acoustic wave device

Abstract

We have revisited the Blake-Tolstoi theory ͓Coll. Surf. 47, 135 ͑1990͔͒ for molecular and hydrodynamic slip and applied it to the fundamental description of acoustic wave devices coupled to a liquid of finite thickness. The aim is to provide a framework for a predictive model for slip, based on surface-liquid interactions and contact angle. This theory provides a description of slip that links hydrodynamic boundary slip to a schematic, molecular description involving the wettability of the liquid-solid interface. We redevelop the model, using current acoustic sensors notation, then evaluate its qualitative behavior as a predictive model for slip length in the context of acoustic wave devices. Finally, we discuss the limitations of the model and consider the advantages of a predictive model for boundary slip.

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

“…From White, 1997. surface acoustic wave sensors, cantilevers, and quartz crystal microbalances that are useful for characterizing fluid viscosity and density, and detecting the presence of monolayers due to binding or growth, biopolymers or biomolecules, or even entire cells and tissue. A comprehensive review of the area requires an entirely separate effort, and in light of the reviews by Grate et al (1993), Marx (2003), and Lucklum and Hauptmann (2006), the other areas of sensor development for microfluidics, using optics, for example, as reported by Monat et al (2007), not to mention the work by McHale et al (2003) on Love wave and shear-horizontal wave sensors, the review of work on biosensors by Länge et al (2008) and biomolecular binding in acoustic sensing by Cavić et al (1999), the article by Ellis et al (2003) on predicting the effects of slip at the interface, and even the use of tailored electrode configurations such as the ones reported by Kondoh et al (2007), we focus upon actuation in lieu of sensing in most of what follows, because the recent developments in the application of acoustics at the microscale and beyond appear to principally be on actuation.…”

“…Their modeling of the fluid as a Maxwell viscoelastic fluid was useful in forming a theoretical model of the phenomena, although it did not include compressibility. Because the fluid tended to spread upon exposure to the SAW, Ellis et al (2003) sought to model the slip induced by the acoustic wave at the solid-fluid interface, recasting the Blake-Tolstoi theory of molecular and hydrodynamic slip (Blake, 1990) for this purpose. Notwithstanding the many limitations of these theories, they found that as the fluid's contact angle increases (associated with a decrease in disjoining pressure), the magnitude of the resonant frequency shift decreases due to the reduction in the negative disjoining pressure.…”

Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

“…1. The definition of slip length used in some recent slip studies [33,37,38,39], and formalised by Ellis and Hayward [33] as (their notation)…”

“…Kanazawa and Gordon [32] analytically coupled a half-space of Newtonian fluid to a piezoelectric Quartz Crystal Microbalance (QCM), in which a solid interface oscillates in shear mode, using the NSBC. Further reports have presented experiments [33,34,35,36] and analysis [33,34,35,37,38,39] describing slip of a Newtonian fluid adjacent to an oscillating surface. A relatively large set of slip lengths measured using a QCM was obtained by Ellis and Hayward [33].…”

The effect of SU-8 patterned surfaces on the response of the quartz crystal microbalance

“…al. [12] have provided a predictive model showing how the equilibrium contact angle on a QCM surface might lead to interfacial slip. Recently, McHale and Newton [13] have shown how a hydrodynamic slip boundary condition can provide a theoretical basis for either a trapped mass response or an interfacial slip response.…”