Fluid viscoelasticity controls acoustic streaming via shear waves

TL;DR

This work develops a two-region theoretical framework for acoustic streaming in viscoelastic fluids inside rectangular microchannels using the Oldroyd-B model and a second-order perturbation expansion. A streaming coefficient $C_s$ is introduced to capture the combined influence of Reynolds and viscoelastic stresses, predicting streaming enhancement ($C_s>1$), suppression ($0\le C_s\le1$), or reversal ($C_s<0$) as functions of the Deborah number $De$ and the viscous diffusion number $Dv$. The authors validate the theory with experiments in DI water and polyethylene oxide solutions, using defocusing particle tracking to map cross-sectional streaming and observe SE, SS, and SR in agreement with the $De$–$Dv$ phase map. They further link these transitions to viscoelastic shear waves, characterized by energy storage and dissipation in the shear modulus, providing a mechanism to tune microfluidic pumping and mixing in viscoelastic media.

Abstract

Control of acoustic streaming can significantly impact fluid and particle transport in microfluidics. We report enhancement, suppression, and reversal of acoustic streaming inside a rectangular microchannel by controlling the fluid viscoelastic properties. Our study reveals that the streaming regimes depend on Deborah number ($De$) and viscous diffusion number ($Dv$), expressed in terms of a Streaming Coefficient ($C_s$). We find streaming is enhanced when $C_s>1$, suppressed for $0\leq C_s\leq1$, and reversed when $C_s<0$. We explain the regimes in terms of the interplay between the Reynolds and viscoelastic stresses that collectively drive fluid motion. Remarkably, we discover the role of viscoelastic shear waves in acoustic streaming transition characterized by the ratio of acoustic attenuation length and shear wavelength. We gain deeper insight into the streaming transition by examining energy dynamics in terms of the loss and storage moduli. Our study may find applications in acousto-microfluidics systems for particle handling and fluid pumping/mixing.

Figures (7)

• Figure 1: A sketch of the section of viscoelastic fluid and stationary channel wall with acoustic boundary layer formation. The bulk fluid supports a horizontal 1-D standing sinusoidal pressure wave of wavelength $\lambda_0$ along the $x$ axis of channel. The interaction between oscillating viscoelastic fluid and the stationary wall forms a acoustic boundary layer closed to the wall, represented by $\delta_{ve}$, indicate the short range fluid region with an incompressible solenoidal flow. The region away from the $\delta_{ve}$ is long range field with compressible potential flow, represented by $d$. Using Helmholtz decomposition the total first order fluid velocity is consider as $\boldsymbol{v}_1=\boldsymbol{v}_1^d+\boldsymbol{v}_1^\delta$. A schematic variation of $\boldsymbol{v}_1^d$ (red), $\boldsymbol{v}_1^\delta$ (blue) and $\boldsymbol{v}_1$ (black) is shown with arrows, which indicate the direction of field.
• Figure 2: Schematic diagram showing the experimental set up.
• Figure 3: Variation of viscosity of aqueous PEO solutions at different concentrations with shear rate, showing a plateau at low shear rates and negligible shear-thinning in the range relevant to acoustic streaming experiments.
• Figure 4: Analytical variation of streaming velocity profiles in the channel cross-section ($XY$ plane) for Deborah numbers $De = 0$ to $10^3$ at fixed $Dv = 20$. Arrow length and direction represent the relative magnitude and direction of streaming compared to $De=0$ case. (c) Variation of the dimensionless maximum streaming velocity within a quarter of the microchannel cross-section as a function of $De$ at $Dv = 20$, normalized by the Newtonian case $(De=0)$. Labels SE, SS, and SR denote streaming enhancement, suppression, and reversal relative to the purely viscous case ($De = 0$), while $\textrm{SR}^{+}$ and $\textrm{SR}^{-}$ indicate enhancement and suppression in the reversed direction.
• Figure 5: (a) Comparison of theoretical and experimental dimensionless streaming velocity $\langle \tilde{v}_2 \rangle$ profiles across one quarter of the channel cross-section, illustrating streaming enhancement (SE, PEO 1 MDa, $Dv=0.90$, $De=1.75$), streaming suppression (SS, PEO 2 MDa, $Dv=16.21$, $De=110.45$), and streaming reversal (SR, PEO 0.4 MDa, $Dv=16.21$, $De=6.25$), compared with deionized water (DI, $Dv=0$, $De=0$). Arrows indicate streaming direction. (b) Theoretical variation of the dimensionless maximum streaming velocity $\langle \tilde{v}_2 \rangle_{\textrm{max}}^*$ with $De$ for PEO solutions, with experimental data shown as symbols. (c) Analytical prediction of the streaming coefficient $C_s$ as a function of $De$ and $Dv$; symbols denote experimental data. Red ($C_s=1$) and blue ($C_s=0$) dashed lines mark the SE–SS and SS–SR transitions, respectively.