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A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin–Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a “drop vibration rheometer”, suggesting future experiments using either ultrasonic levitation or a microgravity environment.

 

A thin liquid droplet spreads on a soft viscoelastic substrate with arbitrary rheology. Lubrication theory is applied to the governing field equations in the liquid and solid domains, which are coupled through the free boundary at the solid–liquid interface, to derive a set of reduced equations that describe the spreading dynamics. Fourier transform techniques and the finite difference method are used to construct a solution for the dynamic liquid–gas and solid–liquid interface shapes, as well as the macroscopic contact angle. Substrate properties affect the spreading dynamics through the contact angle and internal droplet flow fields, and these mechanisms are revealed. Increased substrate softness increases the spreading rate, whereas increased viscoelasticity decreases the spreading rate. For the case of a purely elastic substrate, the spreading power-law exponent recovers Tanner's law in the rigid limit and increases with substrate softness.

 

Surfactants are often added to particle suspensions in the flow of Newtonian or non-Newtonian fluids for the purpose of reducing particle-particle aggregation and particle-wall adhesion. However, the impact on the flow behavior of such surfactant additions is often overlooked. We experimentally investigate the effect of the addition of a frequently used neutral surfactant, Tween 20, at the concentration pertaining to microfluidic applications on the entry flow of water and three common polymer solutions through a planar cavity microchannel. We find that the addition of Tween 20 has no significant influence on the shear viscosity or extensional flow of Newtonian water and Boger polyethylene oxide solution. However, such a surfactant addition reduces both the shear viscosity and shear-thinning behavior of xanthan gum and polyacrylamide solutions that each exhibit a strong shear-thinning effect. It also stabilizes the cavity flow and delays the onset of flow instability in both cases. The findings of this work can directly benefit microfluidic applications of particle and cell manipulation in Newtonian and non-Newtonian fluids. 

Surface waves are excited at the boundary of a mechanically vibrated cylindrical container and are referred to as edge waves. Resonant waves are considered, which are formed by a travelling wave formed at the edge and constructively interfering with its centre reflection. These waves exhibit an axisymmetric spatial structure defined by the mode number $n$ . Viscoelastic effects are investigated using two materials with tunable properties; (i) glycerol/water mixtures (viscosity) and (ii) agarose gels (elasticity). Long-exposure white-light imaging is used to quantify the magnitude of the wave slope from which frequency-response diagrams are obtained via frequency sweeps. Resonance peaks and bandwidths are identified. These results show that for a given $n$ , the resonance frequency decreases with viscosity and increases with elasticity. The amplitude of the resonance peaks are much lower for gels and decrease further with mode number, indicating that much larger driving amplitudes are needed to overcome the elasticity and excite edge waves. The natural frequencies for a viscoelastic fluid in a cylindrical container with a pinned contact-line are computed from a theoretical model that depends upon the dimensionless Ohnesorge number ${Oh}$ , elastocapillary number ${Ec}$ and Bond number ${Bo}$ . All show good agreement with experimental observations. The eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as a damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects. 

Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion–contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction–expansion microchannel of similar dimensions.