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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.

 

Thin-film flow down a fibre exhibits rich dynamics and is relevant to applications such as desalination, fibre coating and fog harvesting. These flows are subject to instabilities that result in dynamic bead-on-fibre patterns. We perform an experimental study of shear-thinning flow down fibres using 20 different xanthan gum solutions as our working liquid. The bead-on-fibre morphology can be oriented either symmetrically or asymmetrically on the fibre, and this depends upon the surface tension, fibre diameter and liquid rheology, as defined by the Ostwald power-law index. For highly shear-thinning liquids, it is possible for the pattern to be complex and exhibit simultaneously both asymmetric large beads and symmetric small beads in the isolated and convective flow regimes. We quantify the transition between flow regimes and bead dynamics for the asymmetric morphology, and compare with Newtonian flow, as it depends upon the experimental parameters. Finally, the dimensionless bead frequency is shown to scale with the Bond number for all of our experimental data (symmetric and asymmetric).

 

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. 

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.

 

The energetics of drop deposition are considered in the capillary-ballistic regime characterized by high Reynolds number and moderate Weber number. Experiments are performed impacting water/glycol drops onto substrates with varying wettability and contact-angle hysteresis. The impacting event is decomposed into three regimes: (i) pre-impact, (ii) inertial spreading and (iii) post contact-line (CL) pinning, conveniently framed using the theory of Dussan & Davis ( J. Fluid Mech. , vol. 173, 1986, pp. 115–130). During fast-time-scale inertial spreading, the only form of dissipation is CL dissipation ( $\mathcal {D}_{CL}$ ). High-speed imaging is used to resolve the stick-slip dynamics of the CL with $\mathcal {D}_{CL}$ measured directly from experiment using the $\Delta \alpha$ - $R$ cyclic diagram of Xia & Steen ( J. Fluid Mech. , vol. 841, 2018, pp. 767–783), representing the contact-angle deviation against the CL radius. Energy loss occurs on slip legs, and this observation is used to derive a closed-form expression for the kinetic K and interfacial $\mathcal{A}$ post-pinning energy $\{K+\mathcal {A}\}_p/\mathcal {A}_o$ independent of viscosity, only depending on the rest angle $\alpha _p$ , equilibrium angle $\bar {\alpha }$ and hysteresis $\Delta \alpha$ , which agrees well with experimental observation over a large range of parameters, and can be used to evaluate contact-line dissipation during inertial spreading. The post-pinning energy is found to be independent of the pre-impact energy, and it is broken into modal components with corresponding energy partitioning approximately constant for low-hysteresis surfaces with fixed pinning angle $\alpha _p$ . During slow-time-scale post-pinning, the liquid/gas ( $lg$ ) interface is found to vibrate with the frequencies and mode shapes predicted by Bostwick & Steen ( J. Fluid Mech. , vol. 760, 2014, pp. 5–38), irrespective of the pre-impact energy. Resonant mode decay rates are determined experimentally from fast Fourier transforms of the interface dynamics. 

Dynamic wetting phenomena are typically described by a constitutive law relating the dynamic contact angleθto contact-line velocityU_CL. The so-called Davis–Hocking model is noteworthy for its simplicity and relatesθtoU_CLthrough a contact-line mobility parameterM, which has historically been used as a fitting parameter for the particular solid–liquid–gas system. The recent experimental discovery of Xia & Steen (2018) has led to the first direct measurement ofMfor inertial-capillary motions. This opens up exciting possibilities for anticipating rapid wetting and dewetting behaviors, asMis believed to be a material parameter that can be measured in one context and successfully applied in another. Here, we investigate the extent to whichMis a material parameter through a combined experimental and numerical study of binary sessile drop coalescence. Experiments are performed using water droplets on multiple surfaces with varying wetting properties (static contact angle and hysteresis) and compared with numerical simulations that employ the Davis–Hocking condition with the mobilityMa fixed parameter, as measured by the cyclically dynamic contact angle goniometer, i.e. no fitting parameter. Side-view coalescence dynamics and time traces of the projected swept areas are used as metrics to compare experiments with numerical simulation. Our results show that the Davis–Hocking model with measured mobility parameter captures the essential coalescence dynamics and outperforms the widely used Kistler dynamic contact angle model in many cases. These observations provide insights in that the mobility is indeed a material parameter.