Effect of blockage ratio on flow of a viscoelastic wormlike micellar solution past a cylinder in a microchannel.

We present experiments on the flow of a viscoelastic wormlike micellar solution around cylinders (radius R) confined in straight microchannels (width W). Thirteen flow geometries are tested where the blockage ratio is varied over a wide range 0.055 ≤ BR = 2R/W ≤ 0.63. Experiments are performed at negligible Reynolds number, and for Weissenberg numbers Wi = λU/R up to 1000, where U is the average flow speed and λ is the relaxation time of the fluid. Micro-particle image velocimetry is used to characterise the flow state at each BR and Wi. In all of the geometries, a first critical Weissenberg number marks a transition from symmetric flow to an asymmetric but time-steady flow state, while a second higher critical Weissenberg number marks the onset of time-dependent flows. However, we report a clear shift in behaviour over a narrow intermediate range of 0.33 ≲ BR ≲ 0.41. Channels with BR ≤ 0.33 fall in a 'low' BR regime, with instabilities that originate from the downstream stagnation point, while those with BR ≥ 0.44 fall in a 'high' BR regime, with instabilities developing at the upstream stagnation point. Behaviour within the newly-identified intermediate BR regime is complex due to the competing influence of the two stagnation points. We summarise all our results in a flow state diagram covering Wi-BR parameter space, clearly defining the different regimes of blockage ratio for the first time. Our results contribute to the understanding of the complexities of viscoelastic flow in this benchmark geometry.

Upstream wall vortices in viscoelastic flow past a cylinder.

We report a novel inertia-less, elastic flow instability for a viscoelastic, shear-thinning wormlike micellar solution flowing past a microcylinder in a channel with blockage ratio BR = 2R/W = 0.5 and aspect ratio α = H/W ≈ 5, where R ≈ 100 µm is the cylinder radius, W is the channel width, and H is the channel height. The instability manifests upstream of the cylinder and changes form with increasing Weissenberg number over the range 0.5 ≲ Wi = Uλ/R ≲ 900, where U is the average flow velocity and λ is the terminal relaxation time of the fluid. Beyond a first critical Wi, the instability begins as a bending of the streamlines near the upstream pole of the cylinder that breaks the symmetry of the flow. Beyond a second critical Wi, small, time-steady, and approximately symmetric wall-attached vortices form upstream of the cylinder. Beyond a third critical Wi, the flow becomes time dependent and pulses with a characteristic frequency commensurate with the breakage timescale of the wormlike micelles. This is accompanied by a breaking of the symmetry of the wall-attached vortices, where one vortex becomes considerably larger than the other. Finally, beyond a fourth critical Wi, a vortex forms attached to the upstream pole of the cylinder whose length fluctuates in time. The flow is highly time dependent, and the cylinder-attached vortex and wall-attached vortices compete dynamically for space and time in the channel. Our results add to the rapidly growing understanding of viscoelastic flow instabilities in microfluidic geometries.

Bifurcations in flows of complex fluids around microfluidic cylinders.

Flow around a cylinder is a classical problem in fluid dynamics and also one of the benchmarks for testing viscoelastic flows. The problem is of wide relevance to understanding many microscale industrial and biological processes and applications, such as porous media and mucociliary flows. In recent years, we have developed model microfluidic geometries consisting of very slender cylinders fabricated in glass by selective laser-induced etching. The cylinder radius is small compared with the channel width, which allows the effects of the stagnation points in the flow to dominate over the effects of squeezing between the cylinder and the channel walls. Furthermore, the cylinders are contained in high aspect ratio microchannels that render the flow field approximately two-dimensional (2D) and therefore conveniently permit comparison between experiments and 2D numerical simulations. A number of different viscoelastic fluids including wormlike micellar and various polymer solutions have been tested in our devices. Of particular interest to us has been the occurrence of a striking, steady-in-time, flow asymmetry that occurs for certain non-Newtonian fluids when the dimensionless Weissenberg number (quantifying the importance of elastic over viscous forces in the flow) increases above a critical value. In this perspective review, we present a summary of our key findings related to this novel flow instability and present our current understanding of the mechanism for its onset and growth. We believe that the same fundamental mechanism may also underlie some important non-Newtonian phenomena observed in viscoelastic flows around particles, drops, and bubbles, or through geometries composed of multiple bifurcation points such as cylinder arrays and other porous media. Knowledge of the instability we discuss will be important to consider in the design of optimally functional lab-on-a-chip devices in which viscoelastic fluids are to be used.

Stagnation points control chaotic fluctuations in viscoelastic porous media flow.

Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting widespread industrial and biological processes such as enhanced oil recovery and drug delivery. Understanding the influence of the pore structure or geometry on the onset of flow instability can lead to fundamental insights into these processes and, potentially, to their optimization. Recently, for viscoelastic flows through porous media modeled by arrays of microscopic posts, Walkama et al. [D. M. Walkama, N. Waisbord, J. S. Guasto, Phys. Rev. Lett 124, 164501 (2020)] demonstrated that geometric disorder greatly suppressed the strength of the chaotic fluctuations that arose as the flow rate was increased. However, in that work, disorder was only applied to one originally ordered configuration of posts. Here, we demonstrate experimentally that, given a slightly modified ordered array of posts, introducing disorder can also promote chaotic fluctuations. We provide a unifying explanation for these contrasting results by considering the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the nature of the originally ordered post array. This work provides a general understanding of how pore geometry affects the stability of viscoelastic porous media flows.

Tristability in Viscoelastic Flow Past Side-by-Side Microcylinders.

Viscoelastic flows through microscale porous arrays exhibit complex path selection and switching phenomena. However, understanding this process is limited by a lack of studies linking between a single object and large arrays. Here, we report experiments on viscoelastic flow past side-by-side microcylinders with variable intercylinder gap. With increasing flow rate, a sequence of two imperfect symmetry-breaking bifurcations forces selection of either one or two of the three possible flow paths around the cylinders. Tuning the gap length through the value where the first bifurcation becomes perfect reveals regions of bistability and tristability in a dimensionless flow rate-gap length phase diagram.

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations.

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields.

Phosphonium Polyelectrolyte Complexes for the Encapsulation and Slow Release of Ionic Cargo.

Polyelectrolyte complexation, the combination of anionically and cationically charged polymers through ionic interactions, can be used to form hydrogel networks. These networks can be used to encapsulate and release cargo, but the release of cargo is typically rapid, occurring over a period of hours to a few days and they often exhibit weak, fluid-like mechanical properties. Here we report the preparation and study of polyelectrolyte complexes (PECs) from sodium hyaluronate (HA) and poly[tris(hydroxypropyl)(4-vinylbenzyl)phosphonium chloride], poly[triphenyl(4-vinylbenzyl)phosphonium chloride], poly[tri(n-butyl)(4-vinylbenzyl)phosphonium chloride], or poly[triethyl(4-vinylbenzyl)phosphonium chloride]. The networks were compacted by ultracentrifugation, then their composition, swelling, rheological, and self-healing properties were studied. Their properties depended on the structure of the phosphonium polymer and the salt concentration, but in general, they exhibited predominantly gel-like behavior with relaxation times greater than 40 s and self-healing over 2-18 h. Anionic molecules, including fluorescein, diclofenac, and adenosine-5'-triphosphate, were encapsulated into the PECs with high loading capacities of up to 16 wt %. Fluorescein and diclofenac were slowly released over 60 days, which was attributed to a combination of hydrophobic and ionic interactions with the dense PEC network. The cytotoxicities of the polymers and their corresponding networks with HA to C2C12 mouse myoblast cells was investigated and found to depend on the structure of the polymer and the properties of the network. Overall, this work demonstrates the utility of polyphosphonium-HA networks for the loading and slow release of ionic drugs and that their physical and biological properties can be readily tuned according to the structure of the phosphonium polymer.

Purely Elastic Fluid-Structure Interactions in Microfluidics: Implications for Mucociliary Flows.

Fluid-structure interactions lie at the heart of the complex, and often highly coordinated, motions of actively driven microscale biological systems (e.g., translating cilia, flagella, and motile cells). Due to the highly viscoelastic nature of most relevant biological fluids and the small length scales involved, the viscous and inertial forces in such flows are dominated by elasticity. However, elastic effects are often overlooked in studies seeking to address phenomena like the synchronization of beating cilia. In this study, unique microfluidic experiments are presented to demonstrate that inertia-free viscoelastic flows can lead to highly regular beating of an immersed (passive) flexible structure, herein named "purely-elastic" fluid-structure interaction. It is also shown how two such flexible structures can achieve an extraordinary degree of synchronization, with a correlation coefficient approaching unity. The synchronization is a result of the generation of localized elastic stresses in the fluid that effectively link the two objects. These purely elastic interactions may be important to consider toward developing a complete understanding of the motions of microscale biological systems.

Modelling the deflection of rowing oar shafts.

The deflection of rowing oar shafts subjected to a static load was investigated. Two sets of sculling oars of different design stiffness were tested at three different lengths from 2.66 to 2.70 m. Loads up to 201 N were applied to the blade end of the oar shafts, and deflections were measured at six positions along the length of the shafts. The experimental results were compared with theoretical predictions obtained by modelling the oar shafts as homogenous end-loaded cantilever beams. The results show that the oar shafts are not uniform, in contradiction to the assumed model, but rather are most compliant near the sleeves and up to 80% stiffer towards the blades. The effect of oar shaft stiffness and length on the deflection angle at the blade end of the oar shaft was at most 1.18 ± 0.01°. The measured variation of stiffness along the shaft has implications for boat propulsion and rowing performance.