Session B31: Microflows Meet Soft Matter II: Deformation

Viscous flows with thin, compliant boundaries

Viscous fluids flowing in channels with solid, but compliant, boundaries are common in a range of biological and industrial settings. The presence of such compliance can qualitatively alter the behaviour of such systems, forcing us to revisit the basic principles with which viscous flows are usually understood: the reversibility of Stokes flow no longer holds and the relationship between flux and driving pressure may be nonlinear. In other situations, the mere presence of boundary compliance, combined with capillarity is enough to spontaneously generate fluid motion. I will give examples of some of these unusual behaviours, focussing on situations in which the compliant boundary is in some sense thin, as well as discussing the validity of the different models of boundary compliance.   

Slicing Soft Materials

We experimentally study the slicing of soft materials. We use a rheometer to press a circular cutting tool into these materials (a steel “cookie cutter”) at a controlled rotation speed and controlled speed in the normal direction. Typical rates are 100 rad/s angular speed and 10 microns/s normal speed. The rheometer allows us to measure the normal force and torque required to press the cutter through a material. The soft materials we use to experiment with are mainly Styrofoam and Clay. From examining the fluctuations of torque and normal force over time, we find that the most effective cutting occurs with slower normal speed, and that cutting is less sensitive to the rotation rate of the cutter.   

Valve Elasticity for Optimal Lymphatic Pumping

The lymphatic system transports interstitial fluid, fatty acid, and immune cells and maintains this vital function by pumping the lymphatic fluid via networks of contracting lymphatic vessels and elastic valves. The interplay of peristaltic motion of the lymphatic vessels and valves achieve unidirectional flow against adverse pressure gradient while minimizing any backflow. Despite the significance, research into the lymphatic system has been limited, especially regarding the function of lymphatic valves. We use fully coupled, three-dimensional fluid-structure interaction model to study the performance of compliant lymphatic valves in the lymphatic vessel that undergoes peristaltic motion. Parameters such as adverse pressure gradient, contraction frequency, contraction amplitude, and elasticity of the lymphatic valves are varied to investigate their effects on the flow rate and pumping efficiency, which are compared against their valve-less counterparts. The results suggest that lymphatic valves significantly extend the range of operational adverse pressure gradients. Furthermore, the simulations reveal the optimum valve elasticity enhancing pumping performance.   

Soft hydraulics: Theory of flow in deformable microchannels

The hydraulic resistance of conduits of any cross-section can be calculated from exact unidirectional flow solutions of the steady Stokes equations. Recently, however, experiments on internal flows in channels with soft boundaries have showm that wall deformation leads to a nonlinear relationship between the volumetric flow rate and the pressure drop. Thus, the soft hydraulic resistance is not simply a constant dependent on the cross-sectional shape. We propose a perturbative approach to solving soft hydraulics problems. The Stokes equations are coupled to the equations of linear elasticity. For a long and slender geometry, the flow problem is reduced to lubrication theory. The deformation of the elastic wall is reduced to a two-dimensional problem in each flow-wise cross-section. Closed-form solutions for the deformation (either from the full elasticity problem or through simplifications via plate theory) allow us to predict the resistance of soft hydraulic elements. Our theory compares favorably to microscale flow experiments, as well as to three-dimensional two-way coupled direct numerical simulations. The effect of non-Newtonian fluid rheology will also be addressd.   

Devising and characterizing a non-perturbative manipulator in 3D microfluidic channels

Thanks to the lack of inertia of fluids, hydrodynamic forces in the Stokes regime, such as a microscale flow, are products of only flow pattern geometry. Consequently, an object entrained in a microfluidic flow cannot sense any variations if the surrounding flow remains uniform such that it is strain-free. This concept thus suggests the capacity of a microfluidic device for non-perturbative manipulations, which has not been fully explored. Here, we investigate the capability of such non-perturbative manipulations in a microscope-compatible 3D microfluidic device having vertically offset channels converging on a middle chamber. Using symmetry arguments, we illustrate a minimum of 6 channels are necessary to realize microscale manipulations along arbitrary directions, completely strain-free at the chamber center. By introducing two independent strain rate tensor invariants for characterizing flow perturbation, we demonstrate a finite volume with substantially low strain rate can be achieved around the strain-free center and can thus enable effectively non-perturbative manipulation over a spatial scale much greater than the size of the manipulated objects. We also fabricated such a microfluidic device and demonstrated its non-perturbative manipulation capabilities in experiments.   

The interaction of elastomeric coatings with viscous flows: how incompressible is PDMS?

Elastic substrates bounding fluid flows are common in many experimental and industrial settings; their principal purpose is usually to drive or suppress the flow of fluid. In particular, PDMS is one of the most frequently used materials in microfluidic platforms, since it is easily designed into complex channel shapes. The deformation of such PDMS and other elastomeric layers is becoming increasingly recognised, but the model appropriate for describing its deformation depends on how close to incompressible the coating is. While the Poisson ratio is usually quoted as being in the range of 0.49 – 0.5, the precise value may change the behaviour of the coating and have knock-on consequences. We will present a model for thin, near-incompressible elastic foundations, and discuss how its application to examples of fluid-structure interaction problems at low Reynolds number can depend sensitively on how incompressible the coating is.   

Active Foam: Connecting Structure, Dynamics and Control

By inflating and deflating voxels within a polydisperse 2-D air-liquid foam, we demonstrate a system where we perturb soft materials in a radially-symmetric manner. These cyclic perturbations can be coordinated spatially and temporally to encode ("write") mechanical properties into the material. In addition to experiments, we will discuss a new simulation method used to test distributed local control strategies to achieve global behavior. We can estimate where regions of topological rearrangements occur by connecting microstructural mechanics with the dynamics of slowly oscillating sources and sinks in the material. We address the significant complexity that arises from polydispersity and initial topological disorder. The goal of this work is to understand fundamental principles of confluent tissues and develop functional synthetic analogs.   

Active sieving : from flapping nano-doors to vibrating nanotubes

Filtering specific molecules is a challenge faced for several vital needs: from biomedical applications like dialysis to the intensive production of clean water. The domain has been boosted over the last decades by the possibilities offered by nanoscale materials. Filtration is however always designed according to a passive sieving perspective: a membrane with small and properly decorated pores allows for the selection of the targeted molecules. This inevitably impedes the flux and transport, making separation processes costly in terms of energy. Here we investigate alternative approaches to separation and filtration. We explore the possibility of non-equilibrium sieving, harnessing the difference in the molecular dynamics of particles to separate them across "active" nanopores.   

Fibre-reinforced microfluidic droplets

Soft microfibers can be strongly bent by capillary forces and even be reversibly coiled inside fluid cavities. If present, hydrodynamic forces may compete with capillary forces, uncoil the microfiber and induce its deployment from its original coiled state.
Here we fabricate a microfiber coiled within a droplet that is attached on the wall of a microfluidic channel. This is done by photocuring a thin liquid jet of hydrogel (PEG-DA) and transporting the resulting soft microfibre to the carefully prepared droplet for adequate coiling. The mechanical response of the hybrid system is then investigated under increasing flow rates.
The present results open opportunities to form the building blocks of microfluidic elements with high on-off ratio that may be useful for the design of on-chip tunable circuits for bioengineering applications.   

Pulp friction: lubricating properties of soft particle suspensions

Friction between two sliding surfaces is often reduced with a lubricant. Lubricants can contain particles that help mitigate dissipation. The mechanics of friction is complex, especially when soft substrates/particles and lubricating fluids are involved. We shine new light on the complex mechanics of particle based lubrication by evaluating the lubricating properties of particle suspensions. We synthesize custom soft micron-sized gel particles to create a soft particle suspension that acts as model lubricant. The suspension lubrication deviates from typical Stribeck behavior as we find four frictional flow regimes. These frictional regimes are influenced by the particle size, deformability and the amount of particles in suspension, which allows us to propose mechanisms for the different lubrication regimes. We verify some hypotheses by performing lubrication experiments with soft substrates and hard particles.   

Propagation and interactions of hydraulic fractures in model heterogeneous solids

The propagation of cracks in heterogeneous environments is a very rich and complex scientific problem, with implications in many fields, from geology, to everyday life and industrially-relevant processes. Interactions of the propagating crack with material heterogeneities, defects, interfaces and other cracks ultimately determine the path that the crack follows, as well as the occurrence of crack branching and merging.
Addressing such interactions in experiments is however extremely challenging, since it requires at the same time a fine control of the crack propagation and a detailed knowledge of the material response to the crack itself, which is typically nonlinear and dynamic.
In this work we study the propagation of hydraulic fractures in model, well-controlled colloidal materials, using microfluidics coupled to an innovative dynamic light scattering technique providing time- and space-resolved information on the local strain and the microstructural damage caused in the material by the propagating crack. Our preliminary results suggest that combining such information with a fine control of the mechanical and structural properties of our model samples can pave the way for a more comprehensive understanding of crack propagation in heterogeneous media.   

Effect of the 3D swelling of microgels on their 2D phase behavior at the liquid-liquid interface

We investigate soft, temperature-sensitive microgels at fluid interfaces and how changing temperature across the microgels' volume phase transition temperature, which leads to swelling/deswelling of the microgels in the aqueous phase, affects the phase behavior within the monolayer. We combine compression isotherms, AFM imaging, and ellipsometry.
At low compression, the interaction between microgels is dominated by their highly stretched corona and the phase behavior of the monolayers is the same. The polymer segments within the interface lose their temperature-sensitivity. At high compression, the portions of the microgels located in the aqueous side of the interface become relevant and prevail in their interactions. These portions are able to collapse and, consequently, the isostructural phase transition is altered. Thus, the temperature-dependent swelling perpendicular to the interface (3D) affects the compressibility parallel to the interface (2D). Our results highlight the distinctly different behavior of soft, stimuli-sensitive microgels as compared to rigid nanoparticles.   

Underactuated fluidic control of continuous multistable structures

This work addresses the challenge of underactuated pattern generation in continuous multistable structures. The examined structure is a slender membrane, actuated by a viscous fluid, which can concurrently sustain two different equilibria states, separated by transition regions. We first demonstrate the formation and motion of a single transition region and then sequencing of several such moving transition regions to achieve arbitrary patterns by controlling the inlet pressure of the actuating fluid. Finally, we show that non-uniform membrane properties, along with the transient dynamics of the fluid, can be leveraged to directly control any segment of the membrane.