Session Q26: Microscale Non-Newtonian and Complex Flows I

Passive and active particle dynamics in microhydrodynamic flows of complex fluids

There is a rich history in the literature on the effects of particles in Newtonian flows, but when the suspending fluid is also complex, as it is in many applications from environmental flows such as avalanches or mudslides, to energy applications such as down-hole scenarios in the oilfield, to biophysical flows such as cells in the human body, the rheology of these suspensions is far less understood. Particles can interact with nonlinear non-Newtonian stresses in these complex suspensions to significantly alter flows and an ongoing effort is to characterize and understand these effects.

In this talk, I will discuss a number of instances where particles suspended in complex fluids lead to markedly different dynamics and rheology for microhydrodynamic flows. For example, particles suspended in a Newtonian fluid will increase the apparent viscosity of the fluid due to the additional dissipation caused by the disruption of streamlines, called the Einstein viscosity; however, if instead the suspending fluid is shear-thinning, the higher strain-rates induced by the particles will also produce a competing apparent reduction of the viscosity and for a dilute suspension of particles in a weakly shear-thinning fluid, these combined effects lead to modified Einstein viscosity. Anisotropic particles can undergo complex degenerate dynamics, even in steady shear of Newtonian fluids (known Jeffery orbits for spheroids), here we discuss how shear-thinning rheology can affect these dynamics. Finally we discuss how active particles (biological or otherwise) can display completely different behaviour in complex fluids, such as reciprocal swimmers that in a Newtonian fluid would not produce net motion but in a complex fluid move and whose motion is directly coupled with the non-Newtonian rheology of the fluid and hence act as a nonlinear microrheometer.   

Heterogeneity and the role of entanglements during the extrusion of fiber suspensions

The flow of fiber suspensions occurs in industrial processes such as paper making and filtration. Recently, flexible (high aspect ratio) polymeric microfiber suspensions have been demonstrated to form gel-like materials under shear stress or during extrusion. Using microscopic imaging, we systematically studied the extrusion process in three dimensions. We found that during extrusion and dependent of the extrusion flow rate the extrudate volume fraction varies relative to the initial suspension volume fraction. At a small flow rate, the channel is clogged and the extrudate is purely the solvent. At a higher flow rate, the microfibers are extruded but at a higher volume fraction than their pre-extrusion state. The extrudate volume fraction reaches a plateau when the pre-extrusion volume fraction exceeds a critical value. Using rheometric measurements, we observed that the critical volume fraction is related to the emergence of yield stress in the suspension. A model to rationalize the experimentally generated extrusion phase diagram will be presented.   

Tuning interfacial rheology and particle microstructure with Janus particles

Particle-laden fluid interfaces are ubiquitous in nature and have attracted considerable research interest, due to their exceptional ability to stabilize interface-rich materials such as emulsions, foams and cocontinuous blends. Here, we explore the effect of a small amount of additive on the interfacial rheology and the microscopic structure of such an interface. Using a custom-built interfacial stress rheometer, we show that the addition of a small amount of platinum-polystyrene (Pt-PS) Janus particles (1:40 ratio of Janus versus PS) within a monolayer of PS colloids can lead to more than an order-of-magnitude increase in the surface modulus of the monolayer with enhanced elasticity, greatly improving the stability of the interface. This drastic change in interfacial rheology is associated with the formation of local particle clusters surrounding each Janus particle. We further develop a simple model based on interparticle interactions, which qualitatively explains the origin of local particle clusters and the increase of the interfacial elasticity. Our systematic experiments demonstrate a new way to tune the microstructure and stability of particle-laden fluid interfaces.   

Twist And Snap: Heterogeneous Defect Nucleation via Frank-Read Sources in Nematic Liquid Crystals

Topological defects can nucleate heterogeneously, as when a pinned dislocation segment in a crystal bows out under stress and snaps off repeatedly, emitting concentric dislocation loops, known as a Frank-Read source. A similar mechanism can arise in a nematic liquid crystal containing a pinned disclination. We consider a disclination half-loop pinned to a planar anchoring layer [1]. When director twist is imposed on the top substrate, the half-loop expands and snaps off new disclination loops leaving the original half-loop intact [2,3]. We model this mechanism via a 3D Lebwohl-Lasher rotor model, representing a uniaxial nematic with equal Frank constants. We study the Frank-Read mechanism and explore the effects of temperature and twist rate. Using a materials-by-design approach, we propose that a liquid crystal cell with a patterned array of Frank-Read sources will demonstrate a rheological response that depends on disclination half-loop sizes, density, orientation, and pattern. Defect half-loops pinned on colloids may also serve as sources. We discuss the importance of this mechanism in rheology of both passive and active nematics. [1] Guo et al doi:10.1002/adom.202100181, [2] Long et al doi:10.1039/d0sm01899f, [3] Angelo http://tiny.cc/jangelo.   

Local deformation fields in active soft matter induced by internal stresses

In many active soft materials, force generation, storage, and dissipation occur across length and time scales. This multiscale interaction between active force generating units and dissipative structural units is the defining character of active materials. Understanding how deformations induced by internal stresses propagate across these materials can provide insights into the underpinning mechanisms of this behavior. Here we present a method to measure such deformation fields. Specifically we use microscopy images to investigate systems driven by transient internal active stresses. We illustrate the application of this method in various actomyosin networks. 

We first start by showing how active stresses propagate in a 2d liquid crystal formed by short actin filaments. We then show how deformation fields in disordered actin networks change with network viscoelasticity. Finally, we measure the local strain fields of stress fibers in single cells, which are induced by myosin mini-filaments and F-actin retrograde flow. The convoluted feedback loops in the cells can be better understood by performing these measurements while perturbing multiple controlling pathways of the actomyosin cytoskeleton, including those that alter the active stresses and the viscoelasticity of the network.   

Fluorescent streak velocimetry of non-Newtonian fluids

Here, we demonstrate how fluorescent streak velocimetry can be used to characterize flow in non-Newtonian fluids. By seeding a fluid with 2 μm colloids and imaging its flow using long exposure times (20-100 ms), we generate data which encodes information about flow velocity and acceleration in individual images. To analyze these images, we have created a user-friendly and open-source computational package. We demonstrate this technique by characterizing the channel flow profiles of several non-Newtonion fluids: micellar Cetylpyridinium Chloride solution, Carbopol 940, and Polyethylene Glycol. Our measurement resolution is sufficient to distinguish the distinct non-Newtonian flow profiles from each other and from the Newtonian profile. We will also present results of this method from more complex geometries, where significant acceleration is created due to a modified channel geometry.   

Experimental study on the motion of a confined bubble in a non-Newtonian fluid

When a confined long gas bubble translates in a capillary tube, a thin film of liquid separates the bubble surface and the tube inner wall, with its thickness determined by the interplay of viscous, inertial and capillary effects. Although the dynamics of a confined bubble in a Newtonian liquid has been the subject of quite a few studies since the pioneering works of Taylor and Bretherton, the case where the fluid exhibits a non-Newtonian behavior is much less understood, while in applications, such as enhanced oil recovery and drug delivery, the fluids are likely to exhibit non-Newtonian properties. Here we consider the classical Bretherton problem with a non-Newtonian fluid. We provide quantitative measurements of the thickness of deposited liquid film for carboxymethyl cellulose solutions with different concentrations in the range of small Capillary numbers. Depending on the concentration of CMC, the thickness of the liquid film shows distinguished behaviors compared with that of Newtonian case. We further compare our observations with the scaling law considering the effective viscosity to extend the classical Bretherton's correlations to non-Newtonian fluids.  Our results may enrich the fundamental understanding of multi-phase flows involving a non-Newtonian fluid.   

Dipole Alignment of Water Molecules Flowing Through a Carbon Nanotube

Recent years have seen an upsurge of interest in exploring ultrafast transport of water in various nanochannels with potential applications in desalination, separation processes, nanomedicine and energy conversion. However, a quantitative understanding of flow-induced effects in nanochannels is still lacking. We have used molecular dynamics simulations to study pressure-induced flow of water through a (10,10) single-walled carbon nanotube. We find that the dipole moments of water molecules inside the nanotube get aligned by flow, resulting in a net dipole moment in the flow direction. With increasing flow velocity, the net dipole moment first increases and eventually saturates to a constant value. This behavior is qualitatively similar to that in the Langevin theory of paraelectricity with the flow velocity acting as an effective aligning field. We show that the microscopic origin of this behavior is the entry of water molecules inside the nanotube with their dipole vectors preferentially pointing inward along the nanotube axis.   

Soft hydraulics of non-Newtonian fluids flows through compliant conduits

The interplay between hydrodynamic forces and the confining boundaries of compliant conduits brings about rich physics involving fluid--elastic structure interactions. For example, microfluidic devices for lab-on-a-chip technologies are molded from soft polymeric materials. The mechanical compliance of channels in such devices is now recognized as an advantage to be exploited to enable, for example, new approaches to microrheological measurements and new modalities of micromixing. In this context, complex fluids exhibiting non-Newtonian rheological behavior arise. While hydraulics of Newtonian fluids in rigid conduits is now a textbook problem, a theory of soft hydraulics of non-Newtonian fluids remains elusive. In this talk, I will describe how to construct such a theory yielding reduced models that take into account shear-dependent viscosity, hydrodynamic pressure gradients during flow, and the elastic response (bulging and deformation) of the soft conduits due to flow within. First, the relationship between volumetric flow rate and axial pressure gradient is needed. This relationship is challenging (or impossible) to obtain in closed analytical form, notable exceptions are the power-law and Ellis models for the shear-dependent viscosity. Then, I will show how a perturbative approach justifies replacing the channel height or tube radius in the pressure gradient--flow rate relation with an expression that accounts for the pressure-induced deformation of the conduit. The latter can be derived from the analysis of a suitable elasticity problem, for a given cross-sectional conduit geometry. I will conclude with examples of how the proposed theoretical approach reduces 3D coupled, multiphysics problems to a single ODE, which can often be integrated.   

Flow rate-pressure drop relation for viscoelastic fluids in narrow and confined non-uniform geometries

Pressure-driven flows of viscoelastic polymer solutions in narrow non-uniform geometries are ubiquitous in nature and various applications. One of the key interests for such flows is understanding the relationship between the flow rate and pressure drop, which, to date, is studied primarily using numerical simulations. Here, we aim to rationalize the longstanding contradiction between simulations using the "simple" Oldroyd-B and FENE-CR models and experiments for the flow rate-pressure drop relation of viscoelastic fluids in some geometries. To this end, we provide a theoretical framework for calculating the flow rate-pressure drop relation in arbitrarily shaped, narrow channels. Through the combination of the lubrication approximation and the Lorentz reciprocal theorem, our theory allows deriving analytical expressions for the flow rate-pressure drop relation for a wide variety of continuum-level constitutive viscoelastic models in the weakly viscoelastic limit. Furthermore, we discuss the shortcomings of the Oldroyd-B and FENE-CR models and suggest their modification through accounting for additional microscopic features of polymer flows.   

Peeling of elastic sheet using complex fluids at low Reynolds numbers

We investigate the transient fluid structure interactions (FSIs) of a non-Newtonian fluid peeling a elastic  sheet at low Reynolds numbers (Re) .We express the rheology of the fluid through the simplified Phan-Thien-Tanner (sPTT) model. Invoking the lubrication approximation for fluid flow and modeling the structure as series of Hookean springs, we reduce the problem to that of a partial differential equation for the evolution of the deformed height in time and space. An order of magnitude analysis reveals two distinct regimes of peeling, based on the relative magnitude of the viscoelasticity and FSI parameters, further aided by similarity solutions. On inspecting the numerical solution, we infer that the non-Newtonian nature brings the system to a steady state faster in comparison to a Newtonian fluid. We explore this idea by investigating the dynamics of peeling actuated by purely shear thinning fluids. And therefore, we present the results for the peeling actuated by such generalized Newtonian fluids as well. To conclude, this study aims to afford to the experimentalist a system of knowledge to a priori delineate the peeling characteristics of a certain class of complex fluids.   

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Turbulent flow and the hydrodynamic instabilities which may appear, are generally observed when inertia dominates the fluid motion. However, polymeric fluids with viscoelastic properties do not require an inertial flow regime to exhibit such instabilities or even turbulent-like behavior. Instead, these types of fluids need only the correct flow gradients and curvature to develop what has been classified as purely elastic turbulence. Using holographic particle tracking, we elucidate the 3-D flow structures that underly the transition and early stages of purely elastic turbulence in a model mixed flow type system. Furthermore, via measurements of the pressure fluctuations upstream of the cross-channel middle section, and using birefringence polarization to visualize the fluid stresses, we correlate the changes in retardance with both pressure and velocity measurements to show how stress disturbances propagate upstream even in the presence of viscous dissipation. Finally, we further study the spatiotemporal dynamics of the pressure and velocity measurements to fully describe the different regimes in the elastic turbulent regime.   

Time-dependence of local boundary conditions and global throughput for confined, semi-dilute polymer solutions

Confined polymer solution flows are often found, for example, in biological systems and porous media. In such systems, for which the surface to volume ratio is high, interfacial effect are key. Specifically, the flow throughput is highly impacted by boundary effects such as slip or chain adsorption at the wall, and these latter interfacial effects may be time-dependent. In this study, we use evanescent wave microscopy and particle tracking velocimetry to map the flow field within a one-micron layer close to the wall in a 5-micron-thick microfluidic chip. While this technique has been shown very efficient to characterize the near-wall shear rate and hydrodynamic boundary condition, we additionally use state-of-the-art flow sensors to measure the flow rate and pressure drop across the chip simultaneously. Live monitoring of the local flow profile and global flow rate allows a description of the adsorption dynamics of hydrolyzed polyacrylamide chains onto a glass surface, under shear flow. The dependence in the shear rate, chain concentration and electrolyte concentration is studied.