Small-Scale Flow with Deformable Boundaries

Lift at low Reynolds number

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Bio-inspired microfluidics: A review

Biomicrofluidics, a subdomain of microfluidics, has been inspired by several ideas from nature. However, while the basic inspiration for the same may be drawn from the living world, the translation of all relevant essential functionalities to an artificially engineered framework does not remain trivial. Here, we review the recent progress in bio-inspired microfluidic systems via harnessing the integration of experimental and simulation tools delving into the interface of engineering and biology. Development of "on-chip" technologies as well as their multifarious applications is subsequently discussed, accompanying the relevant advancements in materials and fabrication technology. Pointers toward new directions in research, including an amalgamated fusion of data-driven modeling (such as artificial intelligence and machine learning) and physics-based paradigm, to come up with a human physiological replica on a synthetic bio-chip with due accounting of personalized features, are suggested. These are likely to facilitate physiologically replicating disease modeling on an artificially engineered biochip as well as advance drug development and screening in an expedited route with the minimization of animal and human trials.

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the flow forces and the inherently compliant conduits of such microfluidic devices requires careful consideration. While mechanical compliance was initially a side-effect of the manufacturing process and materials used, compliance has now become a paradigm, enabling new approaches to microrheological measurements, new modalities of micromixing, and improved sieving of micro- and nano-particles, to name a few applications. This topical review provides an introduction to the physics of these systems. Specifically, the goal of this review is to summarize the recent progress towards a mechanistic understanding of the interaction between non-Newtonian (complex) fluid flows and their deformable confining boundaries. In this context, key experimental results and relevant applications are also explored, hand-in-hand with the fundamental principles for their physics-based modeling. The key topics covered include shear-dependent viscosity of non-Newtonian fluids, hydrodynamic pressure gradients during flow, the elastic response (deformation and bulging) of soft conduits due to flow within, the effect of cross-sectional conduit geometry on the resulting fluid-structure interaction, and key dimensionless groups describing the coupled physics. Open problems and future directions in this nascent field of soft hydraulics, at the intersection of non-Newtonian fluid mechanics, soft matter physics, and microfluidics, are noted.

Profiling a soft solid layer to passively control the conduit shape in a compliant microchannel during flow

The shape of a microchannel during flow through it is instrumental to understanding the physics that govern various phenomena ranging from rheological measurements of fluids to separation of particles and cells. Two commonly used approaches for obtaining a desired channel shape (for a given application) are (i) fabricating the microchannel in the requisite shape and (ii) actuating the microchannel walls during flow to obtain the requisite shape. However, these approaches are not always viable. We propose an alternative, passive approach to a priori tune the elastohydrodynamics in a microsystem toward achieving a predetermined (but not prefabricated) flow geometry when the microchannel is subjected to flow. That is, we use the interaction between a soft solid layer, the viscous flow beneath it, and the shaped rigid wall above it to tune the fluid domain's shape. Specifically, we study a parallel-wall microchannel whose top wall is a slender soft coating of arbitrary thickness attached to a rigid platform. We derive a nonlinear differential equation for the soft coating's fluid-solid interface, which we use to infer how to achieve specific conduit shapes during flow. Using this theory, we demonstrate the tuning of four categories of microchannel geometries, which establishes, via a proof-of-concept, the viability of our modeling framework. We also explore slip length patterning on the rigid bottom wall of the microchannel, a common technique in microfluidics, as an additional "handle" for microchannel shape control. However, we show that this effect is much weaker in practice.

Flow and deformation characteristics of a flexible microfluidic channel with axial gradients in wall elasticity

Axial gradients in wall elasticity may have significant implications in the deformation and flow characteristics of a narrow fluidic conduit, bearing far-reaching consequences in physiology and bio-engineering. Here, we present a theoretical and experimental framework for fluid-structure interactions in microfluidic channels with axial gradients in wall elasticity, in an effort to arrive at a potential conceptual foundation for in vitro study of mirovascular physiology. Towards this, we bring out the static deformation and steady flow characteristics of a circular microchannel made of polydimethylsiloxane (PDMS) bulk, considering imposed gradients in the substrate elasticity. In particular, we study two kinds of elasticity variations - a uniformly soft (or hard) channel with a central strip that is hard (or soft), and, increasing elasticity along the length of the channel. The former kind yields a centrally constricted (or expanded) deformed profile in response to the flow. The latter kind leads to increasingly bulged channel radius from inlet to outlet in response to flow. We also formulate an analytical model capturing the essential physics of the underlying elastohydrodynamic interactions. The theoretical predictions match favourably with the experimental observations and are also in line with reported results on stenosis in mice. The present framework, thus, holds the potential for acting as a fundamental design basis towards developing in vitro models for micro-circulation, capable of capturing exclusive artefacts of healthy and diseased conditions.

Rotation of a submerged finite cylinder moving down a soft incline

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale

We present the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The force increases as the gap is reduced and shows a saturation at small gap. The results are in excellent agreement with scaling arguments and a quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, an empirical scaling law for the observed saturation of the lift force is given and discussed.

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid-structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be (t/w)²≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate-pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.