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.

Lockhart with a twist: Modelling cellulose microfibril deposition and reorientation reveals twisting plant cell growth mechanisms.

Plant morphology emerges from cellular growth and structure. The turgor-driven diffuse growth of a cell can be highly anisotropic: significant longitudinally and negligible radially. Such anisotropy is ensured by cellulose microfibrils (CMF) reinforcing the cell wall in the hoop direction. To maintain the cell's integrity during growth, new wall material including CMF must be continually deposited. We develop a mathematical model representing the cell as a cylindrical pressure vessel and the cell wall as a fibre-reinforced viscous sheet, explicitly including the mechano-sensitive angle of CMF deposition. The model incorporates interactions between turgor, external forces, CMF reorientation during wall extension, and matrix stiffening. Using the model, we reinterpret some recent experimental findings, and reexamine the popular hypothesis of CMF/microtubule alignment. We explore how the handedness of twisting cell growth depends on external torque and intrinsic wall properties, and find that cells twist left-handedly 'by default' in some suitable sense. Overall, this study provides a unified mechanical framework for understanding left- and right-handed twist-growth as seen in many plants.

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.

Electrokinetics over hydrophobic surfaces.

Segregation of phases in the vicinity of hydrophobic surfaces may turn out to be immensely consequential towards altering the coupling of electrostatics and hydrodynamics over interfacial scales. Here, we review the fundamental advances towards bringing out the various facets of electrokinetic transport over hydrophobic interfaces. We lay significant emphasis on the developments in understanding the slippery electrohydrodynamics over such interfaces, by appealing to the considerations across various spatio-temporal scales as unveiled by molecular dynamics as well as mesoscopic modelling paradigms (such as phase field and lattice Boltzmann). We envisage that despite significant advancements being achieved towards relating the macroscopic slip-length with the underlying molecular or mesoscopic phenomena, future efforts could be directed towards developing more robust statistically based models that may connect rarefied gas dynamics in the segregated phase with bulk electrokinetic transport and possible giant augmentations in the consequent fluid flow.

Flow-induced deformation in a microchannel with a non-Newtonian fluid.

In this work, we have fabricated physiologically relevant polydimethylsiloxane microfluidic phantoms to investigate the fluid-structure interaction that arises from the interaction between a non-Newtonian fluid and the deformable wall. A shear thinning fluid (Xanthan gum solution) is used as the blood analog fluid. We have systematically analyzed the steady flow characteristics of the microfluidic phantom using pressure drop, deformation, and flow visualization using micro-PIV (Particle Image Velocimetry) to identify the intricate aspects of the pressure as well as the velocity field. A simple mathematical formulation is introduced to evaluate the flow induced deformation. These results will aid in the design and development of deformable microfluidic systems and provide a deeper understanding of the fluid-structure interaction in microchannels with special emphasis on biomimetic in-vitro models for lab-on-a-chip applications.

Finite size effects of ionic species sensitively determine load bearing capacities of lubricated systems under combined influence of electrokinetics and surface compliance.

The behaviour and health of lubricated systems in various natural and artificial settings are often characterized by their load bearing capacity. This capacity stemming from the lift force associated with confined fluid flow can be significantly altered due to surface compliance and electrokinetic effects. Here, we highlight the influence of finite size of the ionic species participating in electrokinetic transport with substrate compliance in determining the electromechanical characteristics of lubricated systems. With these new considerations, anomalous trends previously observed for the load bearing capacity corresponding to high values of zeta potential are corrected. Simultaneously, trends associated with the finite ionic size are also found to be reversed, but fall in line with the consistent theory. Importantly, despite an intricate interplay among the various influences - electrokinetic, hydrodynamic, geometric, and elastic - previously established trends due to geometric (non-parallel slider geometry) and elastic effects are found to persist. Specifically, in the presence of electrokinetic effects, an increase in the obliqueness of the slider geometry results in lower values of load bearing capacity while an increase in the stiffness leads to higher values. These results point to a certain robustness in the overall theory and it is hoped that they can contribute to better practical designs of slider bearings and an improved understanding of lubricated sliding surfaces in biological settings.

Electrokinetically modulated peristaltic transport of power-law fluids.

The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields.

Electrohydrodynamics within the electrical double layer in the presence of finite temperature gradients.

A wide spectrum of electrokinetic studies is modeled as isothermal ones to expedite analysis even when such conditions may be extremely difficult to realize in practice. Going beyond the isothermal paradigm, we address here the case of flow induced electrohydrodynamics, commonly streaming potential flows, in a situation where finite temperature gradients do exist. By way of analyzing a model problem of flow through a narrow parallel-plate channel, we show that the temperature gradients applied at the channel walls may have a significant effect on the streaming potential, and, consequently, on the flow itself. Our model takes into consideration all the pertinent phenomenological aspects stemming from the imposed thermal gradients, such as the Soret effect, the thermoelectric effect, and the electrothermal effect, by a full-fledged coupling among the electric potential, the ionic species distribution, the fluid velocity and the local fluid temperature fields, without resorting to ad hoc simplifications. We expect this expository study to contribute significantly towards more sophisticated future endeavors in actual development of micro- and nano-devices for applications simultaneously involving thermal management and electrokinetic effects.

Influence of hydrophobic effects on streaming potential.

We study the influence of hydrophobic effects on streaming potential mediated flow through a narrow confinement. In a clear departure from the approach used in prior works, we use a phase-field model to capture the hydrophobicity-induced depletion in the near wall region, and express the variation of viscosity and permittivity across the interfacial layer in terms of the phase-field variable. We then use these in the determination of the flow velocity, and highlight the sensitive interplay between the intrinsic length scale of the electrical double layer and that of the depletion in terms of the variations of an effective normalized viscosity that captures the electroviscous effect. We expect that this work will be an important step forward in the realistic continuum modeling of interfacial physics in the particular context of streaming potential mediated flows.

Influence of streaming potential on pulsatile pressure-gradient driven flow through an annulus.

We study pulsatile pressure-gradient driven flow through an annular confinement under the influence of streaming potential. Our study considers zeta potentials beyond the traditional Debye-Hückel limits, and takes care against aphysical predictions stemming from traditional Boltzmann statistics through modifications involving the finite size of the ionic species (steric effects). With these considerations, we demonstrate, rather non-intuitively, that an intrinsic asymmetry may be manifested in the velocity profile of the flow through the annulus, as a consequence of the streaming potential effects in presence of Steric interactions. Our findings are likely to provide a new design basis for micro- and nano-scale flow devices involving annular geometries.

Consistent description of electrohydrodynamics in narrow fluidic confinements in the presence of hydrophobic interactions.

Electrohydrodynamics in the presence of hydrophobic interactions in narrow confinements is traditionally represented from a continuum viewpoint by a Navier slip-based conceptual paradigm, in which the slip length carries the sole burden of incorporating the effects of substrate wettability on interfacial electromechanics, precluding any explicit dependence of the interfacial potential distribution on the substrate wettability. Here we show that this traditional way of treating electrokinetics-wettability coupling may lead to serious discrepancies in predicting the resultant transport characteristics as manifested through an effective zeta potential. We suggest that an alternative consistent description of the underlying physics through a free-energy-based formalism, in conjunction with considerations of hydrodynamic and electrical property variations consistent with the pertinent phase-field description, may represent the underlying consequences in a more rational manner, as compared to the traditional slip-based model coupled with a two-layer description. Our studies further reveal that the above discrepancies may not occur solely due to the slip-based route of representing the interfacial wettability, but may be additionally attributed to the act of "discretizing" the interfacial phase fraction distribution through an artificial two-layer route.

Surface-charge-induced alteration of nanovortex patterning in nanoscale confinements with patterned wettability gradients.

We characterize the generation of flow vortices in nanoscale confinements under the combined effects of patterned surface charge density and substrate wettability. Using molecular dynamics simulations, we elucidate the effects of ion solvation and steric interactions toward influencing the resultant transport characteristics, which are otherwise difficult to resolve using classical electrokinetic theory. We also evaluate the velocity slip (local and global) as well as vorticity parameters, in an effort to assess the implications of the generated flow structure from a pseudocontinuum viewpoint. Results from the present study are expected to provide valuable insights on augmentation of nanoscale mixing.

Role of streaming potential on pulsating mass flow rate control in combined electroosmotic and pressure-driven microfluidic devices.

In the present study, we investigate the implications of streaming potential on the mass flow rate control in a microfluidic device actuated by the combined application of a pulsating pressure gradient and a pulsating, externally applied, electric field. We demonstrate that the temporal dynamics due to streaming potential effects may lead to interesting non-trivial aspects of the resultant transport characteristics. Our results highlight the importance of an adequate accounting of the streaming potential effects for temporally tunable mass flow rate control strategies, which may act as a useful design artifice to augment mass flow rates in practical scenarios.

Consistent accounting of steric effects for prediction of streaming potential in narrow confinements.

The traditional modeling framework for determining streaming potential, when taking into consideration finite size effects, suffers from an oversight in that while the model incorporates the size effects in the ion distribution profiles, it neglects these very same effects in the flux contributions, even though diffusivities are intrinsically linked with ionic friction, which again depends on the size of the ions. This oversight may lead to inconsistent quantitative estimates through ad hoc consideration of diffusivity values, apparently independent of the specific size of the ions, which nevertheless determines the ionic profiles. We remedy this theoretical inconsistency by expressing the diffusivity in terms of the ionic radius and investigate the consequences of such a description of the diffusivity-dependent flux, consistent with the ionic distribution profiles, on streaming potential mediated flow predictions. Additionally, we consider the effects of "charge induced thickening" so that both viscosity and diffusivity are expressed as spatially varying functions. As an unintuitive implication, we also show that calculation of nonzero values of streaming potential under the purview of classical Boltzmann distributions, which consider ions to be pointlike charges, is itself a theoretical inconsistency. We believe that the simple framework presented in this paper will pave the way for more sophisticated modeling efforts in the future.