Capillary flow enhancement in rectangular polymer microchannels with a deformable wall

Computational Fluid-Structure Interaction in Microfluidics

Micro elastofluidics is a transformative branch of microfluidics, leveraging the fluid-structure interaction (FSI) at the microscale to enhance the functionality and efficiency of various microdevices. This review paper elucidates the critical role of advanced computational FSI methods in the field of micro elastofluidics. By focusing on the interplay between fluid mechanics and structural responses, these computational methods facilitate the intricate design and optimisation of microdevices such as microvalves, micropumps, and micromixers, which rely on the precise control of fluidic and structural dynamics. In addition, these computational tools extend to the development of biomedical devices, enabling precise particle manipulation and enhancing therapeutic outcomes in cardiovascular applications. Furthermore, this paper addresses the current challenges in computational FSI and highlights the necessity for further development of tools to tackle complex, time-dependent models under microfluidic environments and varying conditions. Our review highlights the expanding potential of FSI in micro elastofluidics, offering a roadmap for future research and development in this promising area.

Elastocapillarity-driven 2D nano-switches enable zeptoliter-scale liquid encapsulation

Biological nanostructures change their shape and function in response to external stimuli, and significant efforts have been made to design artificial biomimicking devices operating on similar principles. In this work we demonstrate a programmable nanofluidic switch, driven by elastocapillarity, and based on nanochannels built from layered two-dimensional nanomaterials possessing atomically smooth surfaces and exceptional mechanical properties. We explore operational modes of the nanoswitch and develop a theoretical framework to explain the phenomenon. By predicting the switching-reversibility phase diagram-based on material, interfacial and wetting properties, as well as the geometry of the nanofluidic circuit-we rationally design switchable nano-capsules capable of enclosing zeptoliter volumes of liquid, as small as the volumes enclosed in viruses. The nanoswitch will find useful application as an active element in integrated nanofluidic circuitry and could be used to explore nanoconfined chemistry and biochemistry, or be incorporated into shape-programmable materials.

Capillary Imbibition in a Diverging Flexible Channel

We study the imbibition of a wetting liquid between flexible sheets that are fixed at both ends. Assuming a narrow gap between the sheets, we solve the lubrication equation coupled with a slender body deformation. When the sheets are parallel, we find that the deformation initially speeds up the flow, as shown in previous studies, but only up to the middle of the channel. As the channel contracts, the hydrodynamic resistance increases and ultimately slows down the filling process. Below a threshold stiffness, the channel collapses and imbibition stops. We propose a scaling of the filling duration near this threshold. Next, we show that if the sheets are initially tilted with a minimal angle, the channel avoids collapse. The liquid front pulls the diverging sheets and spreads in a nearly parallel portion, which maintains the capillary propulsion and enhances the wicking. Therefore, while it is established that diverging rigid plates imbibe liquids slower than parallel ones do, we show that elasticity reverses this principle: diverging flexible sheets imbibe liquids faster than parallel ones. We find an optimal tilt angle that gives the shortest filling time.

Capillary Flow Dynamics in Composite Rectangular Microchannels with Rough Walls

In this article, we consider rectangular microchannels composed of glass and thin polymeric walls with different roughness in which opposed walls are of the same material but adjacent walls are not. We propose a model for fluid capillary transport into these rectangular microchannels when horizontally positioned and focus our research on how the microchannel aspect ratio modifies the motion during the initial viscous regimes. The model relies on an effective static contact angle and an effective friction coefficient that averages local magnitudes in the cross section. An extensive experimental investigation with different microchannels enabled us to obtain these coefficients for different aspect ratios. While for low aspect ratios, the effective contact angle presents the smallest values, the effective friction coefficient shows the larger ones. With rough surfaces, the spontaneous occurrence of pinning and depinning events associated with sharp wall defects notably reduces the effective static contact angle even when high aspect ratios are used. The obtained values of the effective friction coefficient show good agreement with previous literature investigations for rough and smooth lateral wall surfaces. Finally, we propose a nondimensional time to establish when contact angle effects dominate the dynamics. We found that for the materials and fluid properties used in this work, these effects become negligible for times larger than t ∼ 1 s.

Elastocapillary interaction between a long rectangular membrane and a liquid drop

We report elastocapillary interaction between a long rectangular membrane fixed along its central axis and a liquid drop dispensed at one of its ends. The introduction of the drop results in the elastocapillary-driven wrapping of the membrane along its width and a concomitant flow in the resulting conduit along its length. Depending upon the drop size (d) and capillary length scale (L_c), we identified general criteria for achieving complete wrapping of the membrane in the dry state from energy considerations. For small droplets satisfying d ≲ L_c, we find that the critical membrane length (W_c) required for complete wrapping is proportional to the elastocapillary length scale (L_ec). In the case of large droplets with d > L_c, the wrapping behavior depends on the ratio of membrane width to elastocapillary length scale (W/L_ec) and the ratio of capillary length scale to the elastocapillary length scale (L_c/L_ec). Our study suggests that the critical membrane width for complete wrapping is smaller in the wet state compared to that in the dry state, which can be attributed to the existence of a transmembrane pressure in the wet state. The effect of membrane thickness and width and drop volume on the length and cross-section of the wrapped conduit and attached width of the wrapped membrane is studied. For small droplets, the resulting elastocapillary flow exhibits an inertial regime at small times, followed by a Washburn regime at intermediate times, and finally an inertial regime, and for large droplets, only an inertial regime is observed throughout.

Domino-like water transport on Tillandsia through flexible trichome wings

Tillandsia usneoides in epiphytic bromeliads takes up water through absorptive trichomes on the shoot surface under extreme environmental conditions. Although previous studies revealed the way by which T. usneoides absorbs water and prevents water loss, its water transport remains unclear. We characterized structures of trichome wings of T. usneoides. Wing length-to-thickness ratio of 136 and trichome interval (d)-to-wing length (l) ratio (d/l) smaller than 1 caused the water film to flatten the wings sequentially, resulting in domino-like water transport. A hinge-like linkage between wing and outer ring cells and the wing size longer than the elastocapillary length (L_EC ) brought about this unique reconfiguration, which is the flattening and recovery of wings. Tillandsia usneoides transported water rapidly on the surface as the water film propagated on the exterior trichomes with flexible wings and the transport distance at the macroscopic scale grew as t^x with x = 0.68 ± 0.04, unlike the conventional scaling of t^0.5 . Empirical and theoretical investigations proved our assumption that external water transport with the domino-like effect predominated over internal vascular transport. Biomimetic trichome wings simulated the domino-like water transport, highlighting the important role of flexible wing arrays.

Synchronization and control of capillary flows in rectangular microchannel with spacers

Liquid control in microchannels is quite important in microfluidic devices used in, for example, lab-on-a-chip and point-of-care applications. Capillary microfluidics, being self-powered, is especially advantageous for use in passive devices, and has attracted significant attention. In this paper, capillary flows in rectangular microchannels with spacers are studied experimentally and theoretically; in particular, capillary flow synchronization (or waiting) behavior is identified and investigated. Based on changes of channel walls, two basic synchronization modes are proposed for flows isolated by spacers in a channel. Experimental results show that the velocities of faster capillary flows are reduced by the liquid pinning effect and that the time delay between two capillary flows is automatically balanced. The synchronization behavior of capillary flows is explained by analyzing the time delay, contact angle variation, and capillary forces. In addition, the quantity of liquid flowing out of the waiting channels is estimated and verified. Then a model for the change in contact angle during synchronization is derived and verified. Finally, we conceive a series of studies of the control of capillary flows for different spacer designs and conduct an experiment to study the dynamic behaviors of a number of capillary flows by adding many spacers in a microchannel. This study expands the applications of capillary microfluidics.

Bio-inspired liquid transport via elastocapillary interaction of a thin membrane with a liquid meniscus

We report bio-inspired (from a hummingbird's tongue) liquid transport via elastocapillary interaction of a thin membrane with a liquid meniscus. A soft wedge-thin rectangular membrane forming a wedge with a rigid substrate and a flat thin rectangular membrane undergo large deformation while interacting with liquid menisci. The membrane deformation leads to the formation of confinement which in turn results in elastocapillary flow along the membrane length. A simple theoretical model based on the Euler Bernoulli law is used to predict the membrane deformation profiles, which compare well with that obtained from experiments. In the wedge case, the membrane surface and liquid are selected such that the Concus-Finn criterion is not satisfied to contrast the present case of elastocapillary flow from the typical corner flow reported in the literature. The meniscus location versus time studies indicated that the flow exhibits the typical Washburn regime with , except for a sudden increase in velocity at the end of the membrane length. The effects of membrane thickness and width, liquids and substrates were studied to determine the expression for the modified Washburn constant W_m in both the wedge and flat membranes. It was found that gravity plays a role for Bo > 0.94 and for Bo = 1.9, the effect of inclination angle on the flow was studied. The elastocapillary flow with thin membranes could open up an opportunity for a new area, namely "membrane microfluidics" or "lab on a membrane", for diagnostics and other applications.

New Drop Fluidics Enabled by Magnetic-Field-Mediated Elastocapillary Transduction

This research introduces a new drop fluidics that uses a deformable and stretchable elastomeric film as the platform instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control the motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil-laden film becomes asymmetrically deformed, thus producing a gradient of Laplace pressure within the droplet and setting it in motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film as well as material variables such as the viscosity of the oil and the interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elastocapillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how elementary operations such as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for the digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film in a Boolean sequence. We anticipate that this method of directing and manipulating water droplets is poised for application in various biochemical reaction engineering situations, an example of which is the polymerase chain reaction (PCR).

Capillary Imbibition into Converging Tubes: Beating Washburn's Law and the Optimal Imbibition of Liquids

We consider the problem of capillary imbibition into an axisymmetric tube for which the tube radius decreases in the direction of increasing imbibition. For tubes with constant radius, imbibition is described by Washburn's law (referred to here as the BCLW law to recognize the contributions of Bell, Cameron, and Lucas that predate Washburn). We show that imbibition into tubes with a power-law relationship between the radius and axial position generally occurs more quickly than imbibition into a constant-radius tube. By a suitable choice of the shape exponent, it is possible to decrease the time taken for the liquid to imbibe from one position to another by a factor of 2 compared to the BCLW law. We then show that a further small decrease in the imbibition time may be obtained by using a tube consisting of a cylinder joined to a cone of 3 times the cylinder length. For a given inlet radius, this composite shape attains the minimum imbibition time possible. We confirm our theoretical results with experiments on the tips of micropipettes and discuss the possible significance of these results for the control of liquid motion in microfluidic devices.