Capillary filling in microchannels patterned by posts

Quantitative model for predicting the imbibition dynamics of viscoelastic fluids in nonuniform microfluidic assays

We develop a mathematical model to quantitatively describe the imbibition dynamics of an elastic non-Newtonian fluid in a conical (nonuniform cross section) microfluidic assay. We consider the simplified Phan-Thien-Tanner viscoelastic model to represent the rheology of the elastic non-Newtonian fluid. Our model accounts for the geometrical features of the fluidic assay, the key parameters affecting the rheological behavior of the fluid, and predicts the imbibition dynamics effectively. By demonstrating the temporal advancement of the filling length in the conical capillary graphically, obtained for pertinent parametric values belonging to their physically permissible range, we report an underlying balance between capillary and viscous forces during imbibition resulting in three distinct regimes of filling. Nonuniformity in the capillary cross section gives rise to an alteration in the viscous force being applied at the contact line (manifested through the alteration in shear rate) during the imbibition process, which upon maintaining a balance with the dominant capillary force results in three different regimes of filling. We believe that the present analysis has a twofold significance. First, this work will enhance the understanding of underlying imbibition dynamics of viscoelastic fluids (most of the biofluids exhibit viscoelastic rheology) in nonuniform fluidic pathways. Second, the developed model is of significant practical relevance for the optimum design of microfluidic assays, primarily used for sample diagnostics in biochemical and biomedical applications.

Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments

We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald–de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling (Digilov 2008 Langmuir 24 , 13 663–13 667 ( doi:10.1021/la801807j )). Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation x ~ t . Such a regime can be called the modified Washburn regime (Washburn 1921 Phys. Rev. 17 , 273–283 ( doi:10.1103/PhysRev.17.273 )).

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.

Capillary Coatings: Flow and Drying Dynamics in Open Microchannels

Capillary flow and drying of polymer solutions in open microchannels are explored over time scales spanning seven orders of magnitude: from capillary filling (10^-3-10 s) to the formation of a dry thin film (a "capillary coating"; 10²-10³ s). During capillary filling, drying-induced changes (increased solids content and viscosity) generate microscale pinning events that impede contact line motion. Three unique types of pinning are identified and characterized, each defined by the specific location(s) along the contact line at which pinning is induced. Drying is shown to ultimately pin the contact line permanently, and the associated total flow distances and times are revealed to be strong functions of channel width and drying rate. In general, lower drying rates coupled with intermediate channel widths are found to be most conducive to longer flow distances and times. After the advancing contact line permanently pins, internal flows driven by uneven evaporation rates continue to drive polymer to the contact line. This phenomenon promotes a local accumulation of solids and persists until all motion is arrested by drying. The effects of channel width and drying rate are investigated at each stage of this capillary coating process. These results are then applied to case studies of two functional inks commonly used in printed electronics fabrication: a PEDOT:PSS (poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate)) ink and a graphene ink. Although drying is shown to permanently arrest flow in both inks, both systems exhibit an increased resistance to pinning unexplained by mechanisms identified in aqueous polymer systems. Instead, arguments based on chemistry, particle size, and rheology are used to explain their novel behavior. These case studies provide insight into how functional inks can be better designed to optimize flow distances and maximize overall dry film uniformity in capillary coatings.

Dynamics of Capillary-Driven Flow in 3D Printed Open Microchannels

Microchannels have applications in microfluidic devices, patterns for micromolding, and even flexible electronic devices. Three-dimensional (3D) printing presents a promising alternative manufacturing route for these microchannels due to the technology's relative speed and the design freedom it affords its users. However, the roughness of 3D printed surfaces can significantly influence flow dynamics inside of a microchannel. In this work, open microchannels are fabricated using four different 3D printing techniques: fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering, and multi jet modeling. Microchannels printed with each technology are evaluated with respect to their surface roughness, morphology, and how conducive they are to spontaneous capillary filling. Based on this initial assessment, microchannels printed with FDM and SLA are chosen as models to study spontaneous, capillary-driven flow dynamics in 3D printed microchannels. Flow dynamics are investigated over short (∼10^-3 s), intermediate (∼1 s), and long (∼10² s) time scales. Surface roughness causes a start-stop motion down the channel due to contact line pinning, while the cross-sectional shape imparted onto the channels during the printing process is shown to reduce the expected filling velocity. A significant delay in the onset of Lucas-Washburn dynamics (a long-time equilibrium state where meniscus position advances proportionally to the square root of time) is also observed. Flow dynamics are assessed as a function of printing technology, print orientation, channel dimensions, and liquid properties. This study provides the first in-depth investigation of the effect of 3D printing on microchannel flow dynamics as well as a set of rules on how to account for these effects in practice. The extension of these effects to closed microchannels and microchannels fabricated with other 3D printing technologies is also discussed.

Nonequilibrium Gibbs' criterion for completely wetting volatile liquids

During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that, for completely wetting volatile liquids, there also exists a dynamically-produced contribution to the critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning that accounts for the nonequilibrium effect of evaporation.

Biologically inspired omniphobic surfaces by reverse imprint lithography

Springtail skin morphology is translated into robust omniphobic polymer membranes by reverse imprint lithography. The combination of overhanging cross-sections and their arrangement in a self-supporting comblike pattern are crucial for mechanically stable coatings that can be even applied to curved surfaces.

Capillary rise dynamics of aqueous glycerol solutions in glass capillaries: a critical examination of the Washburn equation

The classic description of capillary rise given by the Washburn equation was recently questioned in the light of experimental evidence for a velocity dependent dynamic contact angle at a moving contact line. We present a systematic investigation of the capillary rise dynamics of glycerol and aqueous glycerol solutions in vertical glass capillaries of various radii. For pure glycerol, the results of our experiments are in almost perfect agreement with the predictions of the Washburn equation using independently measured values for the liquid and capillary parameters. For aqueous glycerol solutions we observe discrepancies between the theoretical expectations and the experimental results, which are increasing with the water content of the solution. A thorough analysis, combined with scaling arguments, allows us to conclude that dynamic contact angle effects alone cannot provide a consistent explanation for these discrepancies. Rather, they can be perfectly accounted for if the mixture flowing in the capillary would have an effective, increased viscosity (in respect to the nominal value). We suggest and briefly discuss various mechanisms that could contribute to this observed behavior.

Self-similarity of contact line depinning from textured surfaces

The mobility of drops on surfaces is important in many biological and industrial processes, but the phenomena governing their adhesion, which is dictated by the morphology of the three-phase contact line, remain unclear. Here we describe a technique for measuring the dynamic behaviour of the three-phase contact line at micron length scales using environmental scanning electron microscopy. We examine a superhydrophobic surface on which a drop's adhesion is governed by capillary bridges at the receding contact line. We measure the microscale receding contact angle of each bridge and show that the Gibbs criterion is satisfied at the microscale. We reveal a hitherto unknown self-similar depinning mechanism that shows how some hierarchical textures such as lotus leaves lead to reduced pinning, and counter-intuitively, how some lead to increased pinning. We develop a model to predict adhesion force and experimentally verify the model's broad applicability on both synthetic and natural textured surfaces.

Modeling the transport of nanoparticle-filled binary fluids through micropores

Understanding the transport of multicomponent fluids through porous medium is of great importance for a number of technological applications, ranging from ink jet printing and the production of textiles to enhanced oil recovery. The process of capillary filling is relatively well understood for a single-component fluid; much less attention, however, has been devoted to investigating capillary filling processes that involve multiphase fluids, and especially nanoparticle-filled fluids. Here, we examine the behavior of binary fluids containing nanoparticles that are driven by capillary forces to fill well-defined pores or microchannels. To carry out these studies, we use a hybrid computational approach that combines the lattice Boltzmann model for binary fluids with a Brownian dynamics model for the nanoparticles. This hybrid approach allows us to capture the interactions among the fluids, nanoparticles, and pore walls. We show that the nanoparticles can dynamically alter the interfacial tension between the two fluids and the contact angle at the pore walls; this, in turn, strongly affects the dynamics of the capillary filling. We demonstrate that by tailoring the wetting properties of the nanoparticles, one can effectively control the filling velocities. Our findings provide fundamental insights into the dynamics of this complex multicomponent system, as well as potential guidelines for a number of technological processes that involve capillary filling with nanoparticles in porous media.

Droplet spreading and pinning on heterogeneous substrates

The contact angle of a fluid droplet on an heterogeneous surface is analyzed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through applications of depinning transitions of contact lines with nonlocal elasticity and features of pinning-depinning dynamics. Such properties not only depend on disorder strength and surface details, but also on the droplet volume and disorder correlation length. Deviations from Wenzel or Cassie-Baxter behavior are particularly apparent in the case of small droplet volumes and small contact angles.

Bioinspired Directional Surfaces for Adhesion, Wetting and Transport

In Nature, directional surfaces on insect cuticle, animal fur, bird feathers, and plant leaves are comprised of dual micro-nanoscale features that tune roughness and surface energy. This feature article summarizes experimental and theoretical approaches for the design, synthesis and characterization of new bioinspired surfaces demonstrating unidirectional surface properties. The experimental approaches focus on bottom-up and top-down synthesis methods of unidirectional micro- and nanoscale films to explore and characterize their anomalous features. The theoretical component of the review focuses on computational tools to predict the physicochemical properties of unidirectional surfaces.

Partial-post Laplace barriers for virtual confinement, stable displacement, and >5 cm s(-1) electrowetting transport

Laplace barriers composed of full-posts or ridges have been previously reported as a mechanism for virtual fluid confinement, but with unstable displacement (capillary fingering or fluid trapping, respectively). A new platform of 'partial-posts' eliminates the disadvantages of full-posts or ridges, while providing ~60-80% open channel area for rapid electrowetting fluid transport (>5 cm s(-1)). The fluid mechanics of partial-post Laplace barriers are far more complex than previous Laplace barriers as it involves two mechanisms: fluid can first begin to propagate either between, or under, the partial-posts. Careful design of channel and partial-post geometries is required, else one mechanism will dominate over the other. The physics and performance of partial-post Laplace barriers are verified using theoretical equations, experimental results, and dynamic numerical modeling.

Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels

We present a theoretical study of spontaneous imbibition of liquid (4)He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film, and the classical Lucas-Washburn √t scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Wetting of a drop on a sphere

In this work, the equilibrium morphology of a drop on a sphere is analyzed as a function of the contact angle and drop volume experimentally and with analytical effective interfacial energy calculations. Experimentally, a drop on a sphere geometry is realized in an oil bath by placing a water drop on a sphere coated with a dielectric, of which the radii of curvature are comparable with that of the drop. Electrowetting (EW) is used to change the contact angle of the water drop on the sphere. To validate the applicability of EW and the Lippman-Young equation on nonflat surfaces, we systematically investigate the response of the contact angle to the applied voltage (EW response) for various drop volumes and compared the results with the case of a planar surface. The effective interfacial energy of two competing morphologies, namely, the spherically symmetric "completely engulfing" and "partially engulfing" morphologies are calculated analytically. The analytical calculations are then compared to the experimental results to confirm which morphology is energetically more favored for a given contact angle and drop volume. Our findings indicate that the "partially engulfing" morphology is always the energetically more favorable morphology.

Modeling receding contact lines on superhydrophobic surfaces

We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. For the simulations to be feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane that faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts and discuss the form of the meniscus at depinning. We find, in agreement with ref 17 , that the local post concentration is a primary factor in controlling the depinning angle and show that the numerical results agree well with recent experiments. We also present two examples of metastable pinned configurations where the posts are partially wet.