No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Spontaneous capillary flows in piecewise varying cross section microchannels
Abstract
The study of the dynamics of capillary wetting has started in the 1920s with the studies of Lucas, Washburn, and Rideal. The LWR law states a square root dependency with time for the penetration distance. This property was shown to be valid for arbitrary, uniform cross section microchannels.
However, the dynamics of capillary wetting in non-uniform cross section channels is still a subject of investigation.
In this work an analytical model for piecewise varying cross section channels is developed. It is shown that the model compares favorably to experiments. Moreover the results are also in agreement with a former numerical approach.
... Moreover, micro/nanofluidic experiments have more freedom in material selections, pattern designs, and surface treatments, making the studies focus more on essential features of natural porous media. Simultaneously, micro/nanofluidic experiments' findings can be directly used for mathematical or numerical validations and upscaling attempts with observations of pore-scale imbibition [18][19][20][21][22][23][24]. The experiments in Lab-on-a-chip systems provide a promising way to catalyze pore-scale modeling, supplement coreflood findings, and guide fieldscale pilot operations for tight formations [25]. ...
... The main drawback of the models fabricated with two or more materials is the wettability heterogeneity in channels. However, the researchers can either apply a surface treatment [18,63,90,94,95] to create uniform wettabilities in inner channels or fabricate a sandwich-like micromodel [63] to relieve the above problem. ...
... Overall, 19 published papers [18,44,47,53,58,62,63,[65][66][67]80,99,100,103,104,106,114,116,117] from Table 2 to Table 5 are summarized. Although only the depths and widths of channels are provided in the figure, it does not indicate that cross-sections of channels are always rectangles. ...
For waterflooded tight oil formations, imbibition is a dominant mechanism for oil recovery. Although substantial imbibition experiments have been conducted in lab-on-a-chip systems, few of them have etched patterns with representative pore/throat features of tight rocks and are studied in Liquid-Liquid systems. This study aims to summarize the achievements of pore-scale imbibition experiments and point out the potentials/issues faced in applying micro/nanomodels for studying imbibition mechanisms in tight oil formations. This review first summarizes pore/throat features in tight rocks to provide benchmarks for evaluating micro/nanomodel designs. Then, recent efforts on pore-scale imbibition studies are documented based on pore-scale phenomena, testing materials, and pattern designs. Finally, the challenges and recommendations of applying lab-on-a-chip systems for imbibition studies are discussed from six aspects: the representability of channel designs, wettability issues, surface roughness effects, blocking events, pressure handling, and experiment repeatability.
... In the literature, researchers used capillaries (such as straight capillaries (Xiao et al. 2020;Xiao et al. 2019;Walls et al. 2016), capillaries with irregular cross sections (Erickson et al. 2002;Young 2004;Reyssat et al. 2008;Berthier et al. 2016;Gorce et al. 2016), doublet capillaries (Xiao et al. 2019;Nabizadeh et al. 2019;Chatzis and Dullien 1983) to numerically or mathematically investigate imbibition behaviors in pore-throat configurations. Among them, capillaries with irregular cross sections are often employed as they are recognized to be more representative of the porous media (Erickson et al. 2002;Young 2004;Berthier et al. 2016). ...
... In the literature, researchers used capillaries (such as straight capillaries (Xiao et al. 2020;Xiao et al. 2019;Walls et al. 2016), capillaries with irregular cross sections (Erickson et al. 2002;Young 2004;Reyssat et al. 2008;Berthier et al. 2016;Gorce et al. 2016), doublet capillaries (Xiao et al. 2019;Nabizadeh et al. 2019;Chatzis and Dullien 1983) to numerically or mathematically investigate imbibition behaviors in pore-throat configurations. Among them, capillaries with irregular cross sections are often employed as they are recognized to be more representative of the porous media (Erickson et al. 2002;Young 2004;Berthier et al. 2016). Erickson et al. (2002) numerically simulated imbibition processes for a liquid-gas (L-G) system by using the finite element method (FEM). ...
... Reyssat et al. (2008) mathematically and experimentally studied diverging capillaries with a wedge-shaped and power-lawshaped walls for an L-G system. After that, Berthier et al. (2016) conducted three imbibition experiments in open microchannels with irregular cross sections for an L-G system. They also derived an analytical model for matching their experimental data and the simulation results published by Erickson et al. (2002). ...
Due to discrepancies observed between many experimental results and predictions from the Bell–Cameron–Lucas–Washburn (BCLW) imbibition equation, the BCLW equation was often modified by considering the effects of pore/throat characteristics. As previous works mainly focused on liquid–gas systems, the effects of the viscosity ratios are neglected. In this study, the nonwetting-/wetting-phase-viscosity ratio (Ψ) is varied by four orders of magnitude (0.018 to 8), which covers the common fluid viscosity in waterflooded tight reservoirs. Capillaries with irregular cross sections (namely, complex capillaries), which are recognized to more representative for porous media, are used to theoretically study imbibition kinetics in both the liquid–gas and liquid–liquid system. To considering the effects of viscosity ratio, we propose a modified imbibition equation based on the Poiseuille law and a piecewise method to calculate the equivalent radius for complex capillaries. The predictivity of the new imbibition equation is mathematically validated in varying viscosity ratios and geometries characteristics (such as the radius levels and the numbers/length ratios of radius levels). The study proves that an equivalent straight capillary can globally predict imbibition behaviors in complex capillaries. Except for a few scenarios, the equivalent radius of the straight capillary is affected by capillary geometries and viscosity ratios. Only in the early stage of imbibition (lx/l≤0.12Ψ/Ψ-1), the modified imbibition equation can be expressed as a power-law relation (i.e., lx/l∝1Ψtα) as Ψ is higher than 1. In general, it is more suitable to express the imbibition equations in a quadratic form, especially for liquid–liquid imbibition systems.
... The hydraulic resistance can be decomposed in several components varying along the length of the capillary with respect to several factors, such as geometry and physical properties. 26,27 Here, we will focus on general systems where the hydraulic resistance can be decomposed in a constant part, R 0 , and a linearly varying one in space, xR x , where x is the moving capillary interface's position and R x is the hydraulic resistance per unit length. The constant part is equivalent to any constant hydraulic resistors upstream of the flow path, and the linear part issues from the linear increase in viscous losses as the meniscus propagates in a straight channel of constant cross-sectional shape. ...
We present a corollary to Washburn's equation in capillary dynamics. We show that, during capillary filling, in cases where flow path decreases with time, an accelerating capillary flow or reverse-Washburn flow regime occurs. We provide a description of this phenomenon following Washburn's classic analysis and characterize a “reverse-Washburn” capillary flow regime in both inertial and viscous regimes. This regime is observed and characterized in experiments and numerical simulations of recently discovered self-coalescence flows, opening the door to engineering devices with naturally accelerating capillary inflows.
... Whether the capillary flow is stopped at the entrance of the enlargement or not can be determined by the surface free energy analysis. 2,37 By considering the rectangular enlargement as a U-groove, the condition for spontaneous capillary flow into the enlargement is similar to the condition for wicking in a U-groove with corner flow (θ y < θ f = 45°) 2 (5) where θ y must be less than the critical contact angle θ c for spontaneous imbibition. If corner flows are absent (θ y > 45°), the condition for wicking becomes 2 (6) According to eqs 5 and 6, the critical contact angles are θ c = 24.5°(with ...
Imbibition dynamics in a rectangular U-groove that is connected to a sudden enlargement and complicated by the presence of Concus-Finn (CF) filaments is investigated using many-body dissipative particle dynamics. For open-ended sudden enlargement, four flow types are identified and depend on the contact angle θy, the critical angle θf associated with the occurrence of CF filaments, and the critical angle θc associated with the occurrence of main flow. First, for θy > θf and θy > θc, the corner flow is absent, and the main flow stops at the end of the small U-groove. Second, for θc > θy > θf, the corner flow vanishes, but the main flow occurs. Third, for θf > θy > θc, the corner flow takes place in the large U-groove, but the main flow is still absent. Fourth, for θy < θf and θy < θc, both the corner and main flows appear in the large U-groove. Additionally, the flow dynamics is greatly influenced by the length of the large U-groove (le). For closed-ended sudden enlargement, similar findings can be obtained. However, the outcome of the third case is altered for sufficiently small le, and the sudden enlargement can eventually be filled.
... The results were found to reduce the wear rate by about 115 times, and the coefficient of friction by about four times compared to the reference pure nickel (Reinert et al., 2018). In addition, there are many articles in the literature about the lubrication of the surfaces that are in contact with each other due to the thermocapillary effect, capillary effect, gravity effect or microchannel, etc. without external lubrication (Berthier et al., 2016;Dai et al., 2016Dai et al., , 2021Grützmacher et al., 2020). ...
Purpose-This study aims to produce lubricating surfaces with micro-channels by the selective laser melting (SLM) method, and to investigate their tribological behavior. Design/methodology/approach-In this study, three kinds of samples with different geometries were designed, impregnated with oil and then subjected to flow analysis in a virtual environment using Ansys Fluent software. According to the results of these analyses, the best-lubricated surface geometry sample was identified, and a number of geometries were produced by SLM, which is one of the additive manufacturing methods. Tribological tests were performed using a pin-on-disk tribometer with a stainless steel ball as the contact surface. The structural and morphological features were investigated by a three-dimensional profilometer and scanning electron microscopy. Findings-The results obtained showed that the impregnated oil reached the surface of the sample compared to untreated samples, and it was seen that the wear rates were reduced, and that the impregnated oil samples exhibited the highest wear resistance. Originality/value-In this study, solid geometries that are difficult to be produced by other methods are produced with additive manufacturing method, and the surfaces have been given lubricating properties.
... 27,28 Closed form analytical expression has been developed based on the balance between the drag and capillary forces to describe the capillary flow in piecewise varying cross section channels. 29 Other studies have shown that a sudden enlargement and contraction of the flow channel can act as a local and global flow resistor, respectively. 30 In a recent study, a theoretical capillary model was developed for a circular undulating tube with an idealized cosine-type inner wall. ...
Capillary rise is ubiquitous in engineering applications and natural phenomena. In straight channels, the dynamics of capillary rise have been thoroughly investigated and are well understood. However, for nonuniform channels of varying radius, the dynamics remain largely unclear. In this study, the capillary rise in a sinusoidal wavy channel is investigated both analytically and numerically. Specifically, the capillary rate-of-rise of water in sinusoidal channels with different contraction frequencies and amplitudes is derived based on the principle of energy conservation. The change in capillary velocity a nd height over time is further validated by two-phase flow simulations based on the conservative level-set method. The results reveal strong viscous dissipation in the interfacial region resulting from the wave-like wobbling motion of the liquid-air interface, constituting more than 50% of the total viscous dissipation when the channel profile changes rapidly. Failing to account for this interfacial effect will result in significant overestimations of the capillary velocity and erroneous predictions of the capillary rise curve, typically more than 4 times difference in the capillary velocity and more than 2.5 times difference in the time taken to arrive at the maximum height.
... It is similar to what is observed with a widening of a unique channel. [39][40][41] On the other hand, the total flow rate is nearly constant after the second level of bifurcations, as shown in Figure 6b. Using (17), flow rates are given by ...
Velocity of capillary flow in closed or open channels decreases as the flow proceeds down the length of the channel, varying as the inverse of the square root of time or as the inverse of travel distance. In order to increase the flow rate-and extend the duration of the flow-capillary pumps have been designed by mimicking the pumping principle of paper or cotton fibers. These designs provide a larger volume available for the wicking of the liquids. In microsystems for biotechnology, different designs have been developed based on experimental observation. In the present manuscript, the mechanisms at the basis of capillary pumping are investigated using a theoretical model for the flow in an open-channel "capillary tree" (i.e., an ensemble of channels with bifurcations mimicking the shape of a tree). The model is checked against experiments. Rules for obtaining better designs of capillary pumps are proposed-specifically we find: (1) when using a capillary tree with identical channel cross-sectional areas throughout, it is possible to maintain nearly constant flow rates throughout the channel network, (2) flow rate can be increased at each branch point of a capillary tree by slightly decreasing the areas of the channel cross-section and decreasing the channel lengths at each level of ramification within the tree, and (3) higher order branching (trifurcations vs. bifurcations) amplify the flow rate effect. This work lays the foundation for increasing the flow rate in open microfluidic channels driven by capillary flow; we expect this to have broad impact across open microfluidics for biological and chemical applications such as cell culture, sample preparation, separations, and on-chip reactions.
... A similar study was conducted by imitating the surface of the Texas horned lizard as a model for a biomimetic 'liquid diode' where the applied liquid spreads more in one direction than the other [61]. Other researchers focused on attempting to optimise the shape of the capillaries for increased flow by a repeated diverging and converging diameter of a capillary [62,63]. However, these studies are undertaken only in one capillary and do not take interconnectivity into account. ...
Spontaneous spreading of liquids in porous materials is of great industrial relevance and occurs in, for example, diapers, fabrics, paper or paint. Often, it is necessary to manipulate the spreading rate of liquids to result in the desired mass transport, for example to soak up large liquid volumes, as in a diaper. To do this, it is necessary to know the precise mechanism of surface tension driven flow. However, the process is complex and so are the porous materials in terms of both chemical composition and geometry. The mathematical and physical description of the process is often limited to specific cases – for example, the well-known Lucas-Washburn equation describes the speed of a meniscus in capillaries with circular cross-section in a hard material without interconnections. The objective of this thesis is to deepen the understanding of the mechanism with which a liquid spreads in a soft porous material only driven by surface tension. To this end, the liquid dynamics of water and water-based liquids were investigated in various model systems which are similar to porous 3D materials. In an alginate gel, capillaries with circular cross-sections were produced and the spreading rate of water was determined and compared to existing models. Using a method, which involves 3D printing, it was possible to fabricate open channels with rectangular cross-sections in the same alginate gel. The liquid spreading in these channels in geometries of branched channel systems was investigated. The results revealed that the spreading rate in capillaries of circular cross-sections in soft materials was much slower than that anticipated in existing models, which describe hard materials. In open channels of rectangular cross-sections, the presence of side channels slowed down the meniscus in the main channel; the meniscus stopped when it encountered junctions. The stop duration was longer when the side channels were longer, when they were wider, and when their tilting angle was low with respect to the main channel. An analysis of the volume flow indicated that those geometries that had long side channels but are few in number, resulted in faster volume flow. In a porous 3D material, this suggests that the interconnectivity could decrease the volume flow rate. Finally, a calcium alginate gel with straight-aligned pores was produced and characterised as an example of optimal liquid transport. The outcome of this thesis can be used to adjust the geometrical design of porous materials to result in desired liquid transport properties. The stiffness of the material may influence the liquid transport. The thesis also contributes to the discussion on how the liquid takes selective pathways in porous materials.
Keywords: Capillary flow, capillary action, alginate gel, wetting on soft materials
... Compared to the experiments without temperature gradient, additional Marangoni forces lead to a droplet migration towards the cold side of the sample. The capillary and Marangoni forces are balanced by the viscous drag force (wall friction) [28,48]. The Reynolds number of the fluid is even for the fastest velocities smaller than 10 −2 , representing laminar flow. ...
This manuscript aims at investigating the spreading dynamics of an additive-free Poly-(alpha)-olefin (PAO) oil on stainless steel surfaces (AISI 304) having multi-scale surface patterns with and without an applied temperature gradient. For this purpose, single-scale patterns were fabricated by micro-coining, direct laser interference patterning and ultrashort-pulse laser patterning. In a second step, multi-scale patterns were realized by superimposing micro-coined surfaces with the respective laser patterns. In order to precisely adjust the temperature gradient and to study the lubricant's migration on the patterned surfaces, a specially designed test rig was used. Experiments without temperature gradient demonstrated a preferential lubricant spreading parallel to the pattern for all samples. In this context, the multi-scale samples showed a faster lubricant spreading compared to the single-scale patterns, which can be attributed to additional capillary forces and an increased roughness. In case of an applied temperature gradient, purely micro-coined samples showed an increased rate of lubricant spreading compared to the other single-scale samples due to the larger volume to surface area ratio. The multi-scale surfaces demonstrated again the fastest lubricant spreading, which clearly underlines the ability to actively guide lubricant by multi-scale patterning.
... Surprisingly, it seems that liquid withdrawal from an expanding pipe has not been investigated so far; the authors at least were unable to identify related studies in literature. However, a similar geometry as sketched in Fig. 1 is considered in several analytical [41][42][43] and numerical [44][45][46] studies on capillary suction in micropores where liquid is drawn by capillary forces from the larger into the smaller pore (wicking flow). In the present study in contrast, the pipe diameter is in the order of millimeters not micrometers, and the flow is pressure driven opposing to capillary forces for θ e < 90°. ...
To avoid potential damage of the dosing unit in selective catalytic reduction by freezing urea-water-solution, the liquid is usually drained from the delivery line when the vehicle is out of operation. When liquid is sucked back counter to the normal delivery direction, the urea-water-solution is replaced by gas with the risk of air being sucked in. In this paper, we study the liquid back suction process and bubble formation numerically by interface-resolving simulations with a phase field method for a generic simplified geometry. We consider two connected circular tubes with sudden or gradual change of the diameter and provide guidelines for proper numerical setup of such flow problems in order to ensure physically reliable results. We study the influence of the geometry on the liquid draining process through variations of inner and outer tube diameters as well as transition inclination angle. The present numerical results indicate that geometrical modification is an effective means to control liquid draining in expanding pipes while preventing gas bubble formation.
... Again the flow in the top channel arrives first at the outlet, i.e. the capillary flow that passes first through the wide section arrives before that passing through the narrow section first. This property agrees with the results from [21,24] developed otherwise. ...
Point-of-care (POC) reaction microchambers are basis features of biotechnological devices. Most of the time biotechnological devices comprise multiple reaction chambers, in order to achieve simultaneously as many reactions as possible, enhancing the efficiency of these devices. Parallelization requires the precise filling and loading of these chambers, and the best synchronization is searched for. De-synchronization triggers the formation of air bubbles and leads to anomalous functioning of the device.
It has been observed that synchronized filling of microchannels and fluidic networks is often an experimental challenge. In fact, this experimental difficulty directly stems from the conceptual approach of the design of the network.
In this work we theoretically investigate the filling of networks, driven by the injection pressure of a pump. The additional effect of capillary forces is also taken into account. Experimental results are compared with the theoretical model. Rules for better synchronization are enounced.
... First in the case of cylindrical duct with the Lucas-Washburn-Rideal law [1][2][3][4] and then extended to a large number of other channel geometries [5,6]. Recent studies have investigated the capillary flow of Newtonian liquids within non-uniform channels [7][8][9][10]. ...
The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR) law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.In this work we consider the Herschel-Bulkley (HB) rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids), the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM) law for power-law fluids. Although HB model cannot reduce to Casson?s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.
... First in the case of cylindrical duct with the Lucas-Washburn-Rideal law [1][2][3][4] and then extended to a large number of other channel geometries [5,6]. Recent studies have investigated the capillary flow of Newtonian liquids within non-uniform channels [7][8][9][10]. ...
The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR) law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.
In this work we consider the Herschel-Bulkley (HB) rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids), the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM) law for power-law fluids. Although HB model cannot reduce to Casson’s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.
Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.
Open microfluidics has attracted increasing attention over the last decade because of its flexibility and simplicity with respect to cell culture and clinical diagnosis. However, traditional valves and pumps are difficult to integrate on open-channel microfluidic chips, in which a liquid is usually driven by capillary forces. Poor fluid control performance is a common drawback of open microfluidics. Herein, we proposed a method for controlling the liquid flow in open channels by controlling the continuous Laplace pressure induced by the deformation of the shape memory microstructures. The uniformly arranged cuboidal microcolumns in the open channels have magnetic/light dual responses, and the bending angle of the microcolumns can be controlled by adjusting Laplace pressure using near-infrared laser irradiation in a magnetic field. Laplace pressure and capillary force drove the liquid flow together, and the controllable fluid transport was realized by adjusting the hydrophilicity of the channel surface and the bending angle of the microcolumns. We demonstrated the controllability of the flow rate and the directional transport of water along a preset path. In addition, the start and stop of water transport were realized via local hydrophobic modification. The proposed strategy improves poor fluid control in traditional open systems and makes fluid flow highly controllable. We tried to extract and detect rhodamine B in tiny droplets on the open microfluidic chip, demonstrating the advantages of the proposed strategy in the separation and analysis of tiny samples.
Purpose
This study aims to produce lubricating surfaces with micro-channels by the selective laser melting (SLM) method, and to investigate their tribological behavior.
Design/methodology/approach
In this study, three kinds of samples with different geometries were designed, impregnated with oil and then subjected to flow analysis in a virtual environment using Ansys Fluent software. According to the results of these analyses, the best-lubricated surface geometry sample was identified, and a number of geometries were produced by SLM, which is one of the additive manufacturing methods. Tribological tests were performed using a pin-on-disk tribometer with a stainless steel ball as the contact surface. The structural and morphological features were investigated by a three-dimensional profilometer and scanning electron microscopy.
Findings
The results obtained showed that the impregnated oil reached the surface of the sample compared to untreated samples, and it was seen that the wear rates were reduced, and that the impregnated oil samples exhibited the highest wear resistance.
Originality/value
In this study, solid geometries that are difficult to be produced by other methods are produced with additive manufacturing method, and the surfaces have been given lubricating properties.
An extensive study of capillary flow of fluids with various viscosities in straight and periodically constricted microchannels with different surface wettability is presented. Capillary filling speed in hydrophilic, less hydrophilic, and hydrophobic microchannels were experimentally monitored and compared with Washburn theoretical model. For all liquids, a linear relationship was found between the square of propagation distance and time, which is expected for Newtonian fluids. Experimental results indicated slower velocity compared to the theoretical prediction due to simplifications of the Washburn model. Capillary filling speed of fluids into long-flurorinated chain silane modified channels confirmed the expected lyophobic nature of the coating (i.e. not favorable for either hydrophilic or hydrophobic liquids). Presence of the precursor film ahead of the three-phase contact line in microscopic level was demonstrated. White light and fluorescent images confirmed the presence of precursor film and capillary evaporation at the interface. Evaporation enhanced the deviation between experimental and theoretical results due to continuous wettability alteration of penetrating fluid.
Open microfluidic capillary systems are a rapidly evolving branch of microfluidics where fluids are manipulated by capillary forces in channels lacking physical walls on all sides. Typical channel geometries include grooves, rails, or beams and complex systems with multiple air–liquid interfaces. Removing channel walls allows access for retrieval (fluid sampling) and addition (pipetting reagents or adding objects like tissue scaffolds) at any point in the channel; the entire channel becomes a “device-to-world” interface, whereas such interfaces are limited to device inlets and outlets in traditional closed-channel microfluidics. Open microfluidic capillary systems are simple to fabricate and reliable to operate. Prototyping methods (e.g., 3D printing) and manufacturing methods (e.g., injection molding) can be used seamlessly, accelerating development. This Perspective highlights fundamentals of open microfluidic capillary systems including unique advantages, design considerations, fabrication methods, and analytical considerations for flow; device features that can be combined to create a “toolbox” for fluid manipulation; and applications in biology, diagnostics, chemistry, sensing, and biphasic applications.
Capillary flows are increasingly used in biotechnology,
biology, chemistry, energy and space applications.
Motivated by these new developments, designs of capillary
channels have become more sophisticated. In particular,
capillary microsystems often use winding channels for
reasons such as compactness, or mixing. The behavior of
capillary microflows in curved channels is still underdeveloped.
In this work, we investigate this type of behavior.
In the case of suspended capillary flows, is shown that the
flow profile in the curved section is approximately analogous
to that in a rectilinear section. In the case of open
U-grooves where inner corners are present, the importance
of the turn sharpness and of the presence of capillary filaments
is pointed out. For sharp turns, and/or in the presence
of precursor capillary filaments, we found the phenomenon
that the inner filament precedes the outer filament in the
channel. Analysis of the capillary flow in curved channels
is performed experimentally using rectangular U-grooves
and suspended channels. The experimental observations are
compared to Surface Evolver numerical software results.
Open-surface microfluidic systems, i.e. microflows with a free surface, are finding increasing use in the fields of biotechnology, biology and medicine, especially in the domain of Point-Of-Care (POC) and home care systems. In such systems the fluids are moved by capillarity, and do not require the use of costly and/or bulky pumps, or other actuation systems. Recently a subcategory of such flows, called “suspended microflows,” has appeared where the liquids flows between vertical walls without supporting walls at the bottom, i.e. surface tension is used to fill and maintain a fluid in microscale structures devoid of a ceiling and floor. The condition for the onset of spontaneous suspended flows has been developed in a preceding article. However, the dynamics of suspended microfluidics has not yet been investigated and we present here a first analysis of their dynamics. Verifications of the theoretical model have been performed using colored water. Applications to the capillary motion of whole blood and to the motion of polymeric liquids have been done. Especially, we show that capillary filling of a suspended turning channel may be an approach to the realization of in-situ giant porous micromembranes.
The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid–air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T
c, below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T
c ≈ (3X
e/2)2/3 and has an associated dimensionless cross-over rise height X
c ≈ (3X
e/2)1/3, where X
e = 1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid–air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems.
Spontaneous capillary flow (SCF) is a powerful method for moving fluids at the microscale. In modern biotechnology, composite channels—sometimes open—are increasingly used. The ability to predict the occurrence of a SCF is a necessity. In this work, using the Gibbs free energy, we derive a general condition for the establishment of SCF in any composite microchannel of constant cross-section, i.e. a microchannel comprising different wall materials and even open parts. It is shown that SCF occurs when the Cassie angle is smaller than teta(Cassie)< pi/2. For a homogeneous confined channel, this relation collapses to the well-known hydrophilic contact angle teta<pi/2.
In this study, the interfacial and electrokinetic phenomena of mixtures of isopropyl alcohol (IPA) and deionized (DI) water in relation to semiconductor wafer drying is investigated. The dielectric constant of an IPA solution linearly decreased from 78 to 18 with the addition of IPA to DI water. The viscosity of IPA solutions increased as the volume percentage of IPA in DI water increased. The zeta potentials of silica particles and silicon wafers were also measured in IPA solutions. The zeta potential approached neutral values as the volume ratio of IPA in DI water increased. A surface tension decrease from 72 to 23 dynes/cm was measured when the IPA concentration increased to 30 vol %. The surface excess of IPA at the air-liquid interface reached a maximum at around 20 vol % IPA. The adhesion forces of silica particles on silicon wafers were measured using atomic force microscopy in IPA solutions. The adhesion force increased as the volume percent of IPA in water increased. Lower particulate contamination was observed when the wafers were immersed and withdrawn from solutions containing less than 25 vol % IPA.
PLASMA HYDROPHILIZATION AND SUBSEQUENT HYDROPHOBIC RECOVERY ARE STUDIED FOR TEN DIFFERENT POLYMERS OF MICROFABRICATION INTEREST: polydimethylsiloxane (PDMS), polymethylmethacrylate, polycarbonate, polyethylene, polypropylene, polystyrene, epoxy polymer SU-8, hybrid polymer ORMOCOMP, polycaprolactone, and polycaprolactone/D,L-lactide (P(CL/DLLA)). All polymers are treated identically with oxygen and nitrogen plasmas, in order to make comparisons between polymers as easy as possible. The primary measured parameter is the contact angle, which was measured on all polymers for more than 100 days in order to determine the kinetics of the hydrophobic recovery for both dry stored and rewashed samples. Clear differences and trends are observed both between different polymers and between different plasma parameters.
Point-of-care diagnostics will strongly benefit from miniaturization based on microfluidics because microfluidics integrate functions that can together preserve valuable samples and reagents, increase sensitivity of a test, and accelerate mass transport limited reactions. But a main challenge is to incorporate reagents into microfluidics and to make microfluidics simple to use. Here, we integrate microfluidic functional elements, some of which were developed earlier, and reagents such as detection antibodies (dAbs), capture antibodies (cAbs) and analyte molecules for making one-step immunoassays: the integrated device only requires the addition of sample to trigger a cascade of events powered by capillary forces for effecting a sandwich immunoassay that is read using a fluorescence microscope. The microfluidic elements comprise a sample collector, delay valves, flow resistors, a deposition zone for dAbs, a reaction chamber sealed with a polydimethylsiloxane (PDMS) substrate, and a capillary pump and vents. Parameters for depositing 3.6 nL of a solution of dAb on the chip using an inkjet are optimized and the PDMS substrate is patterned with analytes, which provide a positive control, and cAbs. Various storage conditions of the patterned PDMS are investigated for up to 6 months revealing that storage with a desiccant preserved at least 51% of the activity of the cAbs. C-reactive protein (CRP), a general inflammation and cardiac marker, is detected using this one-step chip using only 5 microL of human serum by measuring fluorescent signals from 30 x 100 microm(2) areas of the PDMS substrate in the wet reaction chamber. The one-step chip can detect CRP at a concentration of 10 ng mL(-1) in less than 3 min and below 1 ng mL(-1) within 14 min. The work presented here may spur the adoption of fluorescence immunoassays using capillary driven microfluidics and PDMS substrates for point-of-care diagnostics.
The transport of minute amounts of liquids using microfluidic systems has opened avenues for higher throughput and parallelization of miniaturized bio/chemical processes combined with a great economy of reagents. In this report, we present a microfluidic capillary system (CS) that autonomously transports aliquots of different liquids in sequence: liquids pipetted into the service port of the CS flow unidirectionally through the various sections of the CS, which comprises a 15-pL reaction chamber, into the capillary pump. A CS can thus be operated by simply delivering the different samples to its service port. The liquid transport concept presented here is advantageous because the pumping and valving functions are integrated into the device by means of capillary phenomena, and it therefore does not require any external power supply or control device. Thus, arrays of CSs can easily be formed by cloning a functional CS. Alternatively, the flow of liquids in CSs can also be interactively tuned if desired by (i) forcing the evaporating of liquid out of the capillary pumps and (ii) by contacting a secondary, removable capillary pump to the embedded ones. We illustrate the possibilities of CSs by conducting a surface immunoassay for a cardiac marker, within 25 min, on an area of 100 x 100 microm2, using 16 sequential filling steps.
The engineering and modeling of non-Newtonian power-law fluids (i.e., shear thinning and thickening fluids) in porous media has received wide attention in natural systems, oil recovery, and microfluidic devices. In this work, we theoretically explore the dynamics of power-law fluids in the form of capillary flow confined by a straight tube and a Y-shaped tree network, both of which are basic elements of many advanced materials. The straight tube and the tree network are composed of sub-tubes with different radii and lengths. The proposed model reveals that the evolution of the penetration time to the penetration distance is highly dependent on the viscous and capillary effects. If the viscous resistance is high, the flow is slow. If the capillary pressure increases, the flow accelerates. An interesting question is therefore in what optimal structure is the power-law flow fastest, considering different responses of viscous resistance and capillary force to the structural parameters. Based on optimization of the radius and length distribution of sub-tubes, we find the minimum penetration time of the fluids or the fastest flow in both straight tubes and tree networks under size constraints. The unique optimal transport behaviors of power-law fluids, which are different from those of Newtonian fluids, are analyzed in details with different power components.
Capillary spontaneous flow is an interesting solution to move fluids either in microgravity conditions, i.e. in space, in microfluidic systems. In both cases, gravity is negligible and capillarity is the dominant force.
Spontaneous capillary flow onset as well as the dynamics of capillary flows have been recently documented in the literature for channels of different shapes, confined or open. However, the role of the dynamic contact angle is still unclear. This work aims at bringing a new light on the effect of the dynamic contact angle in the dynamics of capillary flows.
Capillary microfluidics or capillarics has been lately gaining importance in the biotechnological and biological domains. In these domains where biological and chemical targets are transported by fluids, it has been shown that capillary actuation of fluids does not require bulky pumps or syringes and produces microsystems with a low-cost of fabrication, that are user-friendly, portable and compatible with telemedicine.
Capillary systems for biotechnology can be confined or open, i.e. the fluid moves inside a closed channel or in a channel with a boundary with air. In this work, we propose a general expression for the determination of the velocities of spontaneous capillary flows in composite, confined microchannels of arbitrary shapes. This expression generalizes the conventional Lucas-Washburn model which is valid for cylindrical channels. It is shown that the use of an equivalent hydraulic diameter in the Lucas-Washburn model introduces a bias when the shape of the channel cross-section differs notably from a circle.
The approach also shows that relatively large velocities—at the scale of microsystems—can be reached by capillary microflows, depending on the shape of the channel, and that transport distances can be important.
Microfluidic capillary systems operate using capillary forces only and require capillary pumps (CPs) to transport, regulate, and meter the flow of small quantity of liquids. Common CP architectures include arrays of posts or tree-like branched conduits that offer many parallel flow paths. However, both designs are susceptible to bubble entrapment and consequently variation in the metered volume. Here, we present two novel CP architectures that deterministically guide the filling front along rows while preventing the entrapment of bubbles using variable gap sizes between posts. The first CP (serpentine pump) guides the filling front following a serpentine path, and the second one (leading-edge pump) directs the liquid along one edge of the CP from where liquid fills the pump row-by-row. We varied the angle of the rows with respect to the pump perimeter and observed filling with minimal variation in pumping pressure and volumetric flow rate, confirming the robustness of this design. In the case of serpentine CP, the flow resistance for filling the first row is high and then decreases as subsequent rows are filled and many parallel flow paths are formed. In the leading-edge pump, parallel flow paths are formed almost immediately, and hence, no spike in flow resistance is observed; however, there is a higher tendency of the liquid for skipping a row, requiring more stringent fabrication tolerances. The flow rate within a single CP was adjusted by tuning the gap size between the microposts within the CP so as to create a gradient in pressure and flow rate. In summary, CP with deterministic guidance of the filling front enables precise and robust control of flow rate and volume.
Capillary microfluidics or capillarics is gaining importance in the biotechnological domain. It
combines the advantages of capillary actuation that does not require pumps or syringes to move the fluids, with
low-cost fabrication, user-friendliness, portability and telemedicine compatibility. In this work, we present
expressions of the spontaneous capillary flow velocity in different geometrical configurations. It is shown that
relatively large velocities - at the scale of microsystems — can be reached by capillary microflows.
Consequently transport distances can be important
Polymethylmethacrylate (PMMA) films were modified by RF oxygen plasma with various powers applied for different periods, and the effects of these parameters on the surface properties such as hydrophilicity, surface free energy (SFE), chemistry, and topography were investigated by water contact angle, goniometer, X-ray photoelectron spectroscopy (XPS), and atomic force microscopy, and the types of the created free radicals and their decay were detected by electron spin resonance spectroscopy (ESR). SFE and contact angle results varied depending on the plasma parameters. Oxygen plasma treatment (100 W–30 min) enhanced the hydrophilicity of PMMA surface as shown by decreasing the water contact angle from 70° to 26°. XPS analysis showed the change in the amounts of the present functionalities as well as formation of new groups as free carbonyl and carbonate groups. The roughness of the surface increased considerably from ~2 nm to ~75 nm after 100 W–30 min oxygen plasma treatment. ESR analysis indicated the introduction of peroxy radicals by oxygen plasma treatment, and the intensity of the radicals increased with increasing the applied power. Significant decrease in radical concentration was observed especially for the samples treated with higher powers when the samples were kept under the atmospheric conditions. As a conclusion, RF plasma, causes changes in the chemical and physical properties of the materials depending on the applied parameters, and can be used for the creation of specific groups or radicals to link or immobilize active molecules onto the surface of a material. Copyright © 2012 John Wiley & Sons, Ltd.
Microfluidic capillary systems employ surface tension effects to manipulate liquids, and are thus self-powered and self-regulated as liquid handling is structurally and chemically encoded in microscale conduits. However, capillary systems have been limited to perform simple fluidic operations. Here, we introduce complex capillary flow circuits that encode sequential flow of multiple liquids with distinct flow rates and flow reversal. We first introduce two novel microfluidic capillary elements including (i) retention burst valves and (ii) robust low aspect ratio trigger valves. These elements are combined with flow resistors, capillary retention valves, capillary pumps, and open and closed reservoirs to build a capillary circuit that, following sample addition, autonomously delivers a defined sequence of multiple chemicals according to a preprogrammed and predetermined flow rate and time. Such a circuit was used to measure the concentration of C-reactive protein. This work illustrates that as in electronics, complex capillary circuits may be built by combining simple capillary elements. We define such circuits as "capillarics", and introduce symbolic representations. We believe that more complex circuits will become possible by expanding the library of building elements and formulating abstract design rules.
Experiments are performed to observe capillary flow in grooves cut into copper surfaces. Flow kinetics of two liquids, 1-heptanol and eutectic SnPb solder, are modeled with modified Washburn kinetics and compared to flow data. It is shown that both liquids flow parabolically in narrow V-grooves, and the data scale as predicted by the modified Washburn model. The early portions of the flow kinetics are characterized by curvature in the length vs time relationship which is not accounted for in the modified Washburn model. This effect is interpreted in terms of a dynamic contact angle. It is concluded that under conditions of rapid flow, solder spreading can be understood as a simple fluid flow process. Slower kinetics, e.g. solder droplet spreading on flat surfaces, may be affected by subsidiary chemical processes such as reaction.
Penetration of Liquids into Cylindrical Capillaries.—The rate of penetration into a small capillary of radius r is shown to be: dldt=P(r2+4εr)8ηl, where P is the driving pressure, ε the coefficient of slip and η the viscosity. By integrating this expression, the distance penetrated by a liquid flowing under capillary pressure alone into a horizontal capillary or one with small internal surface is found to be the square root of (γrt·cosθ2η), where γ is the surface tension and θ the angle of contact. The quantity (γcosθ2η) is called the coefficient of penetrance or the penetrativity of the liquid.
The problem of capillary-driven flow in a V-shaped surface groove is addressed. A nonlinear diffusion equation for the liquid shape is derived from mass conservation and Poiseuille flow conditions. A similarity transformation for this nonlinear equation is obtained and the resulting ordinary differential equation is solved numerically for appropriate boundary conditions. It is shown that the position of the wetting front is proportional to (Dt)½ where D is a diffusion coefficient proportional to the ratio of the liquid-vapour surface tension to viscosity and the groove depth, and a function of the contact angle and the groove angle. For flow into the groove from a sessile drop source it is shown that the groove angle must be greater than the contact angle. Certain arbitrarily shaped grooves are also addressed.
For V-shaped surface grooves in copper, we have obtained the capillary driven flow kinetics for two liquids: unreactive 1-heptanol and eutectic Sn/Pb solder, which is known to react with copper. We show experimentally that the flow of both liquids in these grooves follows the classical Washburn kinetics, i.e., a Poiseuille flow process, modified to include a dynamic contact angle. Because no subsidiary processes are necessary to fit our data, we propose that in this geometry capillary driven solder flow is too rapid for reaction to provide an appreciable effect. Thus, to observe the effects of Sn/Cu reaction kinetics, the flow rate must be decreased, which the present experiments allow through redesign of the groove geometry and size.
This article describes the design, function, and application of simple microfluidic networks as conduits for the patterned delivery of chemical reactants onto a substrate. It demonstrates how such networks, made in an elastomer, allow simultaneous delivery of functionally distinct molecules onto targeted regions of a surface (Delamarche, E. et al. Science 1997, 276, 779-781). Microfluidic networks generally consume less than microliter quantities of solution and are thus well suited for use when the required reagents are scarce or precious, as often occurs in experiments and technologies that place biochemicals on solid planar substrates. We illustrate some of the particular challenges of doing chemistry inside the narrow confines of capillaries defined by fluidic networks, in addition to the advantages attendant to this approach, in the context of forming patterned arrays of different, and functional, immunoglobulins useful in highly localized biological assays.
This paper reports on the development and application of a surface modification technique as an improved method for bonding polymer microfluidic substrates. This technique readily produced complete microfluidic chips via plasma oxidation followed by silane reagent treatment on the polymer surface. Characterization of the bonded chips was performed using scanning electron microscopy (SEM), water contact angle measurement, and tensile strength measurement. SEM images showed that the integrity of the channel features was successfully preserved. A bond strength approaching that of solvent welding was demonstrated. This technique has been successfully applied to bond dissimilar polymer substrates (polymethylmethacrylate (PMMA), amorphous polyethylene terephthalate (APET), polycarbonate (PC)), and is also applicable to bonding a hard polymer substrate to polydimethylsiloxane (PDMS) or glass.
We might be at the turning point where research in microfluidics undertaken in academia and industrial research laboratories, and substantially sponsored by public grants, may provide a range of portable and networked diagnostic devices. In this Progress Report, an overview on microfluidic devices that may become the next generation of point-of-care (POC) diagnostics is provided. First, we describe gaps and opportunities in medical diagnostics and how microfluidics can address these gaps using the example of immunodiagnostics. Next, we conceptualize how different technologies are converging into working microfluidic POC diagnostics devices. Technologies are explained from the perspective of sample interaction with components of a device. Specifically, we detail materials, surface treatment, sample processing, microfluidic elements (such as valves, pumps, and mixers), receptors, and analytes in the light of various biosensing concepts. Finally, we discuss the integration of components into accurate and reliable devices.
The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface.
We report the filling kinetics of different liquids in nanofabricated capillaries with rectangular cross-section by capillary force. Three sets of channels with different geometry were employed for the experiments. The smallest dimension of the channel cross-section was respectively 27, 50, and 73 nm. Ethanol, isopropanol, water and binary mixtures of ethanol and water spontaneously filled nanochannels with inner walls exposing silanol groups. For all the liquids the position of the moving liquid meniscus was observed to be proportional to the square root of time, which is in accordance with the classical Washburn kinetics. The velocity of the meniscus decreased both with the dimension of the channel and the ratio between the surface tension and the viscosity. In the case of water, air-bubbles were spontaneously trapped as channels were filled. For a binary mixture of 40% ethanol and water, no trapping of air was observed anymore. The filling rate was higher than expected, which also corresponds to the dynamic contact angle for the mixture being lower than that of pure ethanol. Nanochannels and porous materials share many physicochemical properties, e.g., the comparable pores size and extremely high surface to volume ratio. These similarities suggest that our nanochannels could be used as an idealized model to study mass transport mechanisms in systems where surface phenomena dominate.
In this study the wetting behavior of converging-diverging and diverging-converging capillaries is investigated numerically using an in-house written, finite-element code. An interface tracking procedure based on the predicted change in the total liquid volume, to update the interface location, and Cox's formulation, to determine the dynamic contact angle and the interface shape, is proposed and used. Flow simulations revealed that both converging-diverging and diverging-converging capillaries exhibit significantly slower wetting behavior than straight capillaries and that any deviation in the capillary diameter necessarily tends to slow the overall wetting speed. This behavior was attributed to local regions of very low capillary pressure and high viscous retardation force when the capillary diameter at the interface was significantly larger than the capillary diameter over the upstream fluid. Though the local wetting velocities were different, when equivalent capillaries were compared it was found that both converging-diverging and diverging-converging capillaries had the same total fill time independent of the number of irregular regions, suggesting that the simple model is sufficient for predicting the overall effect. The influence of surface tension and contact angle on the total wetting time was found to be similar for both straight and irregularly shaped capillaries.
Method of anisotropically etching silicon, United States Patent 5501893
- F Laermer
- A Schilp
F. Laermer, A. Schilp, Method of anisotropically etching silicon, United States
Patent 5501893, 1994.
Autonomous microfluidic capillary system
- R Safavieh
- D Juncker
R. Safavieh, D. Juncker, Autonomous microfluidic capillary system, Anal.
Chem. 74 (2002) 6139-6144.
- R Lucas
R. Lucas, Ueber das Zeitgesetz des Kapillaren Aufstiegs von Flussigkeiten,
Kolloid Z 23 (1918) 15.