Line tension, i.e., the force on a three-phase contact line, has been a subject of extensive research due to its impact on technological applications including nanolithography and nanofluidics. However, there is no consensus on the sign and magnitude of the line tension, mainly because it only affects the shape of small droplets, below the length scale dictated by the ratio of line tension to surface tension σ/τ. This ratio is related to the size of constitutive molecules in the system, which translates to a nanometer for conventional fluids. Here, we show that this ratio is orders of magnitude larger in lyotropic liquid crystal systems comprising micrometer-long colloidal particles. Such systems are known to form spindle-shaped elongated liquid crystal droplets in coexistence with the isotropic phase, with the droplets flattening when in contact with flat solid surfaces. We propose a method to characterize the line tension by fitting measured droplet shape to a macroscopic theoretical model that incorporates interfacial forces and elastic deformation of the nematic phase. By applying this method to hundreds of droplets of carbon nanotubes dissolved in chlorosulfonic acid, we find that σ/τ ∼ −0.84 ± 0.06 μm. This ratio is 2 orders of magnitude larger than what has been reported for conventional fluids, in agreement with theoretical scaling arguments.

Single-walled carbon nanotubes (SWNT) polarize readily in the presence of electromagnetic (EM) fields, enabling a variety of electrochemical reactions. Here, we study the reaction of transition metal ion salts in the presence of surfactant-stabilized SWNT individually suspended in water when activated by alternating EM fields in the radio frequency (RF), microwave (MW), and optical regimes. Atomic force microscopy (AFM) images show formation of novel SWNT nanoparticle−nanotube structures (nanoPaNTs). The resulting nanoPaNTs include SWNT with metallic nanoparticles at one or both tips (“dumbbells”), SWNT toroids, and straight SWNT “threaded” through multiple SWNT rings to form shish-kebab structures. Mixtures of surfactants and polymer apparently modify the local environment of polarized SWNT in a manner that reduces the energy needed for ring formation. We also infer that electrodeposition reactions proceed on a significantly faster time scale than ring formation. These processes can potentially be used for self-assembly of complex 3-D structures.

In this study, we apply a simple but effective oxidative purification method to purify carbon nanotube (CNT) fibers synthesized via a floating catalyst technique. After the purification treatment, the resulting CNT fibers exhibited significant improvements in mechanical and electrical properties with an increase in strength, Young’s modulus, and electrical conductivity by approximately 81, 230, and 100%, respectively. With the successful dissolution of the CNT fibers in superacid, an extensional viscosity method could be applied to measure the aspect ratio of the CNTs constituting the fibers, whereas high-purity CNT thin films could be produced with a low resistance of 720 Ω/sq at a transmittance of 85%. This work suggests that the oxidative purification approach and dissolution process are promising methods to improve the purity and performance of CNT macroscopic structures.Keywords: carbon nanotube fibers; electrical conductivity; extensional viscosity; mechanical strength; superacid; tactoids;

We study how intrinsic parameters of carbon nanotube (CNT) samples affect the properties of macroscopic CNT fibers with optimized structure. We measure CNT diameter, number of walls, aspect ratio, graphitic character, and purity (residual catalyst and non-CNT carbon) in samples from 19 suppliers; we process the highest quality CNT samples into aligned, densely packed fibers, by using an established wet-spinning solution process. We find that fiber properties are mainly controlled by CNT aspect ratio and that sample purity is important for effective spinning. Properties appear largely unaffected by CNT diameter, number of walls, and graphitic character (determined by Raman G/D ratio) as long as the fibers comprise thin few-walled CNTs with high G/D ratio (above ∼20). We show that both strength and conductivity can be improved simultaneously by assembling high aspect ratio CNTs, producing continuous CNT fibers with an average tensile strength of 2.4 GPa and a room temperature electrical conductivity of 8.5 MS/m, ∼2 times higher than the highest reported literature value (∼15% of copper’s value), obtained without postspinning doping. This understanding of the relationship of intrinsic CNT parameters to macroscopic fiber properties is key to guiding CNT synthesis and continued improvement of fiber properties, paving the way for CNT fiber introduction in large-scale aerospace, consumer electronics, and textile applications.Keywords: aspect ratio; carbon nanotubes; electrical conductivity; fiber spinning; fibers;

Boron nitride nanotubes (BNNTs) are of interest for their unique combination of high tensile strength, high electrical resistivity, high neutron cross section, and low reactivity. The fastest route to employing these properties in composites and macroscopic articles is through solution processing. However, dispersing BNNTs without functionalization or use of a surfactant is challenging. We show here by cryogenic transmission electron microscopy that BNNTs spontaneously dissolve in chlorosulfonic acid as disentangled individual molecules. Electron energy loss spectroscopy of BNNTs dried from the solution confirms preservation of the sp2 hybridization for boron and nitrogen, eliminating the possibility of BNNT functionalization or damage. The length and diameter of the BNNTs was statistically calculated to be ∼4.5 μm and ∼4 nm, respectively. Interestingly, bent or otherwise damaged BNNTs are filled by chlorosulfonic acid. Additionally, nanometer-sized synthesis byproducts, including boron nitride clusters, isolated single and multilayer hexagonal boron nitride, and boron particles, were identified. Dissolution in superacid provides a route for solution processing BNNTs without altering their chemical structure.

Coaxial cables for data transmission are ubiquitous in telecommunications, aerospace, automotive, and robotics industries. Yet, the metals used to make commercial cables are unsuitably heavy and stiff. These undesirable traits are particularly problematic in aerospace applications, where weight is at a premium and flexibility is necessary to conform with the distributed layout of electronic components in satellites and aircraft. The cable outer conductor (OC) is usually the heaviest component of modern data cables; therefore, exchanging the conventional metallic OC for lower weight materials with comparable transmission characteristics is highly desirable. Carbon nanotubes (CNTs) have recently been proposed to replace the metal components in coaxial cables; however, signal attenuation was too high in prototypes produced so far. Here, we fabricate the OC of coaxial data cables by directly coating a solution of CNTs in chlorosulfonic acid (CSA) onto the cable inner dielectric. This coating has an electrical conductivity that is approximately 2 orders of magnitude greater than the best CNT OC reported in the literature to date. This high conductivity makes CNT coaxial cables an attractive alternative to commercial cables with a metal (tin-coated copper) OC, providing comparable cable attenuation and mechanical durability with a 97% lower component mass.Keywords: attenuation; carbon nanotubes; coaxial cables; dip-coating; rheology

We demonstrate that the length of carbon nanotubes (CNTs) can be determined simply and accurately from extensional viscosity measurements of semidilute CNT solutions. The method is based on measuring the extensional viscosity of CNT solutions in chlorosulfonic acid with a customized capillary thinning rheometer and determining CNT aspect ratio from the theoretical relation between extensional viscosity and aspect ratio in semidilute solutions of rigid rods. We measure CNT diameter d by transmission electron microscopy (TEM) and arrive at CNT length L. By studying samples grown by different methods, we show that the method works well for CNT lengths ranging from 0.4 to at least 20 μm, a wider range than for previous techniques. Moreover, we measure the isotropic-to-nematic transition concentration (i.e., isotropic cloud point) φiso of CNT solutions and show that this transition follows Onsager-like scaling φiso ∼ d/L. We characterize the length distributions of CNT samples by combining the measurements of extensional viscosity and transition concentration and show that the resulting length distributions closely match distributions obtained by cryo-TEM measurements. Interestingly, CNTs appear to have relatively low polydispersity compared to polymers and high polydispersity compared to colloidal particles.

The development of microelectrodes capable of safely stimulating and recording neural activity is a critical step in the design of many prosthetic devices, brain–machine interfaces, and therapies for neurologic or nervous-system-mediated disorders. Metal electrodes are inadequate prospects for the miniaturization needed to attain neuronal-scale stimulation and recording because of their poor electrochemical properties, high stiffness, and propensity to fail due to bending fatigue. Here we demonstrate neural recording and stimulation using carbon nanotube (CNT) fiber electrodes. In vitro characterization shows that the tissue contact impedance of CNT fibers is remarkably lower than that of state-of-the-art metal electrodes, making them suitable for recording single-neuron activity without additional surface treatments. In vivo chronic studies in parkinsonian rodents show that CNT fiber microelectrodes stimulate neurons as effectively as metal electrodes with 10 times larger surface area, while eliciting a significantly reduced inflammatory response. The same CNT fiber microelectrodes can record neural activity for weeks, paving the way for the development of novel multifunctional and dynamic neural interfaces with long-term stability.Keywords: brain−machine interfaces; carbon nanotube fibers; deep brain stimulation; long-term recordings; multifunctional microelectrodes; neural interfaces; single-neuron isolation; soft neural microelectrodes; ultrasmall neural probes;

The influence of carbon nanotube (CNT) length on their macroscopic properties requires an accurate methodology for CNT length measurement. So far, existing techniques are limited to short (less than a few micrometers) CNTs and sample preparation methods that bias the measured values. Here, we show that the average length of carbon nanotubes (CNTs) can be measured by cryogenic transmission electron microscopy (cryo-TEM) of CNTs in chlorosulfonic acid. The method consists of dissolving at low concentration CNTs in chlorosulfonic acid (a true solvent), imaging the individual CNTs by cryo-TEM, and processing and analyzing the images to determine CNT length. By measuring the total CNT contour length and number of CNT ends in each image, and by applying statistical analysis, we extend the method to cases where each CNT is long enough to span many cryo-TEM images, making the direct length measurement of an entire CNT impractical. Hence, this new technique can be used effectively to estimate samples in a wide range of CNT lengths, although we find that cryo-TEM imaging may bias the measurement towards longer CNTs, which are easier to detect. Our statistical method is also applied to AFM images of CNTs to show that, by using only a few AFM images, it yields estimates that are consistent with literature techniques, based on individually measuring a higher number of CNTs.Keywords: bootstrap method; carbon nanotubes; chlorosulfonic acid; cryo-TEM; length measurement; statistical re-sampling;

We report the creation of carbon nanotube films from superacids by a scalable process, where film morphology is controlled by initial fluid phases. These films were formed by dip-coating biphasic (isotropic + liquid crystalline) carbon nanotube (CNT) chlorosulfonic acid solutions. Chlorosulfonic acid has low volatility and is therefore removed by solvent extraction instead of conventional drying processes. At intermediate concentrations, the solutions contain liquid crystalline domains which stretch and align streamwise during dip-coating. These elongated domains further act as “nucleating sites” for large, aligned whiskerlike crystallites during subsequent solvent extraction. The final films contain highly aligned CNT crystallites embedded in a mesh of randomly oriented CNTs.

Graphite intercalation compounds (GIC) possess a broad range of unique properties that are not specific to the parent materials. While the stage transition, changing the number of graphene layers sandwiched between the two layers of intercalant, is fundamentally important and has been theoretically addressed, experimental studies revealed only macroscopic parameters. On the microscale, the phenomenon remains elusive up to the present day. Here we monitor directly in real time the stage transitions using a combination of optical microscopy and Raman spectroscopy. These direct observations yield several mechanistic conclusions. While we obtained strong experimental evidence in support of the Daumas–Herold theory, we find that the conventional interpretation of stage transitions as sliding of the existing intercalant domains does not sufficiently capture the actual phenomena. The entire GIC structure transforms considerably during the stage transition. Among other observations, massive wavefront-like perturbations occur on the graphite surface, which we term the tidal wave effect.Keywords: D band origin; graphene; graphite intercalation compounds; Raman spectroscopy; stage transition mechanism

Graphene oxide nanoribbons (GONRs) and chemically reduced graphene nanoribbons (crGNRs) were dispersed at high concentrations in chlorosulfonic acid to form anisotropic liquid crystal phases. The liquid crystal solutions were spun directly into hundreds of meters of continuous macroscopic fibers. The relationship of fiber morphology to coagulation bath conditions was studied. The effects of colloid concentration, annealing temperature, spinning air gap, and pretension during annealing on the fibers’ performance were also investigated. Heat treatment of the as-spun GONR fibers at 1500 °C produced thermally reduced graphene nanoribbon (trGNR) fibers with a tensile strength of 378 MPa, Young’s modulus of 36.2 GPa, and electrical conductivity of 285 S/cm, which is considerably higher than that in other reported graphene-derived fibers. This better trGNR fiber performance was due to the air gap spinning and annealing with pretension that produced higher molecular alignment within the fibers, as determined by X-ray diffraction and scanning electron microscopy. The specific modulus of trGNR fibers is higher than that of the commercial general purpose carbon fibers and commonly used metals such as Al, Cu, and steel. The properties of trGNR fibers can be further improved by optimizing the spinning conditions with higher draw ratio, annealing conditions with higher pretensions, and using longer flake GONRs. This technique is a new high-carbon-yield approach to make the next generation carbon fibers based on solution-based liquid crystal phase spinning.Keywords: carbon fiber; coagulation; fiber spinning; graphene nanoribbon

We present a modification of the vacuum filtration technique for fabricating transparent conductive SWNT thin films with local nematic-like orientational ordering. Dilute SWNT surfactant dispersions are filtered through a vacuum filtration setup in a slow and controlled fashion. The slow filtration creates a region of high SWNT concentration close to the filter membrane. While slowly moving through this region, SWNTs interact and align with each other, resulting in the formation of thin films with local nematic ordering. Scanning electron microscopy and image analysis revealed a local scalar order parameter (S2D) of 0.7–0.8 for slow filtration, three times higher than those produced from “fast filtration” (S2D ≈ 0.24). Orientational ordering is demonstrated with different stabilizing surfactants, as well as with dispersions enriched in metallic SWNTs, produced by density-gradient ultracentrifugation. Simple estimates of relative convective versus diffusive transport highlight the main differences between slow versus fast filtration and the resulting SWNT concentration profiles. Comparisons with previous studies on three stages of liquid-crystal phase transition provide insight into the spontaneous ordering process, indicating the lack of a “healing stage”, which results in a microstructure consisting of staggered domains in our SWNT films.

We report a visible-range nonlinear photoluminescence (PL) from graphene oxide (GO) flakes excited by near-infrared femtosecond laser light. PL intensity has nonlinear dependence on the laser power, implying a multiphoton excitation process, and also strongly depends on a linear polarization orientation of excitation light, being at maximum when it is parallel to flakes. We show that PL can be used for a fully three-dimensional label-free imaging of isotropic, nematic, and lamellar liquid crystalline dispersions of GO flakes in water. This nonlinear PL is of interest for applications in direct label-free imaging of composite materials and study of orientational ordering in mesomorphic phases formed by these flakes, as well as in biomedical and sensing applications utilizing GO.Keywords: graphene oxide; liquid crystals; multiphoton excitation; nonlinear imaging; photoluminescence; self-assembly

Transparent conductive carbon nanotube (CNT) films were fabricated by dip-coating solutions of pristine CNTs dissolved in chlorosulfonic acid (CSA) and then removing the CSA. The film performance and morphology (including alignment) were controlled by the CNT length, solution concentration, coating speed, and level of doping. Using long CNTs (∼10 μm), uniform films were produced with excellent optoelectrical performance (∼100 Ω/sq sheet resistance at ∼90% transmittance in the visible), in the range of applied interest for touch screens and flexible electronics. This technique has potential for commercialization because it preserves the length and quality of the CNTs (leading to enhanced film performance) and operates at high CNT concentration and coating speed without using surfactants (decreasing production costs).Keywords: carbon nanotube; dip-coating; flexible electronics; liquid crystals; transparent conductive films

Dispersion of carbon nanotubes (CNTs) into liquids typically requires ultrasonication to exfoliate individuals CNTs from bundles. Experiments show that CNT length drops with sonication time (or energy) as a power law t-m. Yet the breakage mechanism is not well understood, and the experimentally reported power law exponent m ranges from approximately 0.2 to 0.5. Here we simulate the motion of CNTs around cavitating bubbles by coupling Brownian dynamics with the Rayleigh–Plesset equation. We observe that, during bubble growth, CNTs align tangentially to the bubble surface. Surprisingly, we find two dynamical regimes during the collapse: shorter CNTs align radially, longer ones buckle. We compute the phase diagram for CNT collapse dynamics as a function of CNT length, stiffness, and initial distance from the bubble nuclei and determine the transition from aligning to buckling. We conclude that, depending on their length, CNTs can break due to either buckling or stretching. These two mechanisms yield different power laws for the length decay (0.25 and 0.5, respectively), reconciling the apparent discrepancy in the experimental data.

Attempts at depositing uniform films of nanoparticles by drop-drying have been frustrated by the “coffee-stain” effect due to convective macroscopic flow into the contact line. Here, we show that uniform deposition of nanoparticles in aqueous suspensions can be attained easily by drying the droplet in an ethanol vapor atmosphere. This technique allows the particle-laden water droplets to spread on a variety of surfaces such as glass, silicon, mica, PDMS, and even Teflon. Visualization of droplet shape and internal flow shows initial droplet spreading and strong recirculating flow during spreading and shrinkage. The initial spreading is due to a diminishing contact angle from the absorption of ethanol from the vapor at the contact line. During the drying phase, the vapor is saturated in ethanol, leading to preferential evaporation of water at the contact line. This generates a surface tension gradient that drives a strong recirculating flow and homogenizes the nanoparticle concentration. We show that this method can be used for depositing catalyst nanoparticles for the growth of single-walled carbon nanotubes as well as to manufacture plasmonic films of well-spaced, unaggregated gold nanoparticles.

For the first time, cryo-TEM imaging is used to directly show spontaneous filling of carbon nanotubes immersed in a solvent in the native state at ambient conditions. Multi-walled carbon nanotubes are dissolved in chlorosulfonic acid, and the high contrast between the acid and the carbon shows the difference between filled and unfilled nanotubes.

We report a simple and versatile technique for oriented assembly of gold nanorods on aligned single-walled carbon nanotube (SWNT) macrostructures, such as thin nanotube films and nanotube fibers. The deposition and assembly is accomplished via drop drying of dilute gold nanorod suspensions on SWNT macrostructures under ambient conditions. Guided by anisotropic interactions, gold nanorods, and polygonal platelets spontaneously align with SWNTs, resulting in macroscopic arrays of locally ordered nanorods supported on aligned SWNT substrates. SEM reveals that the scalar order parameter of rods relative to the local average SWNT alignment is 0.7 for rods on SWNT films and 0.9 for rods on SWNT fibers. This self-alignment is enabled by anisotropic gold nanoparticle–SWNT interactions and is observed for a wide range of nanoparticles, including nanorods with aspect ratios ranging from 2–35, thin gold triangular and other polygonal platelets. The plasmonic properties of aligned gold nanorods together with superior electronic, chemical and mechanical properties of SWNTs make these hybrid nanocomposites valuable for the design of self-assembled multifunctional optoelectronic materials and optical metamaterials.Keywords: aligned arrays; fibers; films; gold nanorods; SWNT; template;

We report that chlorosulfonic acid is a true solvent for a wide range of carbon nanotubes (CNTs), including single-walled (SWNTs), double-walled (DWNTs), multiwalled carbon nanotubes (MWNTs), and CNTs hundreds of micrometers long. The CNTs dissolve as individuals at low concentrations, as determined by cryo-TEM (cryogenic transmission electron microscopy), and form liquid-crystalline phases at high concentrations. The mechanism of dissolution is electrostatic stabilization through reversible protonation of the CNT side walls, as previously established for SWNTs. CNTs with highly defective side walls do not protonate sufficiently and, hence, do not dissolve. The dissolution and liquid-crystallinity of ultralong CNTs are critical advances in the liquid-phase processing of macroscopic CNT-based materials, such as fibers and films.Keywords: carbon nanotubes; CNT; cryo-TEM; DWNT; liquid crystals; long nanotubes; MWNT; nanotube carpets; solubility; SWNT; VACNT

We study the solubility and dispersibility of as-produced and purified HiPco single-walled carbon nanotubes (SWNTs). Variation in specific operating conditions of the HiPco process are found to lead to significant differences in the respective SWNT solubilities in oleum and surfactant suspensions. The diameter distributions of SWNTs dispersed in surfactant solutions are batch-dependent, as evidenced by luminescence and Raman spectroscopies, but are identical for metallic and semiconducting SWNTs within a batch. We thus find that small diameter SWNTs disperse at higher concentration in aqueous surfactants and dissolve at higher concentration in oleum than do large-diameter SWNTs. These results highlight the importance of controlling SWNT synthesis methods in order to optimize processes dependent on solubility, including macroscopic processing such as fiber spinning, material reinforcement, and films production, as well as for fundamental research in type selective chemistry, optoelectronics, and nanophotonics.Keywords: diameter; dispersions; single-walled carbon nanotubes; solubility; solutions

By relating nanotechnology to soft condensed matter, understanding the mechanics and dynamics of single-walled carbon nanotubes (SWCNTs) in fluids is crucial for both fundamental and applied science. Here, we study the Brownian bending dynamics of individual chirality-assigned SWCNTs in water by fluorescence microscopy. The bending stiffness scales as the cube of the nanotube diameter and the shape relaxation times agree with the semiflexible chain model. This suggests that SWCNTs may be the archetypal semiflexible filaments, highly suited to act as nanoprobes in complex fluids or biological systems.

We report an industrially scalable, fast, and simple process for the large scale fabrication of optically transparent and electrically conducting thin films of single-walled carbon nanotubes (SWNT). Purified, pristine HiPco SWNTs were dispersed in water at high concentrations with the help of surfactants, rod-coated into uniform thin films, and doped by various acids. We show how to combine different surfactants to make uniform dispersions with high concentration of SWNTs and optimal rheological behavior for coating and drying, including preventing dewetting and film rupture that has plagued earlier attempts. Doping by fuming sulfuric acid yielded the films with best performance (sheet resistance of 100 and 300 Ω/sq for respective transparency of 70% and 90%). We use a figure of merit (FOM) plot for an immediate evaluation and comparison of the performance and microstructure of CNT films produced by different methods. Further scientific engineering will pave the way to the deployment of CNT films in commercial applications.Keywords: coatings; conductive; rheology.; single walled carbon nanotubes; SWNT films; transparent; wire-wound rod coating

By relating nanotechnology to soft condensed matter, understanding the mechanics and dynamics of single-walled carbon nanotubes (SWCNTs) in fluids is crucial for both fundamental and applied science. Here, we study the Brownian bending dynamics of individual chirality-assigned SWCNTs in water by fluorescence microscopy. The bending stiffness scales as the cube of the nanotube diameter and the shape relaxation times agree with the semiflexible chain model. This suggests that SWCNTs may be the archetypal semiflexible filaments, highly suited to act as nanoprobes in complex fluids or biological systems.

We theoretically investigate the separation of individualized metallic and semiconducting single-wall carbon nanotubes (SWNTs) in a dielectrophoretic (DEP) flow device. The SWNT motion is simulated by a Brownian dynamics (BD) algorithm, which includes the translational and rotational effects of hydrodynamic, Brownian, dielectrophoretic, and electrophoretic forces. The device geometry is chosen to be a coaxial cylinder because it yields effective flow throughput, the DEP and flow fields are orthogonal to each other, and all the fields can be described analytically everywhere. We construct a flow-DEP phase map showing different regimes, depending on the relative magnitudes of the forces in play. The BD code is combined with an optimization algorithm that searches for the conditions that maximize the separation performance. The optimization results show that a 99% sorting performance can be achieved with typical SWNT parameters by operating in a region of the phase map where the metallic SWNTs completely orient with the field, whereas the semiconducting SWNTs partially flow-align.

Macroscopic fibers containing only Carbon NanoTubes (CNTs) will yield great advances in high-tech applications if they can attain a significant portion of the extraordinary mechanical and electrical properties of individual CNTs. Doing so will require that the CNTs in the fiber are sufficiently long, highly aligned and packed in an arrangement that is nearly free of defects. Here we review and compare the various methods for processing CNTs into neat fibers. These techniques may be divided into ‘liquid’ methods, where CNTs are dispersed into a liquid and solution-spun into fibers, and ‘solid’ methods, where CNTs are directly spun into ropes or yarns. Currently, these processes yield fibers whose properties are not sufficiently close to optimal; however, the last five years have seen rapid progress, and the production of commercially useful CNT fibers may be achieved in the next few years.

•Effect of viscoelasticity on model gravure printing is studied by FEM.•Elasticity exacerbates gravity effects during late time drainage.•Elastic effects hinder cavity emptying at early time extension.•Adverse elastic effects are activated beyond a critical Weissenberg number.•Free surface normal elastic stress evolution illustrates the adverse effects.High speed roll-to-roll coating and printing are important in both classical and novel processes, e.g., in the emergent flexible electronics industry. Gravure in particular is attractive for its application to printing as well as its high quality and throughput in coating continuous thin films. Despite its long standing use, gravure is still poorly understood especially in the liquid transfer regime and when the coating liquid has a complex rheology. As with any coating flow, the dynamics are governed by many complex phenomena including free surfaces, (de)-wetting, and non-Newtonian rheology; these present observational, modeling, and computational challenges. Accordingly, modeling and computational work are usually limited by the level of detail in describing the physical phenomena. In this work, we compute the influence of viscoelasticity on the transfer of polymer solutions in an idealized gravure process: the liquid is held between a cavity and a flat disk that moves away at a constant velocity, with pinned contact lines on both the disk and cavity. Our computations show that when the disk separation velocity is sufficiently high as measured by the Weissenberg number—i.e., the consequent strain rate in the liquid bridge is high compared to the rate of polymer relaxation—large elastic stresses are activated at early times and induce an adverse drainage into the cavity. Gravity or other forces eventually overwhelm this elastic drainage at later times when stretching dynamics decay in importance. When gravitational and elastic drainage act in concert, they compete with the viscous forces that promote liquid transfer; this competition manifests as an optimum disk velocity for maximal liquid transfer. With the appropriate scaling, we find that the optimal disk velocities over a range of parameters reduce to an optimal Weissenberg number of about 0.1, which agrees well with experiments in the literature.

Though computational techniques for two-dimensional viscoelastic free surface flows are well developed, three-dimensional flows continue to present significant computational challenges. Fully coupled free surface flow models lead to nonlinear systems whose steady states can be found via Newton’s method. Each Newton iteration requires the solution of a large, sparse linear system, for which memory and computational demands suggest the application of an iterative method, rather than the sparse direct methods widely used for two dimensional simulations. The Jacobian matrix of this system is often ill-conditioned, resulting in unacceptably slow convergence of the linear solver; hence preconditioning is essential. We propose a variant sparse approximate inverse preconditioner for the Jacobian matrix that allows for the solution of problems involving more than a million degrees of freedom in challenging parameter regimes. Construction of this preconditioner requires the solution of small least squares problems that can be simply parallelized on a distributed memory machine. The performance and scalability of this preconditioner with the GMRES solver are investigated for two- and three-dimensional free surface flows on both structured and unstructured meshes in the presence and absence of viscoelasticity. The results suggest that this preconditioner is an extremely promising candidate for solving large-scale steady viscoelastic flows with free surfaces.

Fundamental understanding of the formation and pinch-off of viscoelastic filaments is important in applications involving production of drops (e.g., ink-jet printing, micro-arraying, and atomization). In addition to delaying pinch-off, in some cases, viscoelasticity is known to cause the so-called beads-on-string structure, i.e., a number of small droplets interconnected by thin filaments. In a recent publication [H. Matallah, M.J. Banaai, K.S. Sujatha, M.F. Webster, J. Non-Newtonian Fluid Mech. 134 (2006) 77–104], it was shown that the simulation of an elongating filament modeled by the Phan-Thien/Tanner (PTT) equation with the Gordon–Schowalter (GS) convected derivative, which allows non-affine motion of polymer molecules in the continuum, results in the formation of the beads-on-string structure. On the other hand, such bead formation is not reported in calculations with other viscoelastic models that are also strain-hardening like the PTT model but do not have the GS convected derivative (see, e.g., [M. Yao, S.H. Spiegelberg, G.H. McKinley, J. Non-Newtonian Fluid Mech. 89 (2000) 1–43]). This starkly different behavior of the PTT equation with the GS convected derivative is investigated here. During the elongation of the filament, regions of shear form inside the filament due to its initially curved surface. Because of the presence of the GS convected derivative in the PTT equation – which is known to cause unphysical oscillations in stress in simple step shear flow – the shear stress within the PTT filament exhibits temporal oscillations. The onset of these oscillations coincides with the symmetrical migration of the location of the single maximum in the axial component of the rate-of-strain tensor from the center of the filament to two other locations, one in each half of the filament. This is followed by a similar movement of the location of the maximum in the axial elastic stress inside the filament. These two events eventually lead to the formation of a bead-like structure. The occurrence of the bead is also shown to depend on the extent of the polymer contribution to the total viscosity compared to that of the solvent.

The log-conformation formulation has alleviated the long-standing high Weissenberg number problem associated with the viscoelastic fluid flows [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285]. This formulation ensures that solutions of viscoelastic flow problems are physically admissible, and it is able to capture sharp elastic stress layers. However, the implementations presented in literature thus far require changing the evolution equation for the conformation tensor into an equation for its logarithm, and are based on loosely coupled (partitioned) solution procedures [M.A. Hulsen, et al., Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech. 127 (2005) 27–39]. A simple alternate form of the log-conformation formulation is presented in this article, and an implementation is demonstrated in the DEVSS-TG/SUPG finite element method. Besides its straightforward implementation, the new log-conformation formulation can be used to solve all the governing equations (continuity, conservation of momentum and constitutive equation) in a strongly coupled way by Newton’s method. The method can be applied to any conformation tensor model. The flows of Oldroyd-B and Larson-type fluids are tested in the benchmark problem of a flow past a cylinder in a channel. The accuracy of the method is assessed by comparing solutions with published results. The benefits of this new implementation and the pending issues are discussed.

Spray coating is a scalable and high-throughput process for fabrication of transparent and conducting coatings (TCCs) composed of single-walled carbon nanotubes (SWNTs). Presently the fundamentals of this process are not well understood. We show that suppression of coalescence of spray droplets by sufficiently rapid heat- and mass-transfer yields homogeneous SWNT films by preventing the formation of ‘coffee stains’ of larger length scale. Such heat and mass transfer is driven by differential evaporation between the top and edges of the drops, whereas thermal and compositional effects on surface tension and buoyancy are weak. Ultrasonic spraying ensures that the droplets are deposited without significant splashing, and delayed splashing at higher Weber number is evidenced. We find that the performance of spray-coated TCCs made from HiPCO SWNTs is limited by bundle diameter rather than length of the constituent SWNTs and bundes. Vapor acid doping with concentrated sulfuric acid roughly doubles the conductivity of the TCCs.

We study the effect of viscoelasticity on the fluid dynamics of slot coating flow of dilute polymer solutions. The fluid is modeled by the Oldroyd-B and FENE-P equations in a conformation tensor formulation. The fully coupled equations of the flow are solved by the DEVSS-TG finite element method together with the elliptic domain mapping method to capture the unknown free surface. We observe that dilute solutions, where the presence of polymer molecules affects the flow field, behave qualitatively differently from ultra-dilute solutions, where the presence of polymer molecules does not alter the flow field. In dilute solutions: (1) the stagnation point on the free surface moves towards the static contact line and the recirculation zone shrinks with increasing Weissenberg number; (2) once the stagnation point reaches the static contact line, the hoop stress on the free surface changes sign from negative to positive, which destabilizes the flow; (3) the region of most severe polymer stretch and distortion also moves to the static contact line. The field variables, such as velocity, velocity gradient and conformation tensor, become singular due to a geometric singularity at the static contact line which leads to the failure of the computational method. In contrast, in ultra-dilute solutions, the computations fail when the mesh can not capture steep stress boundary layers at the free surface. The low-flow limit of inertialess slot coating flow is examined in terms of the Elastocapillary number; the coating window for uniform coating narrows as the liquid grows more elastic.

Many applications of viscoelastic free surface flows requiring formation of drops from small nozzles, e.g., ink-jet printing, micro-arraying, and atomization, involve predominantly extensional deformations of liquid filaments. The capillary number, which represents the ratio of viscous to surface tension forces, is small in such processes when drops of water-like liquids are formed. The dynamics of extensional deformations of viscoelastic liquids that are weakly strain hardening, i.e., liquids for which the growth in the extensional viscosity is small and bounded, are here modeled by the Giesekus, FENE-P, and FENE-CR constitutive relations and studied at low capillary numbers using full 2D numerical computations. A new computational algorithm using the general conformation tensor based constitutive equation [M. Pasquali, L.E. Scriven, Theoretical modeling of microstructured liquids: a simple thermodynamic approach, J. Non-Newtonian Fluid Mech. 120 (2004) 101–135] to compute the time dependent viscoelastic free surface flows is presented. DEVSS-TG/SUPG mixed finite element method [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409] is used for the spatial discretization and a fully implicit second-order predictor–corrector scheme is used for the time integration. Inertia, capillarity, and viscoelasticity are incorporated in the computations and the free surface shapes are computed along with all the other field variables in a fully coupled way. Among the three models, Giesekus filaments show the most drastic thinning in the low capillary number regime. The dependence of the transient Trouton ratio on the capillary number in the Giesekus model is demonstrated. The elastic unloading near the end plates is investigated using both kinematic [M. Yao, G.H. McKinley, B. Debbaut, Extensional deformation, stress relaxation and necking failure of viscoelastic filaments, J. Non-Newtonian Fluid Mech. 79 (1998) 469–501] and energy analyses. The magnitude of elastic unloading, which increases with growing elasticity, is shown to be the largest for Giesekus filaments, thereby suggesting that necking and elastic unloading are related.

The domain deformation method has been applied successfully to steady state free surface flows where the volume of the flow domain is unknown [V.F. de Almeida, Gas–liquid counterflow through constricted passages, Ph.D. thesis, University of Minnesota, Minneapolis, MN 1995; P.A. Sackinger, P.R. Schunk, R.R. Rao, A Newton–Raphson pseudo-solid domain mapping technique for free and moving boundary problems: a finite element implementation, J. Comput. Phys. 125 (1996) 83–103; L.C. Musson, Two-layer slot coating, Ph.D. thesis, University of Minnesota, Minneapolis, MN 2001]; however, this method does not handle effectively problems where the volume of the flow domain is known a priori. This work extends the original domain deformation method to a new isochoric domain deformation method to account for the volume conservation. Like in the original domain deformation method, the unknown shape of the flow domain is mapped onto a reference domain by using the equations of an elastic pseudo-solid; the difference with the original method is that this pseudo-solid is considered incompressible. Because of the incompressibility, the pseudo-pressure of the mapping appears as a Lagrange multiplier in the equations, and it is determined only up to an arbitrary uniform datum. By analyzing the coupled fluid flow-mapping problem, we show that, in the finite-element setting, such pressure datum can be specified by replacing one continuity equation in the fluid domain.

For the first time, cryo-TEM imaging is used to directly show spontaneous filling of carbon nanotubes immersed in a solvent in the native state at ambient conditions. Multi-walled carbon nanotubes are dissolved in chlorosulfonic acid, and the high contrast between the acid and the carbon shows the difference between filled and unfilled nanotubes.