Interface Curvature Research Articles

Poly(diethylene glycol methylether methacrylate) Brush-Functionalized Anodic Alumina Nanopores: Curvature-Dependent Polymerization Kinetics and Nanopore Filling.

We report on the synthesis and characterization of poly(diethylene glycol methylether methacrylate) (PDEGMA) brushes by surface-initiated atom transfer radical polymerization inside ordered cylindrical nanopores of anodic aluminum oxide with different pore radii between 20 and 185 nm. In particular, the dependence of polymerization kinetics and the degree of pore filling on the interfacial curvature were analyzed. On the basis of field emission scanning electron microscopy data and thermal gravimetric analysis (TGA), it was concluded that the polymerization rate was faster at the pore orifice compared to the pore interior and also as compared to the analogous reaction carried out on flat aluminum oxide substrates. The apparent steady-state polymerization rate near the orifice increased with decreasing pore size. Likewise, the overall apparent polymerization rate estimated from TGA data indicated stronger confinement for pores with increased curvature as well as increased mass transport limitations due to the blockage of the pore orifice. Only for pores with a diameter to length ratio of ∼1, PDEGMA brushes were concluded to grow uniformly with constant thickness. However, because of mass transport limitations in longer pores, incomplete pore filling was observed, which leads presumably to a PDEGMA gradient brush. This study contributes to a better understanding of polymer brush-functionalized nanopores and the impact of confinement, in which the control of polymer brush thickness together with grafting density along the nanopores is key for applications of PDEGMA brushes confined inside nanopores.

Inorganic Nanoparticles Challenging Lamellar and Non-Lamellar Model Membranes

Nonlamellar lipid aqueous phases, such as reverse cubic or hexagonal phases, are ubiquitous in nature and they present a curve lipid aqueous interface on the nanoscale. The role of curvature for biomolecular interactions has been increasingly recognised. it has shown that synthetic planar lipid membranes can be used to mimic the interaction between inorganic nanoparticles (NPs) and membrane. Such studies provide relevant insights on the main factors implied in cellular trafficking and cytotoxic effects, but this type of particles are also used in nanomedicine to enhance imaging and also in therapeutic applications. The impact of NPs on curved membranes, i.e. nonlamellar phases, are much less studied. We are able to prepare lipid mesophase surface films with controlled and tuneable structure, which allows us to study the interaction of nanoparticles with lamellar and nonlamellar lipid films. The structural effects on the lipid films of gold nanoparticles (AuNPs) of different shape and surface functionalization have been studied using Neutron Reflectometry. We used spin coated layers of glycerol monooleate (GMO), forming a cubic phase, and mixtures of GMO/diphosphatidylcholine (DOPC) forming a lamellar phase. Hydrophobic and cationic particles added to the lamellar phase cause an increase in diffuse scattering, probing the presence of the particles in the film. Both the cationic and hydrophobized AuNPs seem to inserted in the cubic phase lipid film. The AuNP rods seems to perturb the lipid film structure and hydrophobic rods decrease the stability of the lipid film to a large extent. Complementary confocal microscopy imaging revealed the morphology changes of the film structure as a consequence of the particle addition. The results will be discussed in terms of particle shape and the curvature of the lipid aqueous interface.

Micellar Fd3m cubosomes from monoolein – long chain unsaturated fatty acid mixtures: Stability on temperature and pH response

HypothesisControl of the nanostructure of self-assembled systems may be achieved through manipulation of surfactant molecular packing and interfacial curvature. In order to phase engineer the inverse micellar cubosomes in some monoolein-fatty acid systems, lipids with wedge shaped molecular geometry were incorporated to promote the formation of this phase, that is of interest as potential sustained released nanocarriers. ExperimentsLiquid crystalline nanoparticle dispersions of monoolein with some cis unsaturated fatty acids were prepared and their partial temperature-composition phase diagrams and structure were established using high throughput Small Angle X-ray Scattering (SAXS) and cryogenic transmission electron microscopy (cryo-TEM). The pH responsiveness of these systems was evaluated in the presence of phosphate buffered saline (PBS). FindingsThe partial temperature-composition phase diagrams of five nanoparticle formulations containing monoolein and unsaturated fatty acids were established and identified the presence of micellar cubosomes in each of these systems. The results indicate that temperature, fatty acid concentration and structure, as well as pH all directly impact the formation and stability of this phase. Low energy inverse micellar cubic to emulsion phase transformations were identified in the monoolein with oleic acid and vaccenic acid systems at physiological temperatures that may be advantageous for staged therapeutic release strategies in nanomedicine.

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method**Project supported by the National Natural Science Foundation of China (Grant Nos. 51728601 and 51771118), the Fund of the State Key Laboratory of Solidification Processing in NPU (Grant No. SKLSP201901), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2242019K1G003).

Pattern selection during crystal growth is studied by using the anisotropic lattice Boltzmann-phase field model. In the model, the phase transition, melt flows, and heat transfer are coupled and mathematically described by using the lattice Boltzmann (LB) scheme. The anisotropic streaming-relaxation operation fitting into the LB framework is implemented to model interface advancing with various preferred orientations. Crystal pattern evolutions are then numerically investigated in the conditions of with and without melt flows. It is found that melt flows can significantly influence heat transfer, crystal growth behavior, and phase distributions. The crystal morphological transition from dendrite, seaweed to cauliflower-like patterns occurs with the increase of undercoolings. The interface normal angles and curvature distributions are proposed to quantitatively characterize crystal patterns. The results demonstrate that the distributions are corresponding to crystal morphological features, and they can be therefore used to describe the evolution of crystal patterns in a quantitative way.

Eutectic solidification in Al-Ni for L-PBF conditions: a phase-field simulation study

Two-phase solidification microstructures of regular binary eutectic alloys are composed of lamellar or rod-like pattern. The corresponding characteristic length scale λ is the spacing between lamellae or rods and results from an interplay between lateral diffusion and capillary, i.e. interfacial curvature. The basic theory had been developed by Jackson and Hunt (JH) in the 1960’s and has been proven successfully for “slow” solidification. It leads to a scaling relation v⋅λ2=const. with v the growth velocity. In this work, we investigated eutectic solidification in Al-Ni for the faster growth rates in L-PBF processing by means of phase-field simulations. The consequences of the fast solidification on the deviation from the JH-scaling and the appearance of new features in the growth pattern are shown. Simulation results are confronted with microstructures seen in L-PBF build samples. Eventually, we discuss the opportunity to derive the local solidification speed from microstructure analysis.

Polymorphic calcium alginate microfibers assembled using a programmable microfluidic field for cell regulation.

Effectively guiding and accurately controlling cell adhesion and growth on the surfaces of specific morphological materials are key issues and hot research topics for optimizing biomaterials. Herein, novel polymorphic alginate microfibers formed through microfluidic spinning technology in a single microchip are presented. Through programming the flow and reaction kinetics in microchannels, other than self-modified micromorphic channel geometry, polymorphic microfibers with precisely tuned curvature-adjustable morphology can be obtained. Finite element (FE) simulations of the flow field (unidirectional fluid-solid coupling) proved the efficacy of the proposed control strategy. Moreover, the specific disordered-ordered cell arrangements showed a linear relationship between bioinspired alginate microfibers with different curvatures and the orientation angle of L929 cells, and diversified growth morphologies, including oblate ellipse, star, tree and strip shapes, occurred on the customizable interface curvature of the calcium alginate microfibers, providing a paradigm for using specific structured natural biomedical materials for cell regulation. This work represents a new design concept for manufacturing polymorphic fibrous biomedical materials through a unique marriage of the fields of green chemistry, hydromechanics, and biomaterials, which should be very useful for guiding the controllable construction of alginate materials for use in structural materials for biomedical and engineering purposes.

Analytical Fresnel laws for curved dielectric interfaces

Fresnel laws and the corresponding Fresnel reflection and transmission coefficients provide the quantitative information of the amount of reflected and transmitted (refracted) light in dependence on its angle of incidence. They are at the core of ray optics at planar interfaces. However, the well-known Fresnel formulae do not hold at curved interfaces and deviations are appreciable when the radius of curvature becomes of the order of several wavelengths of the incident light. This is of particular importance for optical microcavities that play a significant role in many modern research fields. Their convexly curved interfaces modify Fresnel’s law in a characteristic manner. Most notably, the onset of total internal reflection is shifted to angles larger than critical incidence (Martina and Henning 2002 Phys. Rev. E 65 045603). Here, we derive analytical Fresnel formulae for the opposite type of interface curvature, namely concavely curved refractive index boundaries, that have not been available so far. The accessibility of curvature-dependent Fresnel coefficients facilitates the analytical, ray-optics based description of light in complex mesoscopic optical structures that will be important in future nano- and microphotonic applications.

A new surface tension formulation for particle methods

In this paper, a new formulation based on the continuum surface force model (CSF) is developed for particle methods. In the new formulation, two measures are taken to amend the two drawbacks faced by previous formulations of the CSF model. One measure is that the interface curvature is calculated using the surface divergence of the unit normal instead of the divergence as done in previous formulations. This measure completely removes errors artificially stemming from interior particles that are caused by numerical discretization. Another measure taken is that the size of the particle interaction domain is determined based on the physical characteristic length, rather than taken as a fixed multiple of the particle spacing, as in previous formulations. This treatment is based on the knowledge of the nature of the fractional dimensionality of the surface/curve, for which the measured values of macroscopic characteristics are dependent on the measurement scale. Through the curvature calculation of a unit circle, the relation between the size of the particle interaction domain and the critical size of droplet/bubble breakup is established. The former, which is taken as approximately 0.38 times the latter, is accurate enough to obtain a reasonable interface curvature, even with severe irregularity. The new formulation is tested and verified using three numerical cases, including the oscillation and decay of a square drop under surface tension, the coalescence of two drops after a head-on collision, and the Rayleigh-Taylor instability. It is shown that the new formulation is robust and accurate in calculating the surface tension and is able to adapt to different situations.

The Sensitivity of Estimates of Multiphase Fluid and Solid Properties of Porous Rocks to Image Processing

X-ray microcomputed tomography (X-ray μ-CT) is a rapidly advancing technology that has been successfully employed to study flow phenomena in porous media. It offers an alternative approach to core scale experiments for the estimation of traditional petrophysical properties such as porosity and single-phase flow permeability. It can also be used to investigate properties that control multiphase flow such as rock wettability or mineral topology. In most applications, analyses are performed on segmented images obtained employing a specific processing pipeline on the greyscale images. The workflow leading to a segmented image is not straightforward or unique and, for most of the properties of interest, a ground truth is not available. For this reason, it is crucial to understand how image processing choices control properties estimation. In this work, we assess the sensitivity of porosity, permeability, specific surface area, in situ contact angle measurements, fluid–fluid interfacial curvature measurements and mineral composition to processing choices. We compare the results obtained upon the employment of two processing pipelines: non-local means filtering followed by watershed segmentation; segmentation by a manually trained random forest classifier. Single-phase flow permeability, in situ contact angle measurements and mineral-to-pore total surface area are the most sensitive properties, as a result of the sensitivity to processing of the phase boundary identification task. Porosity, interfacial fluid–fluid curvature and specific mineral descriptors are robust to processing. The sensitivity of the property estimates increases with the complexity of its definition and its relationship to boundary shape.

Linking continuum-scale state of wetting to pore-scale contact angles in porous media

HypothesisWetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. We hypothesize that the wetting state of a porous medium can be described in terms of topological arguments that constrain the morphological state of immiscible fluids, which provides a direct link between the continuum-scale metrics of wettability and pore-scale contact angles. ExperimentsWe perform primary drainage and imbibition experiments on Bentheimer sandstone using air and brine. Topological properties, such as Euler characteristic and interfacial curvature are measured utilizing X-ray micro-computed tomography at irreducible air saturation. We also present measurements for the United States Bureau of Mines (USBM) index, capillary pressure and pore-scale contact angles. Additional studies are performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions. FindingsWe demonstrate that contact angle distributions for a porous multiphase system can be predicted within a few percent difference of directly measured pore-scale contact angles using the presented method. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous media.

Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow.

We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analog of Hele-Shaw flow. Here we are concerned with the development of pinch-off singularities characterized by a blowup of the interface curvature and the bubble subsequently breaking up into two; these singularities do not occur in the corresponding two-dimensional Hele-Shaw problem. By applying a numerical scheme based on the level set method, we show that solutions to our problem can undergo pinch-off in various geometries. A similarity analysis suggests that the minimum radius behaves as a power law in time with exponent α=1/3 just before and after pinch-off has occurred, regardless of the initial conditions; our numerical results support this prediction. Further, we apply our numerical scheme to simulate the time-dependent development and translation of axially symmetric Saffman-Taylor fingers and Taylor-Saffman bubbles in a cylindrical tube, highlighting key similarities and differences with the well-studied two-dimensional cases.

Rifting of Extensional Flows on a Sphere.

The front of a fluid that displaces a less viscous fluid in shear-dominated flows is known to be stable. We show that in predominantly extensional flows on a sphere, a similar front of a strain-rate-softening fluid can become unstable and evolve fingerlike patterns comprised of rifts and tongues. The number of rifts and tongues declines with time and is selected by competition between interfacial hoop stress, geometric stretching, momentum dissipation, and spatial curvature. Our results elucidate fracture dynamics in complex fluids under extension and are applicable to a wide range of systems, including planetary-scale ice shelves as in snowball epochs and icy moons.

Polymeric Solvation Shells around Nanotubes: Mesoscopic Simulation of Interfaces in Nanochannels

Interfacial interactions in biphasic polymeric fluids confined in a nanochannel are studied by using dissipative particle dynamics. The effects of an arrested nanotube at the interfaces of short-chain polymer models are elucidated, and its interactions with the polymers are varied systematically. The results confirm the experimental notion that a particle can bear an excess of anisotropic interfacial stresses and consequently stabilize interface curvatures. In the presence of limited capillary effects in nanofluidic channels, the solvation shells in the vicinity of the nanotube and their related interactions become more dominant. The solvation shells are characterized by the density oscillations around the nanotube. While the oscillation intensity depends on the polymer–nanotube interactions, its characteristic length is only a function of the molecular structure of the polymer. The oscillations disappear within a certain number of shells away from the nanotube that is comparable to experimental values for low molecular weight liquids. Detailed analyses of the interface shape based on capillary wave theory reveal the impacts of such solvation forces. This study offers insights into how the polymeric solvation shells around nanoparticles can influence the interface shape, the nanoparticle–nanoparticle interactions, and the nanoparticle–wall interactions. Our findings can lead to promising applications in nanofluidics and in drug delivery using nanoparticles.

Thermodynamic consistency of a pseudopotential lattice Boltzmann fluid with interface curvature.

Thermodynamic consistency of pseudopotential lattice Boltzmann models is a major topic that needs comprehensive evaluations. When interface is flat, pseudopotential models can give density-pressure isotherms in excellent agreement with those from equation of state. When interface is curved, thermodynamic equilibriums are affected by interface curvature, and consistency of pseudopotential models has not been systematically evaluated. In this study, we show that the effect of Laplace pressure on phase equilibrium is quantitatively consistent with Kelvin equation at high reduced temperatures (≥0.7). At low temperatures, inconsistency that can be attributed to the effect of orientation of the interface was noted, and it can be improved by tuning of the pseudopotential. By relating interfacial tension of a simulated fluid to that of a real fluid, the lattice spacing of pseudopotential model is found to be on the order of several molecular diameters, the typical range of intermolecular interactions. Interfacial thickness at different temperatures in pseudopotential model compared well with experiments and molecular dynamics simulations, which confirms that the calculated length scale is reasonable. Evaluation of a free energy lattice Boltzmann model indicate that it is consistent with Kelvin equation at high temperatures. The free energy model, however, is not as accurate as the tested pseudopotential model, and discrepancies may come from the relative inaccuracies in the predictions of vapor densities and the thinner interfaces.

Influence of submerged heating on vertical Bridgman crystal growth of silicon under travelling magnetic field

The effect of a submerged heater on the Bridgman crystal growth process under travelling magnetic field is studied. It is known that the magnetic field generates melt flow from crystal center to crucible wall which can suppress morphological instability development, but it also increases the curvature of the crystallization front. The advantage of the submerged heater method is the ability of better control over the temperature distribution in the vicinity of the solid-liquid interface, as well as the constancy of the growth zone geometry, in particular the height of the melt above the phase boundary, which helps reduce the axial heterogeneity of the resulting crystal. Within the steady state approach we perform numerical simulation of Bridgman growth process under simultaneous action of travelling magnetic field and a submerged heater. It is shown that the submerged heater can intensify the flow in the radial direction generated by travelling magnetic field near the growing crystal while the curvature of the crystallization interface remains almost unaffected. On the other hand, it is also possible to decrease significantly the flow close to the crystallization front.

Crack arrest through branching at curved weak interfaces: An experimental and numerical study

The phenomenon of arrest of an unstably-growing crack due to a curved weak interface is investigated. The weak interface can produce the deviation of the crack path, trapping the crack at the interface, leading to stable crack growth for certain interface geometries. This evidence could be exploited as a technical solution for a new type of crack arrester, with a negligible impact on the global stiffness, strength and weight of the structure. In order to exploit this concept, an experimental campaign based on photo-elasticity and digital image correlation (DIC) is carried out, showing the capability of curved weak interfaces to arrest cracks. The experiment is repeated for several geometrical configurations through the modification of the interface curvature radii. The phenomenon of crack deviation and subsequent arrest at the interface is also investigated by a computational model based on the finite element method. The computational predictions provide the rationale for the interpretation of the experimental observations, and distinguish between the different behaviours of concave and convex interfaces. Consequently, as is shown in the present study, the curved interface concept fosters new routes for the attainment of structures with enhanced fracture resistance capacities, which are of paramount importance for materials and components used in extreme conditions.

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. Scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

Effective Surface Free Energy of Crystalline Phase Nuclei

Molecular-dynamics simulation by the mean lifetime, forward flux sampling, and seeding method has been employed to study the kinetics of the spontaneous crystallization of a supercooled Lennard-Jones liquid. The limiting values of supercooling (supercompression) of a liquid phase have been determined within wide ranges of temperature and pressure, with nucleation rate being varied by 195 orders of magnitude. The dependence of the effective surface free energy of crystalline phase nuclei on the dividing surface curvature has been calculated from the obtained data with the use of the classical nucleation theory. The calculations have been performed for three isotherms and four isobars. The first (Tolman length) and second corrections to the effective surface free energy for the interface curvature have been determined.

Activation of Nrf2 by lead sulfide nanoparticles induces impairment of learning and memory.

Lead sulfide nanoparticles (PbS NPs) are semiconductor materials that have been widely applied to light-emitting diodes (LEDs), biological fluorescent probes, infrared detection, solar receivers, ion-selective electrodes, and ion-sensitive materials. However, the effects of PbS NPs on the central nervous system are still unclear. Thus, this study aimed to determine, using rats, the mechanism of action of PbS NPs, exposure to which results in persistent alterations in nervous system function. The results of the Morris water maze test showed that PbS NPs significantly impaired learning and memory. Compared with that in the control group, the lead content in the hippocampal tissue was significantly elevated after PbS NP exposure. Exposure to PbS NPs led to increased oxidative damage in blood and hippocampal tissues, and significantly inhibited the activities of superoxide dismutase (SOD), glutathione peroxidase (GSH-Px), and catalase (CAT) while increasing the serum malondialdehyde (MDA) content. In addition, reactive oxygen species triggered the activation of Nrf2 and the antioxidant system, including HO-1, r-GCS, and GSH-Px. Moreover, we observed significant apoptosis in the hippocampi of the rats using the TUNEL assay and transmission electron microscopy. The MOD values from the TUNEL assay of the hippocampi were all significantly higher than those of the control group, which increased as the concentration of the PbS NPs increased. There were also changes in the ultrastructure of the hippocampal neurons and synapses in the PbS-treated rats, including a shorter synaptic active zone, smaller curvature of the synaptic interface, and thicker postsynaptic density. Therefore, PbS NP exposure could lead to increased brain lead content, oxidative damage, and apoptosis.

Effect of liquid phase composition on the experimental determination of binary gas diffusivities in an isothermal Stefan diffusion column

The Stefan diffusion column was designed in the 19th Century to determine binary gas diffusivities, DAB’s. Typically, pure liquid A is overlaid by gases A and stagnant B, with a steady gas B sweep at the top to remove the evaporated-diffused A. Experimental diffusivities DAB,exp may be obtained from transient interfacial descent data, but column end effects impacting such determination have been ignored or neglected in the literature. This study addresses experimentally and theoretically for the first time the role played by liquid phase composition on DAB determination using the Stefan column. Specifically, changes in interfacial curvature were sought by adding a nonvolatile liquid I (glycerol) to a volatile liquid A (ethanol). Mixtures of known initial composition xA0 were tested in isothermal evaporation-diffusion experiments at ∼65 °C using atmospheric air (B). A one-dimensional transport model for gas A was used to analyze the interfacial descent data. The average DAB,exp errors did not differ significantly between the liquid mixture groups and those for pure ethanol (range for the latter of +9.9 to +17.1%). However, considerable scatter in DAB,exp occurred as the mixtures became more dilute in ethanol, with the coefficient of variation increasing more than ten-fold in the xA0 = 0.146 group. This variability cannot be explained by differences in surface tension exclusively, but may also result from changes in liquid physical and transport properties as well as diffusion of liquid A. A more comprehensive modeling of the liquid phase in conjunction with gas phase transport is necessary to obtain accurate DAB’s.