Capillary Surfaces Research Articles

Min-max theory for capillary surfaces

Abstract We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existence of nontrivial, smooth, almost properly embedded surfaces with any given constant mean curvature 𝑐, and with smooth boundary contacting at any given constant angle 𝜃. Moreover, if 𝑐 is nonzero and 𝜃 is not π 2 \frac{\pi}{2} , then our min-max solution always has multiplicity one. We also establish a stable Bernstein theorem for minimal hypersurfaces with certain contact angles in higher dimensions.

Functionalization of High-Density Polyethylene Capillaries for Open Tubular Ion Chromatography.

Ion chromatography is the anion analysis benchmark. A miniature form, Open Tubular Ion Chromatography (OTIC), has attractive attributes for efficient ion separations. Here, we fabricate and characterize high-density polyethylene (HDPE) open tubular anion exchange columns (OTCs). We attach positively charged latex particles onto negatively charged capillary surfaces. For efficient OTIC, column diameters need to be < ∼20µm; functionalizing the bore is challenging. Methods to introduce acid groups to an HDPE capillary bore, e.g., sulfonation using chlorosulfonic or sulfuric acid solutions, with or without grafting of an aromatic ring through photo- or chemical grafting first, are explored. Following quaternary ammonium latex attachment, the ion exchange capacity and separating abilities of each OTC were measured as an index of OTC performance. Gradual loss of capacity was observed for many of these; high-resolution mass spectrometry confirmed the leaching of detached oxidized/sulfonated oligomeric fragments and consequent poisoning of the latex sites. Ways to ameliorate this and/or to rejuvenate the columns are also described.

Static profiles of capillary surfaces in the annular space between two coaxial cones under microgravity

Static profiles of capillary surfaces in the annular space between two coaxial cones under microgravity

Multi-scale spectral methods for bounded radially symmetric capillary surfaces

Multi-scale spectral methods for bounded radially symmetric capillary surfaces

A variational-difference method for numerical simulation of equilibrium capillary surfaces

Objectives. A variational-difference method for numerical simulation of equilibrium capillary surfaces based on the minimization of the energy functional is proposed. As a test task a well-known axisymmetric hydrostatic problem on equilibrium shapes of a drop adjacent to a horizontal rotating plane under gravity is considered. The mathematical model of the problem is built on the basis of the variational principle: the shape of the drop satisfies the minimum total energy for a given volume. The problem of the functional minimization is reduced to a system of nonlinear equations using the finite element method. To solve the system a Newton's iterative method is applied.Methods. The variational-difference approach (the finite element method) is used. The finite linear functions are chosen as basic functions.Results. Equilibrium shapes of a drop on a rotating plane are constructed by the finite element method in a wide range of defining parameters: Bond number, rotational Weber number and wetting angle. The influence of these parameters on the shape of a drop is investigated. The numerical results are matched with the results obtained using the iterative-difference approach over the entire range of physical stability with respect to axisymmetric perturbations.Conclusion. The finite element method responds to the loss of stability of a drop with respect to axisymmetric perturbations. Therefore it can be used to study the stability of the equilibrium of axisymmetric capillary surfaces.

Capillary surfaces: Stability, index and curvature estimates

Abstract In this paper, we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immersed in general 3-manifolds with boundary. We also study noncompact capillary surfaces with finite index and show that, under suitable curvature assumptions, such surface is conformally equivalent to a compact Riemann surface with boundary, punctured at finitely many points. We then prove that a weakly stable capillary surface immersed in a half-space of R 3 \mathbb{R}^{3} which is minimal or has a contact angle less than or equal to π / 2 \pi/2 must be a half-plane. Using this uniqueness result, we obtain curvature estimates for strongly stable capillary surfaces immersed in a 3-manifold with bounded geometry.

Spectral methods for capillary surfaces described by bounded generating curves

We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit fluids in capillary tubes, sessile drops, and fluids in annular tubes as well as other examples.We present a pseudo-spectral method for approximating solutions of the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.

Strategies to enhance the moisture-barrier qualities of concrete mixtures to improve their durability

Moisture transport in concrete significantly impacts its durability attribute, which in turn affects the useful service life of the built concrete infrastructure. A host of physical, chemical, and mechanical deterioration processes of concrete depend on the presence of moisture inside the concrete. Enhancement of the moisture-barrier characteristic of concrete can thus be the key to improving its durability. This paper reports the test results of various strategies implemented to reduce the moisture transport into concrete. These strategies include (i) use of fly ash and silica fume as partial replacement of cement for refinement of capillary porosity, discontinuity of pores, and refinement of the chemistry of hydrated cement matrix; (ii) use of milled waste glass as partial replacement of cement to refine the microstructure of cementitious mixture (iii) use of hydrophobic additives to reduce the affinity of capillary pore surfaces to moisture; and (iv) use of polymer emulsion to line capillary pore surfaces to cause partial blockage of the capillary pore system. Five different concrete mixtures including a control mixture were prepared using the above formulations and tested for moisture sorption, acid attack resistance, abrasion resistance, and compressive strength characteristics at 28 and 90 days of concrete age. Test results indicated enhancement in compressive strength, moisture resistance, and other durability characteristics of the modified mix formulations compared to that of control mixture. Mix formulation incorporating fly ash and silica fume as partial replacement of cement proved to be the most effective combination for achieving the desired improvements in mechanical and durability attributes of concrete. The findings of this study are expected to provide guidelines for designing concrete mixtures with enhanced durability when exposed to aggressive environmental conditions.[copyright information to be updated in production process.]

On the Morse Index with Constraints for Capillary Surfaces

On the Morse Index with Constraints for Capillary Surfaces

Rigidity of capillary surfaces in compact 3-manifolds with strictly convex boundary

AbstractIn this paper, we obtain one sharp estimate for the length $L(\partial\Sigma)$ of the boundary $\partial\Sigma$ of a capillary minimal surface Σ2 in M3, where M is a compact three-manifolds with strictly convex boundary, assuming Σ has index one. The estimate is in term of the genus of Σ, the number of connected components of $\partial\Sigma$ and the constant contact angle θ. Making an extra assumption on the geometry of M along $\partial M$, we characterize the global geometry of M, which is saturated only by the Euclidean three-balls. For capillary stable CMC surfaces, we also obtain similar results.

Development of Mathematical Model and Characterization of Internal Surface Obtained by Elasto-Abrasives Magneto-Spiral Finishing (EAMSF)

Abstract The implantation of stents and instruments with capillary action demands super-finished internal surfaces of the manufactured product. Elasto-abrasives magneto-spiral finishing (EAMSF) is the attempt made in this paper to enhance finishing productivity by incorporating the abrasive flow in spiral motion due to the presence of the magnetic field. Here, novel impregnated elasto-magnetic abrasive particles (IMPs) are used in a magnetic field-assisted environment to polish the inner walls of the workpiece. In EAMSF, magnetic force provides excess finishing pressure to the abrasives. In contrast, the high-impact polystyrene (HIPS) elasticity absorbs the extra force of the IMPs on the finishing surface. An Indigenous mathematical relation considering the physics of this superfinishing process indicating material removal shows a close resemblance to the experimental results with an error percentage of 1.03 has been developed. The results of the experimentation reveal that 50% concentration of abrasives and a magnetic field density of 18mT yield a superior surface finish with a Ra value equal to 0.053 µm and maximum material removal of 6.9 mg, while in the absence of a magnetic field, excellent surface finish with a Ra = 0.266 µm and maximum material removal of 5.4 mg is achieved. In the presence of magnetic field density, significant enhancement of material removal, surface finish, and burr removal is observed. Finishing the surface at 50% abrasive concentration with a magnetic field represents regular finishing, and the trench marks on the original surface are removed after finishing.

Advances in stimuli-responsive polymeric coatings for open-tubular capillary electrochromatography

Open-tubular capillary electrochromatography (OT-CEC) is an important tool in separation science due to its effective performance and reusability, and has attracted attention because the coating-process and the coating thickness can be controlled. Although dozens of OT-CEC reviews have been published recently, design of the smart polymer coatings, which can improve the separation efficiency of OT-CEC via external stimuli, remains a challenge. This review describes the advancement of research on OT-CEC stimuli-responsive polymeric coatings (SR-PCs). It covers the latest researches in the design and synthesis of stimuli-responsive polymers, the protocols for their fabrication on capillary inner surfaces, strategies for improving stimuli-responsive OT-CEC separation efficiency and real-world applications.

Low Index Capillary Minimal Surfaces in Riemannian 3-Manifolds

Low Index Capillary Minimal Surfaces in Riemannian 3-Manifolds

A Survey of Delaunay Surfaces with Applications in Capillary Surfaces

In this paper we survey Delaunay surfaces in $\mathbb{R}^{3}$ spanning two coaxial circles which appear as capillary surfaces supported on different solid supports in the absence of gravity. We classify these surfaces based on contact angles and the geometry of the support. Numerical solutions of the Euler Lagrange equation are provided using numerical methods.

Resonant mode scanning to compute the spectrum of capillary surfaces with dynamic wetting effects

Resonant mode scanning to compute the spectrum of capillary surfaces with dynamic wetting effects

SIMULATION OF QUASISTATATICS OF THE PROCESS OF FORMATION OF A LIQUID MENISK TYPE OF HANGING DROP ON THE SUBJECT OF METHODOLOGICAL PROVISION OF MEASUREMENT

A mathematical model has been developed for describing a capillary surface of the hanging drop type in the form of a system of fifth-order nonlinear differential equations, which corresponds to five geometric characteristics of the meniscus: the distance from the meniscus axis to a given point on the capillary surface, the distance from the plane normal to the meniscus surface at an umbilical point to a given point on capillary surface, the angle between the axis of symmetry and the normal to the capillary surface at a given point, the area and volume of the capillary surface bounded by a cut of the horizontal plane passing through a given point. By reducing the equation to a dimensionless form, it was possible to reduce to one setting parameter - the reduced Gaussian curvature at the umbilical point. The numerical solution of the obtained model with the subsequent reduction of the geometric and physical characteristics of the capillary surface to the radius of the capillary made it possible to simulate a quasi-static sequence of the meniscus surfaces. This made it possible to form a methodological basis for determining the static and dynamic surface characteristics of interfaces. Also, modeling the quasi-statics of meniscus formation made it possible to determine with high accuracy the values ​​of the characteristics of the meniscus in extreme cases, such as the moment of maximum pressure in the meniscus and the moment of separation from the end of the capillary. This is the methodological basis for such well-known methods for determining surface characteristics as the method of maximum pressure in the meniscus and the stalagmometric method. Also, if the obtained results are interpreted as a quasi-statics of changes in the parameters of a hanging drop of a solution of surfactants (hanging bubble) at a constant volume, it is possible to determine the dynamics of changes in surface tension. The numerical solution of the system of differential equations and the interpretation of the obtained tabulated results was carried out in the MathWorks MATLAB environment, which made it possible to form multilevel systematized data arrays of capillary surfaces, which can be basic for further interpretation, depending on the task at hand.

Capillary Surfaces in Circular Cylinders

Capillary Surfaces in Circular Cylinders

Electroosmotic flow of generalized Burgers’ fluid with Caputo–Fabrizio derivatives through a vertical annulus with heat transfer

Applying the electric field to a fluid confined between capillary surfaces is the most recent technique used for studying the fluid movement. This technique is known as electroosmotic flow (EOF). The problem of the Caputo–Fabrizio time-fractional derivative of the electroosmotic generalized Burgers’ fluid through a vertical annulus with free convection heat transfer has been investigated. The annulus walls kept at constant values of a zeta potential. The dimensionless governing equations have been solved with the help of the Laplace and finite Hankel transforms. The inversion of Laplace for the transformed functions is calculated numerically. The essential features of the electroosmotic flow (EOF) and the related thermal characteristics are clearly illustrated by the variations in the velocity, the flow rate, the temperature and the Nusselt number. Moreover, comparisons with other non-Newtonian fluids have been discussed. It was found that the presence of the electric double layer (EDL) accelerates the fluid near the walls of the annulus, while in the core region, the reverse flow is noticed.

Covalent Biofunctionalization of the Inner Surfaces of a Hollow-Fiber Capillary Bundle Using Packed-Bed Plasma Ion Implantation.

Hollow-fiber capillary bundles are widely used in the production of medical devices for blood oxygenation and purification purposes such as in cardiopulmonary bypass, hemodialysis, and hemofiltration, but the blood interfacing inner surfaces of these capillaries provide poor hemocompatibility. Here, we present a novel method of packed-bed plasma ion implantation (PBPII) for the modification of the inner surfaces of polymeric hollow-fiber bundles enclosed in a cassette. The method is simple and can be performed on an intact hollow-fiber bundle cassette by the placement of a hollow cylindrical electrode, connected to a negative high-voltage pulse generator, around the cassette. The method does not require the insertion of electrodes inside the capillaries or the cassette. Nitrogen gas is fed into the capillaries inside the cassette by connecting the inlet of the cassette to a gas source. Upon the application of negative high-voltage bias pulses to the electrode, plasma is ignited inside the cassette, achieving the surface modification of both the internal and external surfaces of the capillaries. Fourier transform infrared-attenuated total reflectance spectroscopy of the PBPII-treated capillaries revealed the formation of aromatic C═C bonds, indicating the progressive carbonization of the capillary surfaces. The PBPII treatment was found to be uniform along the capillaries and independent of the radial position in the cassette. Atomic force microscopy of cross sections through the capillaries revealed that the increased stiffness associated with the carbonized layer on the inner surface of the PBPII-treated capillary has a depth (∼40 nm) consistent with that expected for ions accelerated by the applied bias voltage. The modified internal surfaces of the capillary bundle showed a greatly increased wettability and could be biofunctionalized by covalently immobilizing protein directly from the buffer solution. The direct, reagent-free protein immobilization was demonstrated using tropoelastin as an example protein. Covalent binding of the protein was confirmed by its resistance to removal by hot sodium dodecyl sulfate detergent washing, which is known to disrupt physical binding.

An analytical model for void-free priming of microcavities

The present work deals with the microfluidic evolution of capillary surfaces that are formed during the priming of microcavity structures with a non-wetting liquid. Due to the large contact angle of the priming liquid, a trapping of air within the microcavities poses a major impediment to a complete filling. We tackle this issue by developing a two-dimensional analytical model describing the geometrical shape of capillary surfaces formed in microcavity structures. In particular, the model is employed to derive two quantitative conditions for a void-free priming of a microcavity structure in terms of its aspect ratio, rounding parameters and the channel width. Microfluidic experiments are performed to verify the analytical results. Finally, we make use of the model to demonstrate a pressure-driven aliquoting of a non-wetting sample liquid in a flow chamber with an array of 55 microcavities by introducing a second immiscible liquid acting as a sealant. In this way, our work constitutes a basis for the design of microcavity-based liquid aliquoting structures that are used in various fields of application like PCR arrays, cell culture chips or digital reaction arrays.