Uniform Retardation Research Articles

Effect of soluble surfactant on the interface dynamics of a rising droplet

In this study, we present numerical simulations examining the impact of soluble surfactant on the interface dynamics of a rising droplet. To achieve this, the droplet interface is tracked using an arbitrary Lagrangian–Eulerian approach, and the bulk and interfacial surfactant concentration evolution equations fully coupled with the incompressible Navier–Stokes equations are solved. We systematically evaluate the boundary of interfacial dynamics evolution by varying certain dimensionless parameters. Specifically, we study the effects of changes in parameters such as the Langmuir number, the Biot number, the Damkohler number, the bulk Peclet number, and the elastic number on interfacial tangential velocity, interfacial concentration and its gradient, interfacial viscous shear stress, and droplet rising velocity. Our findings confirm the validity of the stagnant-cap model for describing the interfacial fluidity of a surfactant-laden rising droplet. Increasing the Langmuir number and decreasing the Damkohler number can inhibit interface fluidity, but there is a threshold for the Damkohler number. Additionally, the overall increase in interface tension may mask the hindering effect of the locally increased concentration gradient on the interfacial fluidity. The Biot number has no impact on the steady state of the interface, but a slow adsorption rate may result in a bimodal retardation before the interface reaches a steady state. A clear threshold exists for the Peclet number to hinder the interface velocity, and a too high Peclet number leads to strong nonlinearity in the interface physical quantities. Variations in the elastic number significantly affect the evolution of the interface, causing the interface velocity to pass through several states, ranging from almost no retardation, uniform retardation, stagnant-cap retardation to complete retardation.

Temperature and thermal stresses in material of a pad during braking

The transient temperature field and corresponding quasi-static thermal stresses are analysed in a system consisting of a semi-space and a strip. The strip is heated on its outer surface by a heat flux with the intensity equal to the specific power of friction during braking with a uniform retardation. The evolution and distribution in depth from a surface of friction for temperatures and thermal stresses were investigated for the metal-ceramic FMK-11 material of the strip.

Influence of the Pad's Material Properties on the Thermal Stresses during Braking

A three-element model of a braking process for a tribosystem consisting of semi-space, sliding with the time-dependent velocity (braking at uniform retardation) on a surface of a strip deposited on a semi-infinite foundation is considered. The dependencies of temperature and thermal stresses on thermophysical properties of the materials, the time of braking, and the strip thickness were studied. It was proved that there is a possibility of applying the obtained results to modeling of a thermal cracking of frictional elements during braking.

Temperature and thermal stresses in a pad/disc during braking

A two-element model of braking process for a tribosystem consisting of the pad (the strip) sliding with the time-dependent velocity (braking at uniform retardation) on a surface of the disc (the semi-space) is studied. The dependences of temperature and thermal stresses on the boundary conditions on upper surface of the ceramic-metal strip were investigated. It was proved that there is a possibility of applying the obtained results to modelling of a thermal cracking of the frictional elements during braking.

Frictional heating during braking in a three-element tribosystem

A three-element model of braking process is proposed. In order to determine the temperature fields in each element of the model, the analytical solution of a boundary-value problem of heat conduction for tribosystem, consisting of the semi-space, sliding with the time-dependent velocity (braking at uniform retardation) on a surface of the strip deposited on a semi-infinite foundation, is obtained. The results of the numerical analysis for different materials applied in a braking system, cast iron–FMK-11 metal ceramics–steel, are presented.

Characterisation of Photoalignment Materials for Photonic Applications at Visible and Infrared Wavelengths

ABSTRACT In this paper we discuss the processing and characterisation of Linearly Polymerisable Polymers to align Liquid Crystal Prepolymers for use in photonic application. Preliminary results on uniform retardation waveplates for use in free space optics are given.

Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility

The effect of bulk-soluble surfactants on the dynamics of a drop translating through a cylindrical tube under low-Reynolds-number conditions is investigated. Interfacial surfactant adsorption/desorption is modeled according to the Frumkin adsorption framework, and the bulk-insoluble surfactant limit is recovered as the rate of surfactant sorption becomes large compared to that of bulk diffusion. As the equilibrium surface coverage is increased, the mechanism by which drop mobility is reduced changes from uniform retardation at low surface coverage to the formation of a stagnant cap at high surface coverage. For large capillary numbers, the drop does not achieve a steady shape, and eventually it breaks up either through the formation of a penetrating viscous jet of suspending fluid, or by continuous elongation and pinch-off. Surfactants have a destabilizing effect on transient drop shapes by accelerating the formation and development of the penetrating viscous jet that leads to drop breakup. The critical conditions for drop breakup, as well as the mode of breakup, depend on the manner in which the strength of the flow (i.e., the capillary number) is increased.

Effects of artefacts on scanning laser polarimetry of retinal nerve fibre layer thickness measurement

AIMSTo investigate the effects of artefacts on scanning laser polarimetry of the retinal nerve fibre layer.METHODSSix eyes of six normal volunteers and an artificial nerve fibre layer were examined using...

Effect of Insoluble Surfactants on the Pressure-Driven Motion of a Drop in a Tube in the Limit of High Surface Coverage

The effect of surfactants on the axisymmetric pressure-driven motion of a droplet in a tube is investigated under low Reynolds number conditions. In the presence of surface-active impurities, the motion of the drop results in constant redistribution of the adsorbed surfactant along the interface by convection and diffusion, leading to nonuniformities in interfacial tension (i.e., Marangoni stresses) which modify the viscous stress balance at the interface. These, in turn, affect the mobility of the drop and its steady or transient shape deformations. In this study, the steady-state behavior of such a drop is examined in the presence of nondilute concentrations of bulk-insoluble surfactants on the surface of the drop. The boundary integral method is used in conjunction with a finite-difference scheme to solve the unsteady surface convective-diffusion equation for surfactant transport. The Frumkin adsorption framework is used to explore the effects of monolayer saturation and nonideal surfactant interactions on the steady drop shape and speed in the limit of high surface coverage. It is found that for surfactants with strong cohesive interactions, the drop mobility increases with increasing surface coverage, attaining maximum mobility at about 50% initial coverage. Furthermore, surface-convection-dominated systems with strong cohesive interactions exhibit surface flow patterns corresponding to the formation of a stagnant cap at the trailing end of the drop. All other systems exhibit surface flow patterns corresponding to uniform retardation of interface mobility as a fully immobilized interface is approached with increasing surface convection.

The slow motion of a single gas bubble in a non-Newtonian fluid containing surfactants

The drag force experienced by bubbles, rising freely in an inelastic shear-thinning fluid is calculated. In particular, the effect of contaminants is considered when the continuous phase can be represented by the power-law or the three parameter Carreau models. Two cases are examined in order to take into account the effect of surfactants: (a) interfacial mass transfer is taken into account via a perturbation around the thermodynamic equilibrium values using Gibbs elasticity, (b) a continuous distribution of impurities over the whole interface (uniform retardation) leading to Marangoni stresses. The relations obtained are based on perturbation methods around the Newtonian solution. The drag force can be evaluated via the rheological model parameters, the physical properties of the system and the concentration of impurities in the fluid. The presence of contamination was found to increase the drag resulting in a decrease of the rise velocity. Inversely, the effect of shear thinning is to decrease the drag, thus leading to a balance between both effects.

Prevalence and origin of birefringence in 48 garnets from the pyrope-almandine-grossularite-spessartine quaternary

Other| December 01, 1998 Prevalence and origin of birefringence in 48 garnets from the pyrope-almandine-grossularite-spessartine quaternary Anne M. Hofmeister; Anne M. Hofmeister Washington University, Department of Earth and Planetary Sciences, Saint Louis, MO, United States Search for other works by this author on: GSW Google Scholar Rand B. Schaal; Rand B. Schaal Search for other works by this author on: GSW Google Scholar Karla R. Campbell; Karla R. Campbell Search for other works by this author on: GSW Google Scholar Sandra L. Berry; Sandra L. Berry Search for other works by this author on: GSW Google Scholar Timothy J. Fagan Timothy J. Fagan Search for other works by this author on: GSW Google Scholar American Mineralogist (1998) 83 (11-12_Part_1): 1293–1301. https://doi.org/10.2138/am-1998-11-1218 Article history first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Anne M. Hofmeister, Rand B. Schaal, Karla R. Campbell, Sandra L. Berry, Timothy J. Fagan; Prevalence and origin of birefringence in 48 garnets from the pyrope-almandine-grossularite-spessartine quaternary. American Mineralogist 1998;; 83 (11-12_Part_1): 1293–1301. doi: https://doi.org/10.2138/am-1998-11-1218 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyAmerican Mineralogist Search Advanced Search Abstract Forty garnets are anisotropic among 48 in a suite spanning the quaternary system Mg 3 Al 2 Si 3 O 12 - Fe 3 Al 2 Si 3 O 12 - Ca 3 Al 2 Si 3 O 12 -Mn 3 Al 2 Si 3 O 12 (Py-Al-Gr-Sp). The eight isotropic specimens are too thin (>0.4 mm) for detection of weak anisotropy. Birefringence (delta ) in the remaining 40 garnets is low (delta = 0.0001 to 0.0006) and undulatory in appearance, suggesting that most optical anomalies in quaternary garnets, including the pyrope-almandine-spessartine ternary, originate through residual strain. Multiple or alternate origins are not precluded for the few samples with nearly uniform retardation or unusual sector twinning. An inverse correlation exists between degree of birefringence and stresses encountered during tectonic deformation. That is, mantle garnets from kimberlites (e.g., Py 37 Al 36 Gr 27 ) have the highest delta values. As geologic setting is difficult to separate from composition, the inverse trend suggests that birefringence arises partially from internal factors. We propose that the mismatch in size between Ca (super 2+) and Mg (super 2+) exacerbates retention of residual strain. Short-range ordering is not entirely ruled out, but clustering has only been inferred for synthetics in the middle of the Py-Gr binary, a composition range unknown for natural samples, and domains are precluded in the natural samples by the recent X-ray studies of samples from similar localities. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Rotational Motion of a Solute Molecule in a Highly Viscous Liquid Studied by13C NMR: 1,3-Dibromoadamantane in Polymeric Chlorotrifluoroethene

The viscosity-dependent retarding effect of a polymeric solvent on the rotation of small solute molecules is investigated by13C NMR relaxation measurements. It is found that the relaxation data of 1,3-dibromoadamantane in highly viscous polymeric chlorotrifluoroethene can be explained neither by isotropic nor by realistic anisotropic tumbling in a single environment. The experimental data are rationalized in terms of fast exchange between at least two environments with correlation times differing by up to two orders of magnitude. The study shows that a uniform retardation of molecular tumbling by a polymeric solvent, desirable for shifting the NMR observation window in studies of intramolecular mobility, is not always feasible.

Bone maturation in girls with Turner's syndrome.

The mechanism of growth retardation in Turner's syndrome has not been resolved. It is often referred to as a bone dysplasia, although endocrine derangement has not been ruled out. The present study was undertaken to evaluate the maturation of individual bones of the hand and wrist in girls with Turner's syndrome and thereby obtain information which may aid in elaborating the possible mechanism of the growth retardation in girls with Turner's syndrome. Hand and wrist films of 24 girls with Turner's syndrome, 11 normal girls with short stature and 23 normal controls were evaluated, using the references of Greulich and Pyle. Each bone or epiphysis was given an individual 'age'. During childhood the Turner patients showed the greatest delay in bone age of the phalangeal bones while the least delayed were the radius and ulna (long bones) and metacarpals. The carpal bones showed intermediate retardation. This pattern and extent of maturational retardation was clearly different from that of the short stature normal group, who showed uniform retardation of all bones. During adolescence, the phalangeal bones were further retarded and the carpal bones showed a moderate retardation. The unique profile of bone maturation in Turner's syndrome suggests an insult to chondroplasia, which may be related to estrogen deficiency or to an as yet undetermined endocrine or paracrine derangement.

The influence of surface sorption on dispersion in parallel plate fractures

Solute transport in a parallel plate fracture is simulated using a random walk model which accounts explicitly for sorption onto the fracture walls. With the hypothesis that solute must move into the vicinity of the fracture wall in order to participate in the sorption process, three implications follow. (1) In comparison to a nonreactive solute, a sorbing solute requires a greater entrance length along the fracture before transverse homogenization is established. The increase in this entrance length is proportional to the surface retardation factor. (2) At short transport distances, surface sorption leads to a high degree of non-uniform retardation. The transport distance required to establish uniform retardation of the entire solute mass varies greatly with geometric conditions and sorption strength. (3) Surface sorption results in enhanced longitudinal spreading of the solute mass in transport regimes which favor advective transport along the fracture relative to transverse diffusion across the fracture aperture. At distances greater than that required for transverse homogenization, an effective longitudinal dispersion coefficient can be defined that describes this enhanced dispersion for a wide range of fluid velocities. The magnitude of enhanced dispersion increases with sorption strength.

Retardation of sorbing solutes in fractured media

Sorption of a reactive solute during transport in a fractured geologic medium is analyzed under the assumption that within each fracture, retardation varies in proportion to the product of a surface distribution coefficient and the specific surface area of the fracture (i.e., its surface area‐to‐volume ratio). This approach is analogous to the KD model commonly adopted for granular porous media. Numerical migration experiments in discrete fracture networks show that at the plume scale, retardation is both nonuniform and anisotropic. Different segments of the plume, or equivalently different breakthrough fractions at a downstream boundary, are retarded to a different degree. The degree to which various breakthrough fractions are retarded varies as a function of the orientation of the mean hydraulic gradient relative to the orientation of the fracture sets. This variation can be described in the form of a retardation ellipse. The mean arrival time is the only breakthrough fraction that is consistently described by a uniform, isotropic retardation factor. The degree of nonuniformity and anisotropy in the retardation factor is controlled largely by the difference in the mean apertures of each fracture set, the standard deviation in fracture aperture, and the orientation of the fracture sets relative to the mean hydraulic gradient. A larger variability in fracture aperture, or in the orientation of fractures within each set, promotes nonuniform retardation while reducing the degree of anisotropy in the retardation factor. Our results suggest that a transport model based on the conventional advection‐dispersion equation, using a uniform retardation factor, may be conceptually incorrect, even for a dense fracture network. While the effects of nonuniform retardation modify the dispersive flux in a way that could be described by “effective” dispersion coefficients, it is our opinion that a model formulation is needed that clearly separates chemical effects from those due to hydrodynamic dispersion.

The influence of surfactant adsorption on the motion of a fluid sphere in a tube. Part 1. Uniform retardation controlled by sorption kinetics

This paper presents a study of the steady, axisymmetric, creeping translation of a fluid sphere in a tube for the case in which surfactant is adsorbed onto the fluid sphere interface. Marangoni stresses caused by the convective redistribution of surfactant are computed perturbatively in the limit of sorption-controlled uniform retardation, and fully converged numerical solutions of the creeping-flow equations including the Marangoni stress are obtained by a collocation technique.The results indicate that when the fluid sphere moves in a liquid which is at rest at infinity, the Marangoni stress retards the particle velocity. This retardation generally increases with the sphere to tube diameter ratio up to a value of approximately 0.6, whereupon the retardation begins to level off or even become reduced. When the sphere is suspended in a Poiseuille flow, stagnation rings develop on the sphere surface, and the Marangoni stresses that derive from this surface convection pattern can accelerate the fluid particle when the particle velocity is small with respect to the Poiseuille centreline velocity, but in the same direction as that velocity.

Rheology of colloidal suspensions. The isokinetic shear-flow hard-sphere model

The shear-flow rheology of the hard-sphere fluid under isokinetic conditions has been investigated by a computer-simulation method. Numerical results for the shear-rate dependence of the tensors of pressure and diffusivity are reported for four dense fluid states, each over a range of shear rate.The shear stress–shear rate flow curves are obtained initially in the isokinetic form by uniform velocity retardation. Results indicate that the onset of a non-linear stress response, and subsequent non-Newtonian phenomena at higher shear rate, can be understood as a shear perturbation of the equilibrium thermodynamic behaviour of the hard-sphere fluid and its phase transitions.The isokinetic flow curve has no direct experimental counterpart. Arguments based upon a renormalisation of the shear-rate scale, however, indicate that the isokinetic flow curve inverts to describe a general laboratory flow curve with the qualitative features of dense colloidal suspensions when seen against the body of experimental evidence.Other common non-Newtonian phenomena, including time-dependent effects (viscoelasticity, thixotropy, rheopexy) and anisotropic effects (normal differences in pressure, diffusivity and granular energy) are also seen in the isokinetic shear-flow model. The isokinetic pressure tensor–shear-rate flow curve may be used to predict experimental laboratory flow curves when the pressures and shear rates are renormalised to a time-scale corresponding to the ‘granular temperature’ of the experimental system at the same packing fraction.

Existence, Uniqueness, and Construction of the Solution of a System of Ordinary Functional Differential Equations, with Application to the Design of Perfectly Focusing Symmetric Lenses

In the design of perfectly focusing symmetric lenses, one is led, in a natural way, to a set offunctional differential equations; that is, differential equations involving composites of unknown functions, with initial conditions prescribed on the lens axis. This paper concentrateson those features of the equations which make them uniquely solvable. They are: (i) a contractiveness property of the equations near the axis; (ii) a uniform retardation in the arguments of thecomposite functions away from the axis. The second and third sections of this paper generalize and formalize these properties and provide proofs of existence, uniqueness, and continuous dependence on the data for solutions of such generalized systems of functional differential equations. Because of the lens context which motivates our study, the problem in which the contractiveness property (i) above holds is called the ‘local’ problem, and the problem in which the arguments of composite functions are uniformly retarded is called the ‘global’ problem. In the final section of the paper we apply the general results of the preceding sections to prove existence and uniqueness of perfectly focusing symmetric lenses up to distances from the lens axis at which various types of breakdown, discussed in the text, may occur.

RETARDATION OF DROPLET MOTION BY SURFACTANT. PART 1. THEORETICAL DEVELOPMENT AND ASYMPTOTIC SOLUTIONS

Abstract The equations describing the retardation by surfactant of an essentially spherical droplet in creeping flow through an unbounded Newtonian liquid are developed in a general way. The concentration distribution is determined by convection and the coupled mass transfer processes of liquid-phase diffusion, adsorption kinetics, and surface diffusion. Assuming that mass transfer occurs rapidly, an asymptotic solution is obtained showing uniform retardation, treating both phases and all mass transfer mechanisms simultaneously. For slow mass transfer, an asymptotic solution is obtained for stagnant cap behavior.

Oesophageal transit of a radionuclide solid bolus in normals.

The purpose of this study was to evaluate the physiological transit pattern of a compact bolus through the oesophagus in normal subjects. A standard gelatine bolus labelled with 99mTechnetium pertechnetate was swallowed in the erect and the supine positions and traced by a gamma-camera in 20 subjects. In the erect position, the mean overall transit time was 5.5 +/- 1.1 s (SD) which differed significantly (P less than 0.001) from the longer mean overall transit time of 6.9 +/- 1.4 s (SD) in the supine position. The transit patterns differed between erect and supine positions. In the erect position, the bolus travelled at a constant velocity until the most distal part of the oesophagus where a slight retardation of the velocity occurred, whilst in the supine position, a uniform retardation of the velocity was seen which was slightly accentuated in the most distal part. The present data provide a basis for the evaluation of studies on the bolus transport in patients with suspected oesophageal dysfunction.