The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem

The addition of surface tension to the classical Stefan problem for melting a sphere causes the solution to blow up at a finite time before complete melting takes place. This singular behaviour is characterised by the speed of the solid-melt interface and the flux of heat at the interface both becoming unbounded in the blow-up limit. In this paper, we use numerical simulation for a particular energy-conserving one-phase version of the problem to show that kinetic undercooling regularises this blow-up, so that the model with both surface tension and kinetic undercooling has solutions that are regular right up to complete melting. By examining the regime in which the dimensionless kinetic undercooling parameter is small, our results demonstrate how physically realistic solutions to this Stefan problem are consistent with observations of abrupt melting of nanoscaled particles.

Tension between privacy and justice : ordering medical tests

Courts set guidelines for when genetic testing would be ordered - medical testing - life insurers - use of test results - confidentiality.

Mechanical tension as a driver of connective tissue growth in vitro

We propose the progressive mechanical expansion of cell-derived tissue analogues as a novel, growth-based approach to in vitro tissue engineering. The prevailing approach to producing tissue in vitro is to culture cells in an exogenous “scaffold” that provides a basic structure and mechanical support. This necessarily pre-defines the final size of the implantable material, and specific signals must be provided to stimulate appropriate cell growth, differentiation and matrix formation. In contrast, surgical skin expansion, driven by increments of stretch, produces increasing quantities of tissue without trauma or inflammation. This suggests that connective tissue cells have the innate ability to produce growth in response to elevated tension. We posit that this capacity is maintained in vitro, and that order-of-magnitude growth may be similarly attained in self-assembling cultures of cells and their own extracellular matrix. The hypothesis that growth of connective tissue analogues can be induced by mechanical expansion in vitro may be divided into three components: (1) tension stimulates cell proliferation and extracellular matrix synthesis; (2) the corresponding volume increase will relax the tension imparted by a fixed displacement; (3) the repeated application of static stretch will produce sustained growth and a tissue structure adapted to the tensile loading. Connective tissues exist in a state of residual tension, which is actively maintained by resident cells such as fibroblasts. Studies in vitro and in vivo have demonstrated that cellular survival, reproduction, and matrix synthesis and degradation are regulated by the mechanical environment. Order-of-magnitude increases in both bone and skin volume have been achieved clinically through staged expansion protocols, demonstrating that tension-driven growth can be sustained over prolonged periods. Furthermore, cell-derived tissue analogues have demonstrated mechanically advantageous structural adaptation in response to applied loading. Together, these data suggest that a program of incremental stretch constitutes an appealing way to replicate tissue growth in cell culture, by harnessing the constituent cells’ innate mechanical responsiveness. In addition to offering a platform to study the growth and structural adaptation of connective tissues, tension-driven growth presents a novel approach to in vitro tissue engineering. Because the supporting structure is secreted and organised by the cells themselves, growth is not restricted by a “scaffold” of fixed size. This also minimises potential adverse reactions to exogenous materials upon implantation. Most importantly, we posit that the growth induced by progressive stretch will allow substantial volumes of connective tissue to be produced from relatively small initial cell numbers.

Finite element analysis of CFRP strengthened steel hollow sections under tension

This paper presents a nonlinear finite element (FE) model for the analysis of very high strength (VHS) steel hollow sections wrapped by high modulus carbon fibre rein forced polymer (CFRP) sheets. The bond strength of CFRP wrapped VHS circular steel hollow section under tension is investigated using the FE model. The three dimensional FE model by Nonlinear static analysis has been carried out by Strand 7 finite element software. The model is validated by the experimental data obtained from Fawzia et al [1]. A detail parametric study has been performed to examine the effect of number of CFRP layers, different diameters of VHS steel tube and different bond lengths of CFRP sheet. The analytical model developed by Fawzia et al. [1] has been used to determine the load carrying capacity of different diameters of CFRP strengthened VHS steel tube by using the capacity from each layer of CFRP sheet. The results from FE model have found in reasonable agreement with the analytical model developed by Fawzia et al [1]. This validation was necessary because the analytical model by Fawzia et al [1] was developed by using only one diameter of VHS steel tube and fixed (five) number of CFRP layers. It can be concluded that the developed analytical model is valid for CFRP strengthened VHS steel tubes with diameter range of 38mm to 100mm and CFRP layer range of 3 to 5 layers. Based on the results it can also be concluded that the effective bond length is consistent for different diameters of steel tubes and different layers of CFRP. Three layers of CFRP is considered most effective wrapping scheme due to the cost effectiveness. Finally the distribution of longitudinal and hoop stress has been determined by the finite element model for different diameters of CFRP strengthened VHS steel tube.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

A comparison of welfare outcomes for weaner and mature Bos indicus bulls surgically or tension band castrated with or without analgesia: 2. Responses related to stress, health and productivity

Tension banding castration of cattle is gaining favour because it is relatively simple to perform and is promoted by retailers of the banders as a humane castration method. Two experiments were conducted, under tropical conditions using Bos indicus bulls comparing tension banding (Band) and surgical (Surgical) castration of weaner (7–10 months old) and mature (22–25 months old) bulls with and without pain management (NSAID (ketoprofen) or saline injected intramuscularly immediately prior to castration). Welfare outcomes were assessed using a range of measures; this paper reports on some physiological, morbidity and productivity-related responses to augment the behavioural responses reported in an accompanying paper. Blood samples were taken on the day of castration (day 0) at the time of restraint (0 min) and 30 min (weaners) or 40 min (mature bulls), 2 h, and 7 h; and days 1, 2, 3, 7, 14, 21 and 28 post-castration. Plasmas from day 0 were assayed for cortisol, creatine kinase, total protein and packed cell volume. Plasmas from the other samples were assayed for cortisol and haptoglobin (plus the 0 min sample). Liveweights were recorded approximately weekly to 6 weeks and at 2 and 3 months post-castration. Castration sites were checked at these same times to 2 months post-castration to score the extent of healing and presence of sepsis. Cortisol concentrations (mean ± s.e. nmol/L) were significantly (P < 0.05) higher in the Band (67 ± 4.5) compared with Surgical weaners (42 ± 4.5) at 2 h post-castration, but at 24 h post-castration were greater in the Surgical (43 ± 3.2) compared with the Band weaners (30 ± 3.2). The main effect of ketoprofen was on the cortisol concentrations of the mature Surgical bulls; concentrations were significantly reduced at 40 min (47 ± 7.2 vs. 71 ± 7.2 nmol/L for saline) and 2 h post-castration (24 ± 7.2, vs. 87 ± 7.2 nmol/L for saline). Ketoprofen, however, had no effect on the Band mature bulls, with their cortisol concentrations averaging 54 ± 5.1 nmol/L at 40 min and 92 ± 5.1 nmol/L at 2 h. Cortisol concentrations were also significantly elevated in the Band (83 ± 3.0 nmol/L) compared with Surgical mature bulls (57 ± 3.0 nmol/L) at weeks 2–4 post-castration. The timing of this elevation coincided with significantly elevated haptoglobin concentrations (mg/mL) in the Band bulls (2.97 ± 0.102 for mature bulls and 1.71 ± 0.025 for weaners, vs. 2.10 ± 0.102 and 1.45 ± 0.025 respectively for the Surgical treatment) and evidence of slow wound healing and sepsis in both the weaner (0.81 ± 0.089 not healed at week 4 for Band, 0.13 ± 0.078 for Surgical) and mature bulls (0.81 ± 0.090 at week 4 for Band, 0.38 ± 0.104 for Surgical). Overall, liveweight gains of both age groups were not affected by castration method. The findings of acute pain, chronic inflammation and possibly chronic pain in the mature bulls at least, together with poor wound healing in the Band bulls support behavioural findings reported in the accompanying paper and demonstrate that tension banding produces inferior welfare outcomes for weaner and mature bulls compared with surgical castration.

A comparison of welfare outcomes for weaner and mature Bos indicus bulls surgically or tension band castrated with or without analgesia: 1. Behavioural responses

Tension-band castration of cattle is gaining favour because it is relatively simple to perform and is promoted by retailers of the devices as a humane castration method. Furthermore, retailers encourage delaying castration to exploit the superior growth rates of bulls compared with steers. Two experiments were conducted, under tropical conditions, comparing tension banding and surgical castration of weaner (7–10 months old) and mature (22–25 months old) Bos indicus bulls with and without pain management (ketoprofen or saline injected intramuscularly immediately prior to castration). Welfare outcomes were assessed using a wide range of measures; this paper reports on the behavioural responses of the bulls and an accompanying paper reports on other measures. Behavioural data were collected at intervals by direct observation and continuously via data loggers on the hind leg of the bulls to 4 weeks post-castration. Tension-banded bulls performed less movement in the crush/chute than the surgically castrated bulls during the procedures (weaner: 2.63 vs. 5.69, P < 0.001; mature: 1.00 vs. 5.94; P < 0.001 for tension-band and surgical castration, respectively), indicating that tension banding was less painful then surgical castration during conduct. To 1.5 h post-castration, tension-banded bulls performed significantly (all P < 0.05) more active behavioural responses indicative of pain compared with surgical castrates, e.g., percentage time walking forwards (weaner: 15.0% vs. 8.1%; mature: 22.3% vs. 15.1%), walking backwards (weaner: 4.3% vs. 1.4%; mature: 2.4% vs. 0.5%), numbers of tail movements (weaner: 21.9 vs. 1.4; mature: 51.5 vs. 39.4) and leg movements (weaner: 12.9 vs. 0.9; mature: 8.5 vs. 1.5), respectively. In contrast, surgically castrated bulls performed more immobile behaviours compared with tension-banded bulls (e.g., standing in mature bulls was 56.6% vs. 34.4%, respectively, P = 0.002). Ketoprofen administration appeared effective in moderating pain-related behaviours in the mature bulls from 1.5 to 3 h, e.g., reducing abnormal standing (0.0% vs. 7.7%, P = 0.009) and increasing feeding (12.7% vs. 0.0%, P = 0.048) in NSAID- and saline-treated bulls, respectively. There were few behavioural differences subsequent to 24 h post-castration, but some limited evidence of chronic pain (3–4 weeks post-castration) with both methods. Interpretation, however, was difficult from behaviours alone. Thus, tension banding is less painful than surgical castration during conduct of the procedures and pain-related behavioural responses differ with castration method (active restlessness in response to tension banding and minimisation of movement in response to surgical castration). Ketoprofen administered immediately prior to castration was somewhat effective in reducing pain, particularly in the mature bulls.

Line tension of a two dimensional gas-liquid interface

In two dimensional (2D) gas-liquid systems, the reported simulation values of line tension are known to disagree with the existing theoretical estimates. We find that while the simulation erred in truncating the range of the interaction potential, and as a result grossly underestimated the actual value, the earlier theoretical calculation was also limited by several approximations. When both the simulation and the theory are improved, we find that the estimate of line tension is in better agreement with each other. The small value of surface tension suggests increased influence of noncircular clusters in 2D gas-liquid nucleation, as indeed observed in a recent simulation.

Interfacial tension model for catalytically driven nanorods

We present an analysis of the interfacial tension model for the movement of the catalytically driven nanorod. The model considers the convective reaction-diffusion equation for the production and diffusion of oxygen around the bimetallic nanorod. We solve the equation and find the concentration difference, which drives the nanorod. We use our expression to calculate the force on the nanorod and find that the result is within 20% of the results found earlier [ W. Paxton et al., J. Am. Chem. Soc. 128, 14881 (2006) ] by an approximate method. Unlike the earlier results, our results are valid from short to long lengths of the nanorod.

On latent heat of vaporization, surface tension, and temperature

A semitheoretical equation for latent heat of vaporization has been derived and tested. The average error in predicting the value at the normal boiling point in the case of about 90 compounds, which includes polar and nonpolar liquids, is about 1.8%. A relation between latent heat of vaporization and surface tension is also derived and is shown to lead to Watson's empirical relation which gives the change of latent heat of vaporization with temperature. This gives a physico-chemical justification for Watson's empirical relation and provides a rapid method of determining latent heats by measuring surface tension.