Surface tension and buoyancy effects in cellular convection

1964 ◽  
Vol 19 (3) ◽  
pp. 341-352 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Surface Tension ◽  
Order Differential Equation ◽  
Boundary Surface ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Linear Perturbation ◽  
Perturbation Techniques ◽  
Fourier Series Method ◽  
Coupled Cells ◽  
Tightly Coupled

The cells observed by Bénard (1901) when a horizontal layer of fluid is heated from below were explained by Rayleigh (1916) in terms of buoyancy, and by Pearson (1958) in terms of surface tension. These rival theories are now combined. Linear perturbation techniques are used to derive a sixth-order differential equation subject to six boundary conditions. A Fourier series method has been used to obtain the eigenvalue equation for the case where the lower boundary surface is a rigid conductor and the upper free surface is subject to a general thermal condition. Numerical results are presented. It was found that the two agencies causing instability reinforce one another and are tightly coupled. Cells formed by surface tension are approximately the same size as those formed by buoyancy. Bénard's experiments are briefly discussed.

Theory on Thermal Instability of Binary Gas Mixtures in Porous Media

1976 ◽  
Vol 98 (1) ◽  
pp. 35-41 ◽  
Author(s):  
M. L. Lawson ◽  
Wen-Jei Yang ◽  
S. Bunditkul
Keyword(s):  
Fluid Layer ◽  
Perturbation Technique ◽  
Critical Rayleigh Number ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Linear Perturbation ◽  
Onset Of Convection ◽  
Hurwitz Stability ◽  
Binary Gas Mixture ◽  
The Galerkin Method

A theory is developed which predicts the instability of a horizontal layer of porous medium saturated with a binary gas mixture. The lower boundary of the system is maintained at a higher temperature and the upper one at low temperature. The transport equations and coefficients are developed on the basis of kinetic theory. A linear perturbation technique is employed to reduce the governing equations for momentum, heat, and mass transfer to eigenvalue differential equations which are solved by the Finlayson method, the combination of the Galerkin method and the Routh-Hurwitz stability criterion. Only neutral stationary stability is found to occur in the system. Its criterion can be predicted by a simple algebraic equation. Both the critical Rayleigh and wave numbers for the onset of convection are governed by five independent dimensionless parameters, two of which are most influential. The critical Rayleigh number may be lower or greater than that for pure fluid layer depending upon whether thermal diffusion induces the heavier component of the mixture to move toward the cold or hot boundary, respectively. The theory compares well with the experimental results.

Influence of corrugated boundary surface and reinforcement of fibre-reinforced layer on propagation of torsional surface wave

2016 ◽  
Vol 23 (9) ◽  
pp. 1417-1436 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Anirban Lakshman ◽  
Amares Chattopadhyay
Keyword(s):  
Surface Wave ◽  
Dispersion Equation ◽  
Half Space ◽  
Boundary Surface ◽  
Lower Boundary ◽  
Transversely Isotropic ◽  
Wave Number ◽  
Torsional Surface Wave ◽  
Propagation Of Waves ◽  
Boundary Surfaces

These days fibre-reinforced materials are frequently used in construction sector for example in dams, bridges etc. Also the earth structure and artificial structure made by human may contain irregularity or corrugation, therefore, propagation of waves and vibrations through these structures gets affected by them. Motivated by these facts the present problem aims to study the propagation of torsional surface wave in a fibre-reinforced layer with corrugated boundary surface overlying an initially stressed transversely isotropic half-space. The closed form of the dispersion equation has been deduced and the notable effect of reinforcement, undulatory parameter of corrugated boundary surfaces of the layer, corrugation parameter of upper and lower boundary surfaces of the layer, initial stress acting in half-space and wave number on the phase velocity of torsional surface wave has been exhibited. The numerical computation along with graphical illustration has been carried out for fibre-reinforced layer of carbon fibre-epoxy resin and T300/5208 graphite/epoxy material for the transversely isotropic half-space. As a special case of the problem, deduced dispersion equation is found in well-agreement with the classical Love wave equation. Comparative study for reinforced and reinforced free layer has been performed and also depicted graphically. Moreover some analysis is made to highlight the important peculiarities of the problem.

Populations of Tightly Coupled Neurons: The RGC/LGN System

2008 ◽  
Vol 20 (5) ◽  
pp. 1179-1210 ◽  
Author(s):  
Lawrence Sirovich
Keyword(s):  
Cell System ◽  
General Character ◽  
Retinal Ganglion ◽  
Relay Cell ◽  
Transfer Ratio ◽  
Coupled Cells ◽  
Tightly Coupled ◽  
Synaptic Dynamics ◽  
Dynamic Description ◽  
Short Time

A mathematical model, of general character for the dynamic description of coupled neural oscillators is presented. The population approach that is employed applies equally to coupled cells as to populations of such coupled cells. The formulation includes stochasticity and preserves details of precisely firing neurons. Based on the generally accepted view of cortical wiring, this formulation is applied to the retinal ganglion cell (RGC)/lateral geniculate nucleus (LGN) relay cell system, of the early mammalian visual system. The smallness of quantal voltage jumps at the retinal level permits a Fokker-Planck approximation for the RGC contribution; however, the LGN description requires the use of finite jumps, which for fast synaptic dynamics appears as finite jumps in the membrane potential. Analyses of equilibrium spiking behavior for both the deterministic and stochastic cases are presented. Green's function methods form the basis for the asymptotic and exact results that are presented. This determines the spiking ratio (i.e., the number of RGC arrivals per LGN spike), which is the reciprocal of the transfer ratio, under wide circumstances. Criteria for spiking regimes, in terms of the relatively few parameters of the model, are presented. Under reasonable hypotheses, it is shown that the transfer ratio is ≤1/2, in the absence of input from other areas. Thus, the model suggests that the LGN/RGC system may be a relatively unsophisticated spike editor. In the absence of other input, the system is designed to fire an LGN spike only when two or more RGC spikes appear in a relatively short time. Transfer ratios that briefly exceed 1/2 (but are less than 1) have been recorded in the laboratory. Inclusion of brain stem input has been shown to provide a signal that elevates the transfer ratio (Ozaki & Kaplan, 2006). A model that includes this contribution is also presented.

Stability of Hadley Circulations in a Viscoelastic Fluid With Deformable Free Surface

2003 ◽  
Author(s):  
P. N. Kaloni ◽  
J. X. Lou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Viscoelastic Fluid ◽  
Lower Surface ◽  
Horizontal Layer ◽  
Convective Stability ◽  
Rigid Plate ◽  
Temperature Dependent

This paper deals with liner convective stability analysis of Oldroyd B fluid in a thin horizontal layer with a deformable free surface. The lower surface of the layer is in contact with an adiabatic rigid plate and the upper deformable surface is subject to a temperature dependent surface tension. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and the results for various different forms of upper surfaces are presented.

Isothermes of Grain Boundary Tension and Grain Boundary Adsorption in Cu-Sn System

2006 ◽  
Vol 258-260 ◽  
pp. 427-432
Author(s):  
Danil V. Vaganov ◽  
Sergei Zhevnenko
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Grain Boundary ◽  
Pure Copper ◽  
Boundary Surface ◽  
Dilute Solution ◽  
Tin Alloys ◽  
Tension Free

Grain boundary surface tension and surface tension of free surface for pure copper and copper-tin alloys are measured. On the base of these data isothermes of grain boundary tension, free surface tension and isothermes of adsorption are constructed in assumption of a dilute solution.

Imaging of Surface-Tension-Driven Convection Using Liquid Crystal Thermography

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
T. W. Dutton ◽  
L. R. Pate ◽  
D. K. Hollingsworth
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Crystal ◽  
Temperature Distribution ◽  
Liquid Film ◽  
Lower Boundary ◽  
Processing System ◽  
Metal Foil ◽  
Lower Boundary Condition ◽  
Liquid Crystal Thermography

Surface-tension forces can drive fluid motion within thin liquid layers with a free surface. Spatial variations in the temperature of the free surface create surface tractions that drive cellular motions. The cells are most commonly hexagonal in shape and they scale on the thickness of the fluid layer. This investigation documents the formation of cells in the liquid film in the presence of a uniform-heat-flux lower boundary condition. Liquid crystal thermography was used to image the cells and measure the temperature distribution on the lower surface of the liquid layer. A 1.1 mm deep pool of silicone oil was supported on a 50 μm thick electrically heated metal foil. The oil was retained inside an independently heated acrylic ring mounted on the top surface of the foil and a dry-ice cooling plate served as the low-temperature sink above the free surface of the oil. Color images of hexagonal convection cells were captured using liquid crystal thermography and a digital image acquisition and processing system. The temperature distribution inside a typical cell was measured using thermographic image analysis. Experimental issues, such as the use of an independently heated retaining ring to control the height of the liquid film and the utility of a flux-based Marangoni number are discussed.

Experiments on Transient Thermal Convection With Internal Heating—Large Time Results

1983 ◽  
Vol 105 (2) ◽  
pp. 261-266 ◽  
Author(s):  
M. Keyhani ◽  
F. A. Kulacki
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Step Change ◽  
Boundary Layer Theory ◽  
Approximate Theory ◽  
Fourier Number ◽  
Final State ◽  
Volumetric Heating

Experimental data and correlations are presented for the time scales of developing and decaying thermal convection with volumetric heating in a horizontal layer. The layer is bounded by rigid surfaces, with an insulated lower boundary and an isothermal upper boundary. The time for complete flow development/decay, as a result of a step change in volumetric heat generation, is simply parameterized in terms of the Fourier number for the layer, the step change in Rayleigh number, ΔRa, and the initial/final dimensionless maximum core temperature. For developing flows, ΔRa > 0, results are in good agreement with existing experiments and an approximate boundary layer theory. In decaying flows, Fourier numbers are larger than those of previously reported experiments for a motionless final state. Data for turbulent-to-turbulent transitions when ΔRa < 0 suggests that the approximate boundary layer theory underestimates the Fourier number. Experimental uncertainties on measured Fourier numbers are generally well within the limits of uncertainty allowed by the approximate theory.

The Rayleigh—Jeffreys problem with boundary slab of finite conductivity

1968 ◽  
Vol 32 (2) ◽  
pp. 393-398 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Finite Thickness ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Wave Number ◽  
Linear Perturbation ◽  
Finite Conductivity ◽  
Solid Layer ◽  
Onset Of Convection ◽  
Infinite Conductivity ◽  
Bounded Below

Linear perturbation analysis is applied to the problem of the onset of convection in a horizontal layer of fluid heated uniformly from below, when the fluid is bounded below by a rigid plate of inlinite conductivity and above by a solid layer of finite conductivity and finite thickness. The critical Rayleigh number and wave-number are found for various thickness ratios and thermal conductivity ratios. Both numbers are reduced by the presence of a boundary of finite (rather than infinite) conductivity in qualitative agreement with the observation of Koschmieder (1966).

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