Showing papers on "Critical radius published in 1988"

Counterion condensation in micellar and colloidal solutions

Abstract: Asymptotic solutions are obtained to the Poisson–Boltzmann equation for large, highly charged spheres in an ionic solution. It is proved that as the size of the sphere is increased, keeping the surface charge density fixed, there is a critical value for the radius beyond which counterion condensation sets in. This critical radius is much larger than the Bjerrum length but small compared to the Debye length and depends on the ionic strength. An expression is derived for the effective charge. When the radius becomes much larger than the Debye length, it is shown that sufficiently many counterions condense in a shell of thickness small compared to the polyion radius to essentially neutralize the polyion charge.

An analysis of lewis number and flow effects on the ignition of premixed gases

Abstract: We have analysed numerically the ignition of a combustible gas to which heat is added over a specified period at a spherical boundary of small diameter. We solve conservation equations for reactant and sensible enthalpy and allow the gas to undergo a one step chemical reaction. The numerical technique involves a finite difference scheme with an adaptive grid. We find that, until the flame has grown beyond a critical radius, it relies upon the heat source to prevent its extinction. A minimum energy is required for successful ignition. This minimum increases as the Lewis number of the mixture increases. The minimum ignition energy also increases if the flame front is stretched. This behaviour is in very close agreement with experimental observations of the spark ignition of turbulent mixtures.

Expansion of a Spherical Hole in Elastic Food Materials with Surface Tension

Abstract: Expansion of a paraffin oil droplet in a gelatin gel was explained by an equation given by Gent and Tompkins which takes into account the effects of internal pressure, elasticity, and surface tension. The equation suggests that large bubbles monotonously expand as the internal pressure increases but small bubbles have to surpass maxima in the internal pressure for expansion. It was shown that there was a characteristic value in the initial bubble radius, , above which the bubbles expand monotonously as the internal pressure increased, and it was given as (σ: surface tension, E: elasticity). The calculated value of , agreed with the minimum of radii of bubbles reported in the preceding paper, which expanded even at a constant temperature, absorbing the air released from other shrinking small bubbles. However, for the critical radius of bubble expansion at an elevated temperature, further study is needed.

In-situ measurement of the strength of adhesion to surfaces

Abstract: The strength of adhesion of animal cells, microbial cells, biofilms, and other materials to surfaces, is measured by with a device which comprises a circular plate 2 with a central orifice 1 and a supply pipe 4. Feet 3 at the periphery of plate 2 space it a predetermined distance from a surface on which it stands. In use, liquid is pumped through pipe 4 and opening 1 and flows between plate 2 and the surface to remove material adhered to the surface. The radius of the zone of clearance produced by the flow is measured and used to determine the surface shear stress at the critical radius from the formula where ts = surface shear stress q = flow rate u = viscosity r = critical radius h = distance between plate and surface Laminar and non-laminar flows may be used. The flow rate is constant for a fixed measuring time.