A comparison between the experimental process parameters employed for the pulse plating of nanocrystalline nickel and the solution-side mass transfer and electrokinetic characteristics has been carried out. It was found that the experimental process parameters (on-time, off time and cathodic pulse current density) for cathodic rectangular pulses are consistent and within the physical constraints (limiting pulse current density, transition time, capacitance effects and integrity of the waveform) predicted from theory with the adopted postulates. This theoretical analysis also provides a means of predicting the behaviour of the process subject to a change in the system, kinetic and process parameters. The product constraints (current distribution, nucleation rate and grain size), defined as the experimental conditions under which nanocrystalline grains are produced, were inferred from electrocrystallization theory. High negative overpotential, high adion population and low adion surface mobility are prerequisites for massive nucleation rates and reduced grain growth; conditions ideal for nanograin production. Pulse plating can satisfy the former two requirements but published calculations show that surface mobility is not rate-limiting under high negative overpotentials for nickel. Inhibitors are required to reduce surface mobility and this is consistent with experimental findings. Sensitivity analysis on the conditions which reduce the total overpotential (thereby providing more energy for the formation of new nucleation sites) are also carried out. The following lists the effect on the overpotential in decreasing order: cathodic duty cycle, charge transfer coefficient, Nernst diffusion thickness, diffusion coefficient, kinetic parameter (γ) and exchange current density.

Mass transfer and electrocrystallization analyses of nanocrystalline nickel production by pulse plating

An exact analytical study is presented for the electrophoretic motion of a dielectric sphere in the proximity of a large non-conducting plane. The applied electric field is parallel to the plane and uniform over distances comparable with the particle radius. The particle and plane surfaces are assumed uniformly charged and the thin-double-layer assumption is employed. The presence of the wall causes three basic effects on the electrophoretic velocity: first, an electro-osmotic flow of the suspending fluid exists owing to the interaction between the electric field and the charged wall; secondly, the electrical field lines around the particle are squeezed by the wall, thereby speeding up the particle; and thirdly, the wall enhances viscous retardation of the moving particle. In the analysis, corrections to Smoluchowski's classic equation for the electrophoretic velocity in an unbounded fluid are presented for various separation distances between the particle and the wall. Of particular interest is the electrophoresis for small gap widths, in which case the net effect of the plane wall is to enhance the particle velocity. The particle mobility can be increased by as much as 23% when the surface-to-surface spacing is about 0.5% of the sphere radius. For the case of moderate to large separations, the electrophoretic velocity of the particle is reduced by the wall, but this effect is much weaker than for sedimentation. In addition to the translational migration, the electrophoretic sphere rotates at the same time in the direction opposite to that which would occur if the sphere sedimented parallel to a plane wall. The ratio of rotational-to-translational speeds of the sphere is in general larger for electrophoresis than for sedimentation.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112088003039

Electrophoresis of a colloidal sphere parallel to a dielectric plane

Thermocapillary interaction of two bubbles or drops

Droplet interactions in thermocapillary motion

The thermocapillary motion of immiscible spherical droplets placed in an unbounded fluid with a linear temperature distribution is analyzed. For small Marangoni numbers, an exact solution to the Navier-Stokes equations has been found. The velocity field and the terminal velocity of the droplet are the same as those calculated by previous workers in the small Reynolds number limit. Hence the range of applicability of their results has been extended to arbitrary Reynolds numbers, so long as Ma = PrRe remains small (i.e., the convection of energy can be neglected). The shape of the droplet has also been calculated, when the deformations from the spherical shape are small. The results are qualitatively in agreement with the previous results, in the limit Pr → 0, that droplets of the same density as the host fluid do not deform at all, that bubbles tend to deform oblately, and that droplets with the denser fluid inside tend to elongate in the flow direction.

Thermocapillary migration of droplets: an exact solution for small Marangoni numbers

The slow axisymmetric motion of two bubbles in a thermal gradient

The influence of a plane solid or fluid surface on the thermocapillary migration of a gas bubble moving normal to it in a space laboratory is investigated in the quasi-static limit. Results are presented for a suitably defined “interaction” parameter Ω as a function of the scaled distance of the bubble from the plane surface, and compared with similar predictions for buoyant migration.

Thermocapillary migration of a bubble normal to a plane surface

The interaction problem of two bubbles oriented at an arbitrary angle to a thermal gradient in the absence of gravity is studied. The problem is considered in the quasi-static limit, wherein unsteady and convective transport terms are completely neglected in the momentum and energy equations. Instead of bipolar coordinates, an approximation used in a previous analysis of the interaction effects of two bubbles moving along their line of centers in a thermal gradient is applied here to predict the interaction parameter.

The thermocapillary motion of two bubbles oriented arbitrarily relative to a thermal gradient

Mathematical modeling of alternating current modulation of a copper rotating disk electrode in an acid sulfate solution

An experiment was carried out on board a Space Processing Applications Rocket with the aim of demonstrating bubble migration in molten glass due to a temperature gradient under low gravity conditions. During the flight, a sample of a sodium borate melt with a specific bubble array, contained in a platinum/fused silica cell, was subjected to a well defined temperature gradient for more than 4 minutes. Photographs taken at one second intervals during the experiment clearly show that the bubbles move toward the hot spot on the platinum heater strip. This result is consistent with the predictions of the theory of thermocapillary driven bubble motion.

M. Meyyappan

Papers

The slow axisymmetric motion of two bubbles in a thermal gradient

Thermocapillary migration of a bubble normal to a plane surface

The thermocapillary motion of two bubbles oriented arbitrarily relative to a thermal gradient

Mathematical modeling of alternating current modulation of a copper rotating disk electrode in an acid sulfate solution

Experimental observation of the thermocapillary driven motion of bubbles in a molten glass under low gravity conditions