Ain A. Sonin

Molten droplet deposition and solidification at low Weber numbers

Low Weber number deposition of small molten droplets on cold targets is of importance in certain dropwise buildup processes, but at this time, critical elements are absent from our theoretical understanding of the deposition process, and prediction from basic principles is not possible. This paper lays down a framework for understanding low Weber number deposition in terms of similarity laws and experimentation. Based on experiments from the highly viscous limit to the inertia-dominated limit, correlations are given for the spreading velocity, spreading time scales, post-spreading oscillation amplitudes, and oscillation damping time scales. Molten droplets are arrested, and their final solid shape determined, by contact line freezing. In homologous deposition, where the drop and the target are of the same material, the spreading factor is determined principally by the Stefan number, the dimensionless parameter which measures the temperature difference between the fusion point and the target temperature. Some concluding remarks are offered on what needs to be done to accurately compute such deposition processes.

Precise deposition of molten microdrops : the physics of digital microfabrication

Objects, materials or components may be built up by precise deposition of molten microdrops under controlled thermal conditions. This provides a means of ‘digital microfabrication’, or fabrication of 3D objects microdrop by microdrop under complete computer control much in the same way as 2D hard copy is obtained by ink-jet printing. In this paper we present a study of some basic modes of precise deposition and solidification of molten microdrops. The conditions required for controlled deposition are discussed, and experimental results and theoretical analyses are given for various basic deposition modes. These include columnar (i. e. drop-on-drop) deposition at both low and high frequencies, sweep deposition of continuous beads on flat surfaces, and repeated sweep deposition for buildup of larger objects or materials. The theory provides a means for generalizing our particular experimental results, which were obtained with hard waxes, to other melts. An important parameter in the theory is the solidification angle, that is, the apparent contact angle of the solidified melt. Our study indicates that in microscale deposition this angle appears under some conditions to be a property of the melt material, the target material and the characteristic temperatures involved, independent of the spreading dynamics.

Formation and stability of liquid and molten beads on a solid surface

We present an experimental study of the formation and stability of small-scale beads deposited onto a solid surface by sweeping a droplet stream over it. We are concerned particularly with beads formed from molten droplets deposited on a cold substrate, as in the work of Gao & Sonin (1994), but some results of isothermal deposition are also shown. We show that a molten bead forms with parallel contact lines which have been arrested by freezing while the bead itself is still largely in a liquid state, and that the still-molten material is stable when the contact angle is less than ½π and unstable when it exceeds ½π, consistent with Daviss (1980) theory. In addition, we present a relatively simple inviscid theory for small-scale (small Bond number) beads which allows us to compute the wavelength associated with the maximum growth rate of the instability, and show that it agrees with the dominant wavelength in the experiments.

A hydrodynamic theory of desalination by electrodialysis

Abstract A hydrodynamic theory of demineralization by electrodialysis has been developed for a multichannel system with steady laminar flow between plane, parallel membranes. The modeling of the system is found to be governed by four basic similarity parameters: (i) a dimensionless applied potential, (ii) the product of the channel aspect ratio and the inverse Peclet number, (iii) the ratio of brine and dialysate inlet concentrations, and (iv) a parameter measuring membrane resistance. For sufficiently long channels it is shown that there are two distinct regions: a “developing” region where the concentration diffusion layers are growing, and a “developed” region where the diffusion layers fill the channel. Parabolic and uniform velocity profiles are considered and self-consistent solutions are derived for the distributions of salt concentration, electric field and current density in the system, as well as for the total current. An integral method of solution is used. In the limits of low and high polarization analytic solutions are obtained which when matched at their point of equality closely approximate the complete numerical solutions. It is found that under a wide range of operating conditions, the solution for the total current is represented by the empirical formula I ^ = [ 1 − exp ( − Ψ ^ 3 ) ] 1 / 3 , where I and Ψ ^ are, respectively, a dimensionless current and potential embodying the four similarity parameters mentioned. Comparison is made of the calculated limiting total current with experiment.

Theory for electric charging in turbulent pipe flow

Basec on somewhat simplified profiles of turbulent eddy diffusivity and mean vcLacity in turbulent flow, an expression is derived for the convection current in a pipe where electrification occurs at the wall. The expression is in explicit analytic form, and applies for all turbulent Reynolds numbers and all fluid conductivities, from conditions where the Debye length is small compared with the diffusion sublayer (typical aqueous solutions) to conditions where the Debye length is large compared with the sublayer (typical liquid hydrocarbons).

MOTION AND ARREST OF A MOLTEN CONTACT LINE ON A COLD SURFACE : AN EXPERIMENTAL STUDY

An experimental study is presented of the behavior of a molten contact line under conditions which simulate what happens when a molten droplet touches a subcooled solid, spreads partly over it, and freezes. We restrict our attention to the case where the solid and melt are of the same material and have approximately the same thermal properties, and reach two conclusions. First, we show that an advancing molten contact line is arrested at an apparent dynamic contact angle, which for a given material depends primarily on the Stefan number based on the temperature difference between the fusion point and the temperature of the solid over which the melt spreads. Second, during much of the spreading prior to contact-line arrest, the relationship between the melt’s apparent dynamic contact angle and the contact-line speed appears to obey the Hoffman–Tanner–Voinov law with the equilibrium contact angle taken as zero.

Vapor condensation onto a turbulent liquid—I. The steady condensation rate as a function of liquid-side turbulence☆

Abstract Data are presented for the rate of vapor condensation onto a turbulent liquid, the turbulence being isotropic in the horizontal plane and bulk-flow free, and the interface being shear-free and relatively free of waves. A correlation is proposed for the rate coefficient in terms of the liquid-side turbulence intensity, turbulence macroscale and subcooling.

Ion Temperature Sensitive End Effect in Cylindrical Langmuir Probe Response at Ionosphere Satellite Conditions

Computations and experiments are presented for an end effect which can dominate the ion current response of long, cylindrical Langmuir probes in high‐speed collision‐free flows. The end effect, which takes the form of an increase in ion current when the probe is aligned with the flow direction, depends strongly on the plasma properties and flow speed, and can be large even for very long probes when the speed ratio is large and the probe radius small compared with the Debye length. Experimental data are compared with theory, and some apparently contradictory results reported in the literature are reconciled in terms of the end effect.

A porous body model for predicting temperature distribution in wire-wrapped fuel rod assemblies

Abstract A porous body model, new in its application for predicting temperature distributions in wire-wrapped fuel rod assemblies, has been developed. The model developed for thermal transport in wire-wrapped rod bundles is similar in principle to the one which has long been successfully used for heat transfer in fixed beds of packed solids. Although the model is applicable to bundles in forced and mixed (combined forced and free) convection, attention in this paper is confined to bundles operating in forced (negligible natural) convection only. The results obtained from this analysis were found to predict available data with as good a precision as does the more complex analysis.

Brackish water salt rejection by porous hyperfiltration membranes

Abstract A theory is developed for the rejection of multiple salts by a macroporous hyperfiltration membrane, modelled by cylindrical pores, whose interior surfaces acquire a constant potential when in contact with the salt ions. With three ion types and two valences the ion rejections are shown to depend on the ratio of Debye length to pore radius, a dimensionless wall potential, a filtration Peclet number, and the ratios of concentrations and charge numbers of two of the ions of different valence. Numerical solutions for the rejections are given for large Peclet number and analytic solutions when the Debye length is also large.