Dissolution Problem Research Articles

The general solution and its analyticity for growth or dissolution of a gas bubble

The isothermal diffusion of a gas bubble in an infinite liquid which is either supersaturated or undersaturated, subject to an arbitrarily prescribed initial condition and the effect of surface tension at the interface, is studied. One of the objectives of the paper is to investigate the analyticity of the solutions. For this purpose, the prescribed initial condition is considered to be a series of fractional powers of the space variable. It is found that the solution of the problem can be established in series of parabolic cylinder functions and time t. Existence and convergence of the series solutions are considered and proved. For a dissolution problem, the solution always exists. The lifetime of the bubble is determined. On the other hand, the solution of a growing bubble exists only when the initial condition at the interface is below a certain limit. A necessary and sufficient condition for the existence of solutions is established. Some numerical examples of the interfacial position are also given. On the basis of the established solutions, the analyticities of the interfacial boundary and of gas concentration are discussed. The interfacial boundary is analytic in t1/2 if, and only if, the initial condition is an analytic function of the space variable.

A collocation method using B-splines for one-dimensional heat or mass-transfer-controlled moving boundary problems

A collocation method employing B-splines as approximating functions in the space variable and Gaussian quadrature points as the collocation points is developed for treating the heat or mass-transfer-controlled one-dimensional dissolution problems. It is demonstrated that this method provides an alternative technique which is considerably more accurate than the finite-difference method even at the very end of the dissolution process. The method presented here is first applied to the dissolution problem in the plane slab geometry where direct comparison has been made with the exact solution to assess the accuracy of the method. For spherical particle dissolution, the method is then compared with the existing finite-difference solution where it is shown that a more accurate solution can be obtained with considerably fewer equations.

Etude d'un karst calcaire littoral méditerranéen. Exemple du littoral de Nice à Menton

The French Riviera is adorned by three capes which point towards the sea and show on their coast low platforms carved in limestone (3-4 m above sea-level). These are hardly attacked into coastal karsts which show strickingly hackly surfaces, little pools and, sometimes, a notch (a few cm above mean sea level). A two meters wide platform always swashed is often observed. These forms are little but well dra- wed up : this is a «dwarf coastal karst». Many measures of pH and Alcali nit y had been done but no diurnal cycle had been observed. It seems impossible to generalize EMERY's results to anon-tidal sea as West Mediterranean sea. So the famous limestone dissolution problem must be studied on these coasts again. However, the limestone surface zonationis easily explained by biological weathering. Several research workers of Endoume Marine Station have shown that biological erosion is active and that undercutted edges of flat pools can be explained by differencial corrosion processus owing to some species of Entophysalis algae.

Thermodynamics of gas-containing voids in metals

Irradiation of materials frequently induces high supersaturations of vacancies and of dissolved inert gas atoms which may, under certain conditions, co-precipitate into voids. An expression is derived for the free energy change on forming such a void and is expressed in terms of vacancy supersaturations, the concentration and binding energy of the dissolved gas atoms, external pressure, strain energy and such usual ancillary data as surface energy and atomic volume. This free energy may be utilized to obtain boundary conditions for void growth and dissolution problems. An expression is derived for the homogeneous nucleation rate of voids, from which it is seen that externally applied pressures should usually have little effect on void formation. Dissolved gas atoms may, however, contribute as much to the driving force for nucleation as does a very high vacancy supersaturation. Finally, it is noted that in omitting the effects of solvent interstitials, the present analysis is not directly applicable to fast-breeder reactor phenomena.

Heat or mass transfer-controlled dissolution of an isolated sphere

A comprehensive set of finite-difference solutions describing the heat or mass transfer-controlled dissolution of isolated spheres is presented. The analysis is based on a generalized formulation which includes three specific classes of dissolution problems. A coordinate transformation which immobilizes the moving boundary and maps the infinite region of interest into a finite region is used to minimize the difficulties associated with a numerical analysis of this problem. Radius-time and particle lifetime results are reported for ranges of parameters which include the majority of physically important dissolution processes. In addition, the results of this investigation are used to determine the accuracy and range of applicability of various approximate analytical solutions.

A method for the calculation of the correct and most economical concentrations of Elon and hydroquinone in a borax developer for motion picture film

Sulfur is an advantageous material as a promising next-generation positive electrode material for high-energy lithium batteries due to a high theoretical capacity of 1672 mA h g−1 although its discharge potential is somewhat modest: ca. 2 V vs Li/Li+. However, a sulfur positive electrode has some crucial problems for practical use, which are mainly attributed to the dissolution of its intermediate products in charge–discharge processes. In order to resolve the dissolution problem of lithium polysulfide, we attempted to synthesize a sulfur–microporous activated carbon (AC) composite positive electrode. Moreover, we have systematically researched the battery performance of sulfur–microporous AC positive electrode with variations of electrolytes as well as negative electrodes, and found its promising positive electrode performance for a next-generation rechargeable battery.