Sphere-sphere System Research Articles

Investigation about validity of the Derjaguin approximation for electrostatic interactions for a sphere-sphere system

Validity of the Derjaguin approximation for sphere-sphere electrostatic interactions is investigated by explicitly determining the interactions between two spherical colloids using classical density functional theory (CDFT) solved in bispherical coordinates. The validity rules are summarized as follows. (i) For 1:1 type electrolyte, the Derjaguin approximation is effective for colloid sphere having a diameter down to three times the ion diameter only if the bulk concentration is higher than 0.1 M. (ii) With presence of higher-valence counter-ion, the threshold value bulk concentration rises, and increasing the colloid sphere diameter can lower greatly the threshold value bulk concentration. Encouragingly, over the valid parameter region of the Derjaguin approximation a like-charge attraction can be reproduced accurately. (iii) Both too low and too high surface charge strengths contribute to lower the quality of the Derjaguin approximation; increasing the medium permittivity or system temperature improves the accuracy of the Derjaguin approximation. (iv) Based on the mechanism analysis on the above observations, it is concluded that what matters in determining the validity of the Derjaguin approximation is the potential range of the pure inter-surface electrostatic interactions and the local Debye length rather than the bulk Debye length. Besides, the different expressivity of the influencing factors causing the effective inter-surface electrostatic interactions at different conditions determines the behavior the Derjaguin approximation deviates from the full CDFT calculations.

Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces.

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential μ. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T,μ, or L, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping, and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.

Detection of ionizing radiation generated by electrical discharges in the air using sphere-sphere system

The article presents the results of studies on the detection of ionizing radiation generated during electrical discharges. The obtained energy spectra for a system of sphere spark gaps, and the dependence of the obtained energies on the geometric arrangements of the detection devices and of the electrical discharge generating devices are presented. Additionally, the recorded signals from the scintillation detector, and the energy spectrum received for the examined system are also presented. It is significant that the field distribution related to the shape of the spark gaps is of key importance for the received measurement data. The completed studies for the sphere - shaped spark gaps are a part of studies on recording ionizing radiation generated by full and partial discharges in the air and in mineral oil.

구-구갭의 섬락 특성에 미치는 연소화염의 영향

본 연구에서는 구-구갭을 수평 배치하였을 때, 연소화염에 의한 교류 및 직류 플래시오버전압 특성을 조사하였다. 화염에 의한 플래시오버 극성을 조사하기 위해 전압 및 전류파형을 측정하였으며, 플래시오버가 발생되기 전에 쿨롱력에 의한 화염의 형상 변화를 관찰하였다. 또한 플래시오버 전압의 저하 요인으로서 상대공기밀도의 저하 및 연소화염의 열전리 영향에 대해 고찰하였다. 실험 결과, 구-구갭에서 접지측 전극과 갭길이의 비를 k라고 할 때, 화염위치 k=0(접지측), k=0.5(중앙부) 및 k=1.0(전원측)인 경우 화염에 의한 교류 섬락전압의 평균값은 화염이 없을 때에 비해 각각 79.9, 82.9 및 87.5[%] 저하되었으며, 또한 화염의 높이 h=0, h=5 및 h=9[cm]일 때 교류 플래시오버전압의 평균값은 화염이 없는 경우를 기준으로 하였을 때 각각 85.0, 40.8 및 28.2[%] 저하되었다. 소규모 연소화염에서의 열전리 영향은 크지 않는 것으로 나타났다.

Force balance in systems of spherical polyelectrolytes

Equilibrium separation distances in a model system composed of two spherical polyions is analyzed as a function of the pH and ionic strength of the bathing solution. The separations are determined graphically as a force balance between electrostatic repulsion and van der Waals attraction. From basic input such as the surface density of ionizable groups and the corresponding dissociation characteristics of these groups, a self-consistent functional of the potential is developed from which the electrostatic repulsive force may be obtained. For the van der Waals attractive force, the Hamaker functional form for the interaction energy between spheres is used with a Hamaker constant chosen by fitting the asymptotic form of the Hamaker expression to a more rigorous form based on the Lifshitz theory. It is found that the general behavior of the sphere-sphere system as a function of the pH and ionic strength of the bathing solution closely parallels that for systems of parallel cylindrical polyions.