Limit for Small Spheres To Float by Dynamic Analysis

Abstract

Small spheres released above the liquid surface experience a dynamic process to ultimately float or sink, and thus, their behaviors should be considered by dynamic analysis instead of static equilibrium. This study numerically investigates the motion of small spheres after contacting the liquid surface with zero velocity, and the flotation condition is proposed based on the analyses of acting forces and the sphere's motion. Whether the small spheres float is determined by the density ratio, Bond number, and contact angle. A critical contact angle exists, below which the flotation of small spheres is impossible. The decrease in Bond number and increase in hydrophobicity enlarge the limit density ratio for small spheres to float, while exerting little effect on large spheres. The theoretical formulas of the limit density ratio are obtained based on energy balance and agree well with numerical results. The limit density ratio predicted in consideration of a dynamic process is far less than the maximum density ratio predicted by static equilibrium.

Impact Behavior of Hydrophilic Micron Particles on a Planar Gas–Liquid Interface

“…Ji et al established a critical curve, determined by the density ratio, Bond number, and contact angle, to predict the behavior of particles contacting the interface with zero downward velocity. According to the regime map, the micron particles with initial impact velocity should sink into the liquid because the density ratio ρ p /ρ f equals 2.49 and the Bond number ranges from 0.001 to 0.079 in this study.…”

“…The position of the TPCL remains constant and w i decreases slightly because of the confinement effect induced by the viscous and Marangoni stress. Ji et al 31 established a critical curve, determined by the density ratio, Bond number, and contact angle, to predict the behavior of particles contacting the interface with zero downward velocity. According to the regime map, the micron However, some particles still can suspend on the interface.…”

Impact-induced hole growth and liquid film dewetting on superhydrophobic surfaces

“…where In is the modified Bessel function of the first kind, Kn is the Bessel function of the second kind, and n is the order of the Bessel function. 29,34 The analytical solution for the volume V can be deduced as:…”

Analisis Termodinamika Molekul Magnesium Sulphate (MgSO4)

“…Untuk menahan partikel bermuatan agar kecepatan rata-rata tetap digunakan kecepatan hanyut. Kecepatan hanyut (243)(244)(245)(246)(247) mempunyai arah sama dengan medan listrik dan hubungan keduanya dinyatakan dalam suatu konstanta yang disebut dengan mobilitas.…”