Fractal colloidal aggregates with finite interparticle interactions: Energy dependence of the fractal dimension

The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called the...

Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles that are visible to the naked eye or can be seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. On the other hand, a solution is a homogeneous mixture in which no settling occurs and in which the dissolved...

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...

The high insolubility of some precipitates can result in an unfavorable relative supersaturation. This can lead to colloidal particles with a large surface-to-mass ratio, where adsorption is promoted. For instance, in the precipitation of silver chloride, silver ions are adsorbed on the surface of the colloidal particles, forming a primary layer. This layer attracts ions of opposite charge (such as nitrate ions), forming a diffuse secondary layer of adsorbed ions. This electric double layer...

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen bonds, and dispersion...

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...