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...

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...

Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...

In column chromatography, when an analyte is introduced as a narrow band at the top of the column, the solutes begin to separate and broaden, developing a Gaussian profile. This broadening occurs due to various factors, such as longitudinal diffusion.
Longitudinal diffusion occurs when the solute molecules in the mobile phase diffuse from the more concentrated center of the chromatographic band to the more dilute regions on either side, both towards and against the flow direction. This...

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...

The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. The overall ΔGsolution is expressed as the balance of ΔGinteraction against the always-favorable free-energy of mixing, ΔGmixing. Solution formation is favorable if  ΔGsolution is less than zero, whereas it is unfavorable if ΔGsolution is greater than zero. In short, for a solution to form and complete dissolution to take place,...