Settling
Particulates settle under gravity or centrifugal force.
Wikipedia / Wikimedia Commons
Settling is the process where particles move downward through a liquid and accumulate as sediment. Particles subjected to a force—whether from gravity or centrifugal motion—tend to move steadily in the direction of that force. Under gravity, this means particles fall to the bottom of a container, forming sludge or slurry. This operation is important in mining, wastewater and drinking water treatment, biological science, space propellant reignition, and scooping.
In dilute particle solutions, where particles are considered individually, two main forces act on each particle. The primary force is an applied force like gravity, which is generally unaffected by the particle’s velocity. The other is a drag force, which depends on the particle’s speed. A particle at rest experiences no drag, so it accelerates due to the applied force. As it speeds up, drag acts opposite to its motion, slowing further acceleration. Eventually, drag and the applied force become roughly equal, and the particle stops accelerating. This constant speed is called the terminal, settling, or fall velocity, and it can be measured by observing how fast individual particles descend.
Terminal velocity depends on anything that alters drag, so it is strongly influenced by grain size, shape (roundness and sphericity), and density, as well as the fluid’s viscosity and density.
For dilute suspensions, Stokes’ law predicts the settling velocity of small spheres in air or water. This works because viscous forces at the particle’s surface provide most of the retarding force. Stokes’ law is widely used in natural sciences and is expressed as w = 2(ρₚ − ρ_f)gr² / (9μ), where w is settling velocity, ρ is density (p for particle, f for fluid), g is gravity, r is particle radius, and μ is fluid dynamic viscosity. Stokes’ law applies when the particle’s Reynolds number is less than 0.1; experimentally, it holds within 1% for Re ≤ 0.1, within 3% for Re ≤ 0.5, and within 9% for Re ≤ 1.0. As Reynolds numbers increase, fluid inertia becomes more important, and Stokes’ law breaks down, requiring empirical solutions for drag.
In the Newtonian drag regime, a drag coefficient C_d is defined as the ratio of drag force to the fluid’s impact pressure: C_d = F_d / (½ ρ_f U² A). For a spherical particle in this regime, C_d is approximately constant at 0.44, meaning the efficiency of energy transfer from fluid to part
- field
- Physics, Engineering
- known_for
- Process of particulate sedimentation under gravity or centrifugal force
- key_concept
- Terminal velocity and drag regimes (Stokes, transitional, Newtonian)
Lore & Background
Settling occurs when particles experience a force, such as gravity, causing them to move uniformly toward the bottom of a vessel, forming sludge or slurry. For dilute particle solutions, two main forces act on each particle: an applied force (e.g., gravity) and a drag force that opposes motion. Initially at rest, a particle accelerates until drag equals the applied force, reaching terminal velocity. This velocity is affected by grain size, shape, density, and fluid viscosity and density.
Reader's Guide
Stokes' law predicts settling velocity for small spheres in fluid when the Reynolds number is less than 0.1, with the formula w = 2(ρp - ρf)gr²/(9μ). For higher Reynolds numbers, Newtonian drag applies, with a constant drag coefficient of 0.44 for spheres, leading to terminal velocity w = 2.46√((ρp - ρf)gr/ρf). In the transitional regime between Stokes and Newtonian drag, empirical expressions like the Schiller and Naumann equation are used. Hindered settling accounts for particle interactions and container walls, requiring semi-analytic or empirical solutions. These principles are applied in industrial systems such as settling tanks for separating solids or oil from liquids.
Did You Know?
- Stokes' law holds within 1% for Reynolds number ≤ 0.1, within 3% for ≤ 0.5, and within 9% for ≤ 1.0.
- The terminal velocity of a particle is also called settling velocity or fall velocity.
- In the Newtonian drag regime, the drag coefficient for a sphere is approximately constant at 0.44.
- Hindered settling occurs when particle interactions or container walls modify settling behavior.
Frequently Asked Questions
What exactly is Settling?
Settling is a separation method in which solid particles suspended in a liquid gradually sink to the bottom due to gravity or a centrifugal force, eventually forming a layer of sediment. It is one of the oldest and simplest physical purification steps used across many industries.
What forces drive Settling?
Each particle experiences a net downward force—either from gravity pulling it down or from centrifugal acceleration in a spinning vessel. The particle's motion is governed by the balance between that driving force and the fluid drag resisting it, which determines its terminal settling velocity.
What are the key drag regimes in Settling?
Depending on particle size and fluid viscosity, the flow around a settling particle falls into the Stokes (laminar), transitional, or Newtonian (turbulent) regime. Each regime has its own drag-coefficient relationship, which engineers use to predict how fast a given particle will settle.
Where is Settling applied in the real world?
It shows up in mineral processing, drinking-water and wastewater treatment plants, laboratory biology, and even spacecraft propellant management. In each case the goal is to let unwanted solids drop out of a liquid stream so the clarified fluid can be collected separately.
Why is Settling considered a foundational technique?
Because it requires no added chemicals, no membranes, and minimal energy input—just time and proper vessel geometry. It often serves as the first screening step before more sophisticated purification methods take over, making it a workhorse in both industrial and academic settings.
More in Separation And Purification Techniques 1-21
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