Pressureless

Pressureless is a term used to describe a state or model in which the internal pressure of a material or fluid is negligible compared to other forces, so pressure can be set to zero in equations of motion. It serves as a simplifying assumption for studying gravitational, inertial, or diffusive processes without pressure gradients.

In fluid dynamics and astrophysics, pressureless models treat matter as a continuous medium with zero pressure. In cosmology, cold dark matter is commonly modeled as pressureless 'dust', consisting of non-relativistic particles whose dynamics are governed by gravity alone. This approximation captures the growth of large-scale structure but omits pressure support which can resist compression at small scales.

In the mathematics and numerical modeling of fluids, the pressureless Euler equations describe such flows. They can lead to mass concentration and the formation of singularities, such as delta shocks, and are sometimes approximated by sticky particle models in which colliding particles merge while conserving mass and momentum.

In materials science, pressureless sintering is a process in powder metallurgy where powders are heated to diffuse and densify without external applied pressure. This can produce porous ceramics or metals, relying on diffusion and surface tension; the method contrasts with pressing-based techniques and may require careful control of temperature and time.

Limitations include the neglect of pressure effects, which removes a restoring force and the finite sound speed, potentially leading to unphysical results if pressure gradients become important; more complete models often involve multi-phase flows or regularization to handle mass concentration.