Landau–Levich problem

A thin-film fluid problem determining the coating deposited on a plate withdrawn slowly from a liquid bath through the balance of viscous, capillary and gravitational effects.

Version

v1 · 2026-09-08 · History

Domain-specific #

5256

Origin domain

fluid dynamics

Subdomain

specialized structures

Core Idea

The Landau–Levich problem predicts the entrained film connecting a dynamic meniscus to a uniform coating. Lubrication flow and curvature pressure are matched between static and dynamic meniscus regions, yielding the characteristic capillary-number scaling of film thickness. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of fluid dynamics. It is A thin-film fluid problem determining the coating deposited on a plate withdrawn slowly from a liquid bath through the balance of viscous, capillary and gravitational effects.

Scope of Application

Landau–Levich problem belongs to fluid dynamics and is useful where the analyst can specify a plate withdrawn at speed, Newtonian liquid bath, viscosity, density, surface tension, gravity, meniscus regions, capillary number and far-field film thickness, then evaluate the slow-withdrawal, thin-film, wetting and matching assumptions are explicit before using the classical scaling law. The scope is broad within that domain but bounded by the need for the slow-withdrawal, thin-film, wetting and matching assumptions are explicit before using the classical scaling law. Conceptual fluid-mechanics identity, not an industrial operating protocol.

Clarity

The abstraction clarifies a crowded vocabulary by making the slow-withdrawal, thin-film, wetting and matching assumptions are explicit before using the classical scaling law the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Landau–Levich problem can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Landau–Levich problem. Landau–Levich problem compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: a plate withdrawn at speed, Newtonian liquid bath, viscosity, density, surface tension, gravity, meniscus regions, capillary number and far-field film thickness. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the slow-withdrawal, thin-film, wetting and matching assumptions are explicit before using the classical scaling law independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of fluid dynamics because they reuse a plate withdrawn at speed, Newtonian liquid bath, viscosity, density, surface tension, gravity, meniscus regions, capillary number and far-field film thickness, Lubrication flow and curvature pressure are matched between static and dynamic meniscus regions, yielding the characteristic capillary-number scaling of film thickness., and type the carrier, state every parameter and convention in the definition, test that the slow-withdrawal, thin-film, wetting and matching assumptions are explicit before using the classical scaling law, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Landau–Levich problem Domain-specific

Parents (1) — more general patterns this builds on

• Landau–Levich problem is a kind of Equilibrium Prime

  The proposed strict upward parent is prime:equilibrium.

Hierarchy path (1) — routes to 1 parentless root

• Landau–Levich problem → Equilibrium → Fixed Point

Neighborhood in Abstraction Space

Landau–Levich problem sits in a sparse region of the domain-specific corpus (65^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Fluid Flow & Transport (27 abstractions)

Nearest neighbors

• Marangoni number — 0.87
• Stefan adhesion — 0.86
• Chaotic mixing — 0.85
• Frenkel–Kontorova model — 0.85
• Immersed boundary method — 0.85

Computed from structural-signature embeddings · 2026-09-08