Related Experiment Video
Updated: Jul 28, 2026
09:58
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Interface dynamics in hele-shaw flows with centrifugal forces: preventing cusp singularities with rotation
1Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Avenida Diagonal 647, E-08028 Barcelona, Spain.
Summary
We found that rotating Hele-Shaw flows can prevent cusp singularities. A critical rotation rate suppresses these formations for specific initial conditions, offering a way to control fluid dynamics.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Mathematical Physics
Background:
- Hele-Shaw flow describes fluid movement between closely spaced plates.
- Cusp singularities represent a breakdown in the smooth flow behavior.
- Surface tension effects are often studied but can be neglected in certain scenarios.
Purpose of the Study:
- To investigate Hele-Shaw flows in a rotating cell without surface tension.
- To analyze how rotation and injection influence the formation of finite-time cusp singularities.
- To identify conditions that suppress cusp formation.
Main Methods:
- Derivation of exact solutions for rotating Hele-Shaw flows.
- Analysis of the interplay between injection and rotation parameters.
- Mathematical investigation of cusp singularity formation criteria.
Main Results:
- The interplay of injection and rotation modifies cusp formation scenarios.
- A critical rotation rate exists for a subclass of solutions, suppressing cusps for given initial conditions.
- An exact sufficient condition is found to avoid cusps for all initial conditions in the subclass.
Conclusions:
- Rotation is a key factor in controlling singularities in Hele-Shaw flows.
- Understanding critical rotation rates allows for the prevention of flow breakdown.
- Exact conditions for cusp suppression offer predictive power for fluid behavior.
More Related Videos
Related Concept Videos
01:30Dynamics of Circular Motion
An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
01:17Dynamics Of Circular Motion: Applications
Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for...
01:15Thin-Walled Hollow Shafts
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
01:28Irrotational Flow
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
01:17Steady, Laminar Flow Between Parallel Plates
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.