We survey rigorous, formal, and numerical results on the formation ofpoint-like singularities (or blow-up) for a wide range of evolutionequations. We use a similarity transformation of the original equation withrespect to the blow-up point, such that self-similar behaviour is mapped tothe fixed point of an infinite dimensional dynamical system. ...
Creator:
Eggers, Jens (University of Bristol)
Created:
2008-07-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds Ca = Uη/γ of order unity, a near-cusp forms due to the contact line. The radius of curvature of the cusp’s tip scales by the slip length multiplied by an exponential of -Ca. The pressure from the air flow drawn ins...
Creator:
Eggers, Jens (University of Bristol)
Created:
2018-03-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Viscous flow is extremely effective in deforming a freesurface into very sharp features such as tips or cups. Under increaseddriving such free surface singularities may turn unstable, andgive way to secondary structures. In particular, this may be turnedinto a method to 'manufacture' small things by using the nonlinearcharacter of the equations ...
Creator:
Eggers, Jens (University of Bristol)
Created:
2009-12-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We report on recent experimental and theoretical work onthe pinch-off of dilute solutions of flexible polymers. Owing tothestrong extensional hardening of such solutions, pinch-off of aliquid drop is delayed. Instead, long threads of uniformthicknessform, whose radius decreases exponentially in time. We derive arelationship between the thread ra...
Creator:
Eggers, Jens (University of Bristol)
Created:
2009-10-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.