2,628 research outputs found

    Self-similar breakup of polymeric threads as described by the Oldroyd-B model

    Get PDF
    When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations

    Cusp-shaped Elastic Creases and Furrows

    Get PDF
    The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup, which permits to deform the surface of a soft gel in a controlled fashion. The interface first forms a sharp furrow, whose tip size decreases rapidly with deformation. Above a critical deformation, the furrow bifurcates to an inward folded crease of vanishing tip size. We show experimentally and numerically that both creases and furrows exhibit a universal cusp-shape, whose width scales like y3/2y^{3/2} at a distance yy from the tip. We provide a similarity theory that captures the singular profiles before and after the self-folding bifurcation, and derive the length of the fold from large deformation elasticity.Comment: 5 pages, 4 figure

    Flight craft Patent

    Get PDF
    Designing spacecraft for flight into space, atmospheric reentry, and landing at selected site

    Anomalous dimensions of the Smoluchowski coagulation equation

    Get PDF
    The coagulation (or aggregation) equation was introduced by Smoluchowski in 1916 to describe the clumping together of colloidal particles through diffusion, but has been used in many different contexts as diverse as physical chemistry, chemical engineering, atmospheric physics, planetary science, and economics. The effectiveness of clumping is described by a kernel K(x,y)K(x,y), which depends on the sizes of the colliding particles x,yx,y. We consider kernels K=(xy)γK = (xy)^{\gamma}, but any homogeneous function can be treated using our methods. For sufficiently effective clumping 1γ>1/21 \ge \gamma > 1/2, the coagulation equation produces an infinitely large cluster in finite time (a process known as the gel transition). Using a combination of analytical methods and numerics, we calculate the anomalous scaling dimensions of the main cluster growth, calling into question results much used in the literature. Apart from the solution branch which originates from the exactly solvable case γ=1\gamma = 1, we find a new branch of solutions near γ=1/2\gamma = 1/2, which violates scaling relations widely believed to hold universal

    Selection of singular solutions in non-local transport equations

    Get PDF

    Air entrainment through free-surface cusps

    Get PDF
    In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations
    corecore