51 research outputs found
Surface tension of flowing soap films
The surface tension of flowing soap films is measured with respect to the
film thickness and the concentration of soap solution. We perform this
measurement by measuring the curvature of the nylon wires that bound the soap
film channel and use the measured curvature to parametrize the relation between
the surface tension and the tension of the wire. We find the surface tension of
our soap films increases when the film is relatively thin or made of soap
solution of low concentration, otherwise it approaches an asymptotic value 30
mN/m. A simple adsorption model with only two parameters describes our
observations reasonably well. With our measurements, we are also able to
measure Gibbs elasticity for our soap film.Comment: 14 pages, 4 figure
Stability of the Matrix Model in Operator Interpretation
The IIB matrix model is one of the candidates for nonperturbative formulation
of string theory, and it is believed that the model contains gravitational
degrees of freedom in some manner. In some preceding works, it was proposed
that the matrix model describes the curved space where the matrices represent
differential operators that are defined on a principal bundle. In this paper,
we study the dynamics of the model in this interpretation, and point out the
necessity of the principal bundle from the viewpoint of the stability and
diffeomorphism invariance. We also compute the one-loop correction which
possibly yields a mass term for each field due to the principal bundle. We find
that the correction does generate some mass terms with the supersymmetry
broken, while fields in the original IIB matrix model remain massless. The
positivity is not violated as long as the number of bosonic degrees of freedom
is larger than the fermionic counterpart. The generation of mass terms means
that the new mass scale emerges through the loop correction.Comment: 20 pages, 6 figure
Work-minimizing kinematics for small displacement of an infinitely long cylinder
We consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If t represents the time since the commencement of motion and T the final time, then the optimum speed profile is Ct^{1/4}(T-t)^{1/4} , where C is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves
Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid
We determine the globally minimum time T needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined computationally using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a ‘spectral condition’ to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed ∝t1/4 and comes to rest with speed ∝(T−t)1/4 as a function of time t. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping
Monami as an oscillatory hydrodynamic instability in a submerged sea grass bed
The onset of monami ~-- the synchronous waving of sea grass beds driven by a
steady flow -- is modeled as a linear instability of the flow. Unlike previous
works, our model considers the drag exerted by the grass in establishing the
steady flow profile, and in damping out perturbations to it. We find two
distinct modes of instability, which we label Mode 1 and Mode 2. Mode 1 is
closely related to Kelvin-Helmholtz instability modified by vegetation drag,
whereas Mode 2 is unrelated to Kelvin-Helmholtz and arises from an interaction
between the flow in the vegetated and unvegetated layers. The vegetation
damping, according to our model, leads to a finite threshold flow for both
these modes. Experimental observations for the onset and frequency of waving
compare well with model predictions for the instability onset criteria and the
imaginary part of the complex growth rate respectively, but experiments lie in
a parameter regime where the two modes can not be distinguished. % The
inclusion of vegetation drag differentiates our mechanism from the previous
linear stability analyses of monami.Comment: 4 figures, 13 page
Dynamics of evaporative colloidal patterning
Drying suspensions often leave behind complex patterns of particulates, as
might be seen in the coffee stains on a table. Here we consider the dynamics of
periodic band or uniform solid film formation on a vertical plate suspended
partially in a drying colloidal solution. Direct observations allow us to
visualize the dynamics of the band and film deposition, and the transition in
between when the colloidal concentration is varied. A minimal theory of the
liquid meniscus motion along the plate reveals the dynamics of the banding and
its transition to the filming as a function of the ratio of deposition and
evaporation rates. We also provide a complementary multiphase model of colloids
dissolved in the liquid, which couples the inhomogeneous evaporation at the
evolving meniscus to the fluid and particulate flows and the transition from a
dilute suspension to a porous plug. This allows us to determine the
concentration dependence of the bandwidth and the deposition rate. Together,
our findings allow for the control of drying-induced patterning as a function
of the colloidal concentration and evaporation rate.Comment: 11 pages, 7 figures, 2 table
Splashing or not
The splashing of a droplet when impacting a solid surface is common to our everyday experience as well as to industrial applications that require controlled deposition of liquid mass. Still the mechanism for splashing is not well understood. A recent study showed that a decrease in the ambient pressure inhibits splashing, motivating a hypothesis on the existence of a thin film of air trapped between the drop and the surface. The early dynamics of splashing could occur while the drop is still spreading on an air film. To gain insight into this early dynamics,
we supplement the side view with a synchronized bottom view, obtained using a novel Total Internal Reflection technique. I will discuss the existence of a transition regime between spreading and splashing. This regime appears by changing the impact velocity or the ambient pressure, while keeping the other fixed
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