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