Ishan Sharma

Scaling of granular temperature in vibro-fluidized grains

Granular temperature quantifies velocity fluctuations in fluidized granular materials. There is ongoing effort to understand granular temperature T in vibro-fluidized grains through the power law T∝Vpα, where Vp is peak vibrational velocity. However, the present literature disagrees on the value of α. We utilize dimensional analysis and discrete element simulations to show that granular temperature, and therefore the exponent α, depends crucially on a non-dimensional number W representing the competition between vibrational and gravitational energies but is much less sensitive to other system parameters. Furthermore, change in the barycentric height Δhcm of the vibrated grains, and their temperature T, typically behaves differently with Vp. Thus, Δhcm cannot generally be used as a surrogate for T, as is often done at present. Our computations help explain the currently contradictory results on how granular temperature scales with peak vibrational velocity. Finally, we also briefly investigate the dependen...

Contact of a Rigid Cylindrical Punch with an Adhesive Elastic Layer

We investigate the contact of a cylindrical punch with an adhesive elastic layer or film bonded to a rigid substrate. The classical assumption of Hertzian contact are coupled with tools of fracture mechanics to resolve the contact problem. The contact edges singularity is resolved by introducing a Dugdale-Barenblatt model for the adhesive zone extending in front of the contact region. Exact governing equations so obtained are solved by a semi-analytical technique employing Chebyshev polynomials. We also extend the useful JKR approximation to the indentation of elastic layers as a particular case of our general solution.

Planar equilibria of sessile and pendant liquid drops on geometrically non-linear elastic membranes

Equilibrium shapes are obtained for sessile and pendant liquid drops placed on elastic membranes in two-dimensions. The membrane is allowed to undergo large deformations under the action of capillary forces and fluid pressure. We focus on the global characteristics of the system, like the equilibrium shape of the drop, the membrane’s deformed shape, the apparent contact angle and contact size, and their variation with the volume of the drop for different membrane tensions and drop apex curvatures. It is found that the apparent contact angle is not simply a function of material property but of the system’s geometry as well. The contact size for sessile drops shows a non-monotonic behavior with the volume for all drop apex curvatures. However, for pendant drops, the behavior is strictly monotonic below a critical value of the drop apex curvature.Equilibrium shapes are obtained for sessile and pendant liquid drops placed on elastic membranes in two-dimensions. The membrane is allowed to undergo large deformations under the action of capillary forces and fluid pressure. We focus on the global characteristics of the system, like the equilibrium shape of the drop, the membrane’s deformed shape, the apparent contact angle and contact size, and their variation with the volume of the drop for different membrane tensions and drop apex curvatures. It is found that the apparent contact angle is not simply a function of material property but of the system’s geometry as well. The contact size for sessile drops shows a non-monotonic behavior with the volume for all drop apex curvatures. However, for pendant drops, the behavior is strictly monotonic below a critical value of the drop apex curvature.

An exact dual-integral formulation of the indentation of finite, free-standing, end-supported adhesive elastic layers

We study indentation by a rigid cylindrical punch of finite, free-standing, adhesive elastic layers that are supported only at their ends. The adhesion is considered through an adhesive-zone model. Formulating the boundary-value problem, we obtain two coupled Fredholm integral equations of the first kind, which are solved by a collocation method. Results for non-adhesive contact are obtained when adhesion is zero, and they match well with our own finite element computations and earlier approximate analyses. Additionally, we obtain new results for deeper indentation of non-adhesive contact. In the limit of very adhesive and/or very soft solids, we formulate an approximate model similar to the well-known Johnson–Kendall–Roberts (JKR) model for half-spaces. Our results for adhesive contact match well with preliminary indentation experiments on adhesive layers. Finally, we demonstrate the utility of our approach in modelling structural adhesives through a specific example.

Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

We study the dynamics of an inclined tensioned, heavy cable traveling with a constant speed in the vertical plane. The cable is modeled as a beam resisting bending and shear. The governing equation for the transverse in-plane vibrations of the cable are derived through the Newton-Euler method. The cable dynamics is also studied in the limit of zero bending stiffness. In all cases, application of en- ergy balance reveals that the total energy of the system fluctuates even though the oscillations are small and bounded in time, indicating that the system is nonconser- vative. A comprehensive stability analysis is carried out in the parameter space of inclination, traveling speed, pre-tension, bending rigidity and the slenderness of the cable. Effect of damping is also considered. We conclude that, while pre-tension, rigidity and slenderness enhance the stability of the traveling cable, the angle of inclination affects the stability adversely. These results may act as guidelines for safer design and operation.

Rings of non-spherical, axisymmetric bodies

Abstract We investigate the dynamical behavior of rings around bodies whose shapes depart considerably from that of a sphere. To this end, we have developed a new self-gravitating discrete element N-body code, and employed a local simulation method to simulate a patch of the ring. The central body is modeled as a symmetric (oblate or prolate) ellipsoid, or defined through the characteristic frequencies (circular, vertical, epicyclic) that represent its gravitational field. Through our simulations we explore how a ring’s behavior – characterized by dynamical properties like impact frequency, granular temperature, number density, vertical thickness and radial width – varies with the changing gravitational potential of the central body. We also contrast properties of rings about large central bodies (e.g. Saturn) with those of smaller ones (e.g. Chariklo). Finally, we investigate how the characteristic frequencies of a central body, restricted to being a solid of revolution with an equatorial plane of symmetry, affect the ring dynamics. The latter process may be employed to qualitatively understand the dynamics of rings about any symmetric solid of revolution.

Axial segregation of horizontally vibrated binary granular mixtures in an offset-Christmas tree channel

We investigate segregation in a horizontally vibrated binary granular mixture in a closed offset-Christmas tree channel. The segregation phenomenon occurs in two steps: vertical sorting followed by axial segregation. In the first step, sorting occurs via Brazil-nut effect or reverse Brazil-nut effect depending on the particles’ size and density ratios. The two layers thus formed then separate axially towards opposite-ends of the channel with the top layer always moving towards root of the Christmas tree. We discuss the segregation mechanism responsible for axial segregation.