Shreyas Mandre

Associate Professor
Mathematics Institute, University of Warwick
       

Research

As matters of scientic research go, the devil is in the detail. It is blasphemous to subject the fruits of scientific endeavour to the imperfections of everyday language. But not everyone has the leisure and liberty to delve into the depths of the deliberations on scientific topics. This page is dedicated for such individuals. For the scientists and scientifically oriented, it is a must to follow the scientific publications. Generous links to the publications may be found throughout.

We scientists are mere instruments in the hands of nature. We dig around the clues dispersed by her all around so lavishly. We rejoice when we spot one of those clues while being completely oblivious of how many more lie in plain sight and are missed everyday. Collectively, these clues are the brush-strokes that build a picture one stroke at a time. Here are some of my brush strokes.

Feet and fins


Arches in the foot (credit: M. Venkadesan, Yale University)

BBC Scotland radio segment (courtesy: Newsdrive by Mhairi Stuart)

Why do our feet look the way they do? Believe it or not, some of us do ask ourselves this question.

... (read more)

Publications

Venkadesan, Yawar, Eng, Dias, Singh, Tommasini, Haims, Bandi and Mandre. Stiffness of the human foot and evolution of the transverse arch. Nature 579, 97-100 (2020).
PDF Publisher link

Abstract: The stiff human foot enables an efficient push-off when walking or running, and was critical for the evolution of bipedalism. The uniquely arched morphology of the human midfoot is thought to stiffen it, whereas other primates have flat feet that bend severely in the midfoot. However, the relationship between midfoot geometry and stiffness remains debated in foot biomechanics, podiatry and palaeontology. These debates centre on the medial longitudinal arch and have not considered whether stiffness is affected by the second, transverse tarsal arch of the human foot. ... (read more)

Biomechanics Foot Evolution

Dhawale, Mandre and Venkadesan. Dynamics and stability of running on rough terrains. R. Soc. Open Sci. 6: 181729 (2019).
PDF Publisher link

Abstract: Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. ... (read more)

Biomechanics Running

Nguyen, Yu, Bandi, Venkadesan and Mandre. Curvature-induced stiffening of fish fin. J. R. Soc. Interface. 14: 20170247.
PDF Publisher link

Abstract: How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin’s curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. ... (read more)

Biomechanics Fish fins

Fluid mechanical kinematic optimization


The fastest flat-plate under fixed energy budget

In 1696, Johann Bernoulli posed a challenge called the brachistochrone problem, which kickstarted the field of calculus of variations. Here is simplest fluid mechanical version of the brachistochcrone problem.

... (read more)

Publications

Mandre. Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid. J. Fluid Mech., 939 A27 (2022).
PDF Publisher link

Abstract: 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. ... (read more)

Fluid mechanics Optimization Boundary Layers

Mandre. Work-minimizing kinematics for small displacement of an infinitely long cylinder. J. Fluid Mech. 893 R4 (2020).
PDF Publisher link

Abstract: 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. ... (read more)

Fluid mechanics Optimization Boundary Layers

Flowing soap films


Measuring the Marangoni elasticity of soap films.

Ever wondered why you can blow bubbles from soap solution in water, but not from water itself or from a solution of sugar or salt?

... (read more)

Publications

Sane, Mandre and Kim. Surface tension of flowing soap films. J. Fluid Mech. 841, R2 (2018).
PDF Publisher link

Abstract: 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 that the surface tension of our soap films increases when the film is relatively thin or is made of soap solution of low concentration; otherwise, it approaches an asymptotic value of 30 mN/m. ... (read more)

Fluid Mechanics Surfactants

Kim and Mandre. Marangoni elasticity of flowing soap films. Phys. Rev. Fluids 2, 082001(R) (2017).
PDF Publisher link

Abstract: We measure the Marangoni elasticity of a flowing soap film to be 22 mN/m irrespective of its width, thickness, flow speed, or the bulk soap concentration. We perform this measurement by generating an oblique shock in the soap film and measuring the shock angle, flow speed, and thickness. We postulate that the elasticity is constant because the film surface is crowded with soap molecules. Our method allows nondestructive measurement of flowing soap film elasticity and the value 22 mN/m is likely applicable to other similarly constructed flowing soap films. ... (read more)

Fluid Mechanics Surfactants

Mandre. Axisymmetric spreading of surfactant from a point source. J. Fluid Mech. 832, 777-792 (2017).
PDF Publisher link

Abstract: Guided by computation, we theoretically calculate the steady flow driven by the Marangoni stress due to a surfactant introduced on a fluid interface at a constant rate. Two separate extreme cases, where the surfactant dynamics is dominated by the adsorbed phase or the dissolved phase, are considered. We focus on the case where the size of the surfactant source is much smaller than the size of the fluid domain, and the resulting Marangoni stress overwhelms the viscous forces so that the flow is strongest in a boundary layer close to the interface. ... (read more)

Fluid Mechanics Surfactants

Bandi, Akella, Singh, Singh and Mandre. Hydrodynamic signatures of stationary Marangoni-driven surfactant transport. Phys. Rev. Lett. 119, 264501 (2017).
PDF Publisher link

Abstract: We experimentally study steady Marangoni-driven surfactant transport on the interface of a deep water layer. Using hydrodynamic measurements, and without using any knowledge of the surfactant physicochemical properties, we show that sodium dodecyl sulphate and Tergitol 15-S-9 introduced in low concentrations result in a flow driven by adsorbed surfactant. At higher surfactant concentration, the flow is dominated by the dissolved surfactant. Using camphoric acid, whose properties are a priori unknown, we demonstrate this method’s efficacy by showing its spreading is adsorption dominated. ... (read more)

Fluid Mechanics Surfactants

Waving marine grass

Realization of the synchronized wind-induced waving of grass in a flowing soap film.

I bet you have seen gusts of wind exciting synchronized waves on the surface of tall grass field just like observed on the beach.

... (read more)

Publications

Singh, Bandi, Mahadevan and Mandre. Linear stability analysis for monami in a submerged seagrass bed. J. Fluid Mech. 786, R1 (2016).
PDF Publisher link

Abstract: The onset of monami – the synchronous waving of seagrass beds driven by a steady flow – is modelled 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 modes 1 and 2. Mode 1 is closely related to Kelvin–Helmholtz instability modified by vegetation drag, whereas mode 2 is unrelated to Kelvin–Helmholtz instability and arises from an interaction between the flow in the vegetated and unvegetated layers. ... (read more)

Fluid Mechanics Biomechanics Environment

Cheerios effect

Capillary attraction between triangles that show the influence of sharp and flat boundaries.

Pour milk into a bowl, drop in some Cheerios (the breakfast cereal), and notice how they clump together. This attraction is mediated by gravity and surface tension. Each cheerio makes a little depression in the milk-air interface, and the neighbouring one just falls into it.

... (read more)

Publications

He, Nguyen and Mandre. Capillary interactions between nearby interfacial objects. Europhys. Lett. 102, 38001 (2013).
PDF Publisher link

Abstract: We develop a general method to study the capillary interactions between objects of arbitrary shape which float close to each other on an interface, a regime in which multipole expansion is not useful. The force is represented as a power series in the small distance between the objects, of which the leading order is finite. For objects with size a much larger than the capillary length lc, the force scales as (a/lc)1/2 and the prefactor depends on the mean radius of curvature R at the closest points. ... (read more)

Fluid Mechanics Capillary Cheerios Effect

Views