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Droplets that impact the surface of a deep liquid pool may form a vertical jet after the cavity formation event, provided they have sufficient impact energy. Depending on the associated time scales and the effect of the Rayleigh Plateau instability, this jet may either continue to rise, or may form satellite droplets via necking. Collision of these structures with a second incoming droplet, ejected from the same dispensing tip as the first droplet, may result in the formation of various lamellar patterns, depending on the impact conditions, giving rise to liquid mushroom and or umbrella structures. In this research, we experiment for the first time with hydrodynamics of such liquid mushrooms, and study the effect of droplet impact height, surface tension, and viscosity on the dynamics of such lamellar formations. We further explore the role of the orientation of incoming droplet impact, ie whether head on or offset collision with the rising jet or satellite droplet. We discuss the spatiotemporal evolution of the lamella diameters, and its susceptibility to surface tension, viscosity, and droplet impact height. We put forward a theoretical model based on energetics, to predict the maximum spread diameter of the lamellae, which yields accurate predictions with respect to our experiments. Our findings may help to provide important insights towards a fluid dynamic phenomenon observed often in nature and may be important in niche utilities as well.

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and cell nucleus.

We consider a one-dimensional system comprising of $N$ run-and-tumble particles confined in a harmonic trap interacting via a repulsive inverse-square power-law interaction. This is the ``active" version of the Calogero-Moser system where the particles are associated with telegraphic noise with two possible states $\pm v_0$. We numerically compute the global density profile in the steady state which shows interesting crossovers between three different regimes: as the activity increases, we observe a change from a density with sharp peaks characteristic of a crystal region to a smooth bell-shaped density profile, passing through the intermediate stage of a smooth Wigner semi-circle characteristic of a liquid phase. We also investigate analytically the crossover between the crystal and the liquid regions by computing the covariance of the positions of these particles in the steady state in the weak noise limit. It is achieved by using the method introduced in Touzo {\it et al.} [Phys. Rev. E {\bf 109}, 014136 (2024)] to study the active Dyson Brownian motion. Our analytical results are corroborated by thorough numerical simulations.

The dynamic yield stress associated with the flow cessation of cement pastes is measured using a rheometer equipped with various shear geometries such as vane, helical, sandblasted co-axial cylinders, and serrated parallel plates, as well as with the mini-cone spread test. Discrepancies in yield stress values are observed for cement pastes at various volume fractions, with one to two orders of magnitude difference between vane, helical and mini-cone spread measurements on the one hand, and co-axial cylinder and parallel plate measurements on the other hand. To understand this discrepancy, the flow profile of a cement paste in the parallel-plate geometry is investigated with a high-speed camera, revealing the rapid formation of an un-sheared band near the static bottom plate. The width of this band depends upon the rotational velocity of the top plate, and upon the shear time. Recalculation of shear stress shows that the reduced sheared gap alone cannot explain the low measured yield stress. Further exploration suggests the formation of zones with lower particle content, possibly linked to cement particle sedimentation. Here, we argue that the complex nature of cement pastes, composed of negatively buoyant non-Brownian particles with attractive interactions due to highly charged nano-size hydration products, accounts for their complex rheological behavior., Comment: Submitted to Journal Rheologica Acta for the peer review process on 13-March-2024, 11 figures. Also includes supplementary information with 5 figures

The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity $\mathcal{D}$ of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratios, and high activity.

In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appear at fixed values of $\kappa$ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behaviour with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice, and a fixed-point analysis of a functional flow equation on a Bethe lattice., Comment: 6 pages, 4 figures

Several active organisms in nature tend to reside as a community in a viscous fluid medium. We analyze the variation of swimming characteristics of an active swimmer present in a dilute and disperse suspension, modeled as an effective Brinkman medium. This idealized representation of a collection of active swimmers allows one to distinguish the impact of the interior domain available to an individual swimmer as well as the contribution of its neighbors. Darcy's law along with the analytical solution enables the effective resistivity to be predicted as a function of the volume fraction which is in close agreement with the well-known Carman-Kozeny equation. This facilitates the successive analysis of the propulsion speed, power dissipation, and swimming efficiency of the targeted swimmer as a function of the volume fraction which is decisive in nutrient transport and uptake or reproduction in a collective environment. A stress-jump condition is also imposed across a cell to indicate a mean effective force due to the nearby swimmers. At suitable values of this stress-jump coefficient, the relative increase of the migration velocity and swimming efficiency is noticeably higher at an optimum occupancy.

In this article, we report experimental and semi analytical findings to elucidate the electrohydrodynamics EHD of a dielectric liquid droplet impact on superhydrophobic SH and hydrophilic surfaces. A wide range of Weber numbers We and electro-capillary numbers Cae is covered to explore the various regimes of droplet impact EHD. We show that for a fixed We 60, droplet rebound on SH surface is suppressed with increase of electric field intensity. At high Cae, instead of the usual uniform radial contraction, the droplets retract faster in orthogonal direction to the electric field and spread along the direction of the electric field. This prevents the accumulation of sufficient kinetic energy to achieve the droplet rebound phenomena. For certain values of We and Ohnesorge number Oh, droplets exhibit somersault like motion during rebound. Subsequently we propose a semi analytical model to explain the field induced rebound phenomenon on SH surfaces. Above a critical Cae 4.0, EHD instability causes fingering pattern via evolution of spire at the rim. Further, the spreading EHD on both hydrophilic and SH surfaces are discussed. On both wettability surfaces and for a fixed We, the spreading factor shows an increasing trend with increase in Cae. We have formulated an analytical model based on energy conservation to predict the maximum spreading diameter. The model predictions hold reasonably good agreement with the experimental observations. Finally, a phase map was developed to explain the post impact droplet dynamics on SH surfaces for a wide range of We and Cae.

The article reports droplet evaporation kinetics on inclined substrates. Comprehensive experimental and theoretical analyses of the droplet evaporation behaviour for different substrate declination, wettability and temperatures have been presented. Sessile droplets with substrate declination exhibit distorted shape and evaporate at different rates compared to droplets on the same horizontal substrate and is characterized by more often changes in regimes of evaporation. The slip stick and jump stick modes are prominent during evaporation. For droplets on inclined substrates, the evaporative flux is also asymmetric and governed by the initial contact angle dissimilarity. Due to smaller contact angle at the rear contact line, it is the zone of a higher evaporative flux. Particle image velocimetry shows the increased internal circulation velocity within the inclined droplets. Asymmetry in the evaporative flux leads to higher temperature gradients, which ultimately enhances the thermal Marangoni circulation near the rear of the droplet where the evaporative flux is highest. A model is adopted to predict the thermal Marangoni advection velocity, and good match is obtained. The declination angle and imposed thermal conditions interplay and lead to morphed evaporation kinetics than droplets on horizontal heated surfaces. Even weak movements of the TL alter the evaporation dynamics significantly, by changing the shape of the droplet from ideally elliptical to almost spherical cap, which ultimately reduces the evaporative flux. The life time of the droplet is modelled by modifying available models for non-heated substrate, to account for the shape asymmetry. The present findings may find strong implications towards microscale thermo-hydrodynamics.

This article explores the governing role of the internal hydrodynamics and advective transport within sessile colloidal droplets on the self assembly of nanostructures to form floral patterns. Water acetone binary fluid and Bi2O3 nanoflakes based complex fluids are experimented with. Microliter sessile droplets are allowed to vaporize and the dry out patterns are examined using scanning electron microscopy. The presence of distributed self assembled rose like structures is observed. The population density, structure and shape of the floral structures are noted to be dependent on the binary fluid composition and nanomaterial concentration. Detailed microscopic particle image velocimetry analysis is undertaken to qualitatively and quantitatively describe the solutal Marangoni advection within the evaporating droplets. It has been shown that the kinetics, regime and location of the internal advection are responsible factors towards the hydrodynamics influenced clustering, aggregation and self-assembly of the nanoflakes. In addition, the size of the nanostructures and the complex fluids.

We consider an active Brownian particle in a $d$-dimensional harmonic trap, in the presence of translational diffusion. While the Fokker-Planck equation can not in general be solved to obtain a closed form solution of the joint distribution of positions and orientations, as we show, it can be utilized to evaluate the exact time dependence of all moments, using a Laplace transform approach. We present explicit calculation of several such moments at arbitrary times and their evolution to the steady state. In particular we compute the kurtosis of the displacement, a quantity which clearly shows the difference of the active steady state properties from the equilibrium Gaussian form. We find that it increases with activity to asymptotic saturation, but varies non-monotonically with the trap-stiffness, thereby capturing a recently observed active- to- passive re-entrant behavior., Comment: 17 pages, 7 figures; version accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

The present article highlights the role of non-Newtonian (elastic) effects on the droplet impact phenomenology at temperatures considerably higher than the boiling point, especially at or above the Leidenfrost regime. The Leidenfrost point (LFP) was found to decrease with increase in the impact Weber number (based on velocity just before the impact) for fixed polymer (Polyacrylamide, PAAM) concentrations. Water droplets fragmented at very low Weber numbers (~22), whereas the polymer droplets resisted fragmentation at much higher Weber numbers (~155). We also varied the polymer concentration and observed that till 1000 ppm, the LFP was higher compared to water. This signifies that the effect can be delayed by the use of elastic fluids. We have showed the possible role of elastic effects (manifested by the formation of long lasting filaments) during retraction in the improvement of the LFP. However for 1500 ppm, LFP was lower than water, but with similar residence time during initial impact. In addition, we studied the role of Weber number and viscoelastic effects on the rebound behaviour at 405o C. We observed that the critical Weber number till which the droplet resisted fragmentation at 405o C increased with the polymer concentration. In addition, for a fixed Weber number, the droplet rebound height and the hovering time period increased up to 500 ppm, and then decreased. Similarly, for fixed polymer concentrations like 1000 and 1500 ppm, the rebound height showed an increasing trend up to certain a certain Weber number and then decreased. This non-monotonic behaviour of rebound heights was attributed to the observed diversion of rebound kinetic energy to rotational energy during the hovering phase.

We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive and short-ranged forces, aggregate into several motile and dynamical clusters of comparable size, and do not display bulk phase-segregation. In this dynamical steady-state, we find that the cluster size distribution of these aggregates is a scaled function of the density and activity parameters across the three models of active particles with the same scaling function. The velocity distribution of these motile clusters is non-Gaussian. We show that the effective dynamics of these clusters can explain the observed emergent scaling of the mean-squared displacement of tagged particles for all the three models with identical scaling exponents and functions. Concomitant with the clustering seen at high activities, we observe that the static density correlation function displays rich structures, including multiple peaks that are reminiscent of particle clustering induced by effective attractive interactions, while the dynamical variant shows non-diffusive scaling. Our study reveals a universal scaling behavior in the single-file dynamics of interacting active particles., Comment: Accepted for publication in Soft Matter

We study the dynamics of the separation (gap) between a pair of interacting run and tumble particles (RTPs) moving in one dimension in the presence of additional thermal noise. On a ring geometry the distribution of the gap approaches a steady state. We analytically compute this distribution and find that this is exponentially localised in space, in contrast to the `jammed' configuration, seen earlier in the absence of thermal noise. We also study the relaxation which is an exponential, characterised by a time scale $\tau_r$. We observe that this time scale undergoes a crossover from a size independent value to a size dependent form with increasing size $l$ of the ring. We study the full eigenvalue spectrum of the evolution operator $\mathcal{L}$ and find that the spectrum can be classified into four sectors depending on the symmetries of $\mathcal{L}$. For large $l$, we find explicit expressions for the low lying eigenvalues in each of the sectors. On infinite line the separation does not reach a steady state. In the long times we find that the particles behave as interacting Brownian particles, except for the presence of a peak in the distribution at small separation which is a remnant of activity., Comment: 29 pages, 9 figures

The present article experimentally and theoretically probes the evaporation kinetics of sessile saline droplets. Observations reveal that presence of solvated ions leads to modulated evaporation kinetics, which is further a function of surface wettability. On hydrophilic surfaces, increasing salt concentration leads to enhanced evaporation rates, whereas on superhydrophobic surfaces, it first enhances and reduces with concentration. Also, the nature and extents of the evaporation regimes constant contact angle or constant contact radius are dependent on the salt concentration. The reduced evaporation on superhydrophobic surfaces has been explained based on observed via microscopy crystal nucleation behaviour within the droplet. Purely diffusion driven evaporation models are noted to be unable to predict the modulated evaporation rates. Further, the changes in the surface tension and static contact angles due to solvated salts also cannot explain the improved evaporation behaviour. Internal advection is observed using PIV to be generated within the droplet and is dependent on the salt concentration. The advection dynamics has been used to explain and quantify the improved evaporation behaviour by appealing to the concept of interfacial shear modified Stefan flows around the evaporating droplet. The analysis leads to accurate predictions of the evaporation rates. Further, another scaling analysis has been proposed to show that the thermal and solutal Marangoni advection within the system leads to the advection behaviour. The analysis also shows that the dominant mode is the solutal advection and the theory predicts the internal circulation velocities with good accuracy. The findings may be of importance to microfluidic thermal and species transport systems.

Under an increasing applied shear stress ($\sigma$), viscosity of many dense particulate suspensions increases drastically beyond a stress onset ($\sigma_0$), a phenomenon known as discontinuous shear-thickening (DST). Recent studies point out that some suspensions can transform into a stress induced solid-like shear jammed (SJ) state at high particle volume fraction ($\phi$). SJ state develops a finite yield stress and hence is distinct from a shear-thickened state. Here, we study the steady state shear-thickening behaviour of dense suspensions formed by dispersing colloidal polystyrene particles (PS) in polyethylene glycol (PEG). We find that for small $\sigma$ values the viscosity of the suspensions as a function of $\phi$ can be well described by Krieger-Dougherty (KD) relation. However, for higher values of $\sigma$ ($>> \sigma_0$), KD relation systematically overestimates the measured viscosity, particularly for higher $\phi$ values. This systematic deviation can be rationalized by the weakening of the sample due to flow induced failures of the solid-like SJ state. Using Wyart-Cates model, we propose a method to predict the SJ onset from the steady state rheology measurements. Our results are further supported by in-situ optical imaging of the sample boundary under shear., Comment: J. Phys.: Condens. Matter (in press); S.I. Movie can be downloaded from: https://drive.google.com/open?id=1sWgiVMrRnpLiu5uHjTkdHCYuxFrZG4Pl

Droplet deposition after impact on superhydrophobic surfaces has been an important area of study in recent years due to its potential application in reduction of pesticides usage. Minute amounts of long chain polymers added to water has been known to arrest the droplet rebound effect on superhydrophobic surfaces. Previous studies have attributed different reasons like extensional viscosity, dominance of elastic stresses or slowing down of contact line in retraction phase due to stretching of polymer chains. The present study attempts to unravel the existence of critical criteria of polymer concentration and impact velocity on the inhibition of droplet rebound. The impact velocity will indirectly influence the shear rate during the retraction phase, and the polymer concentration dictates the relaxation timescale of the elastic fluids. Finally we show that the Weissenberg number (at onset of retraction), which quantifies both the elastic effects of polymer chains and the hydrodynamics, is the critical parameter in determining the regime of onset of rebound suppression, and that there exists a critical value which determines the onset of bounce arrest. The previous three causes, which are manifestations of elastic effects in non-Newtonian fluids, can be related with the proposed Weissenberg number criterion., Comment: 11 pages, 8 figures

The present article reports the governing influence of substituting the M2 site in nanoscale MFe2O4 spinel ferrites by different magnetic metals Fe,Mn,Co,Ni on magnetorheological and magneto elastoviscous behaviors of the corresponding magnetorheological fluids MRFs. Different doped MFe2O4 nanoparticles have been synthesized using the polyol assisted hydrothermal method. Detailed steady and oscillatory shear rheology have been performed on the MRFs to determine the magneto-viscoelastic responses. The MRFs exhibit shear thinning behavior and augmented yield characteristics under influence of magnetic field. The steady state magnetoviscous behaviors are scaled against the governing Mason number and self similar response from all the MRFs have been noted. The MRFs conform to an extended Bingham plastic model under field effect. Transient magnetoviscous responses show distinct hysteresis behaviors when the MRFs are exposed to time varying magnetic fields. Oscillatory shear studies using frequency and strain amplitude sweeps exhibit predominant solid like behaviors under field environment. However, the relaxation behaviors and strain amplitude sweep tests of the MRFs reveal that while the fluids show solid like behaviors under field effect, they cannot be termed as typical elastic fluids. Comparisons show that the MnFe2O4 MRFs have superior yield performance among all. However, in case of dynamic and oscillatory systems, CoFe2O4 MRFs show the best performance. The viscoelastic responses of the MRFs are noted to correspond to a three element viscoelastic model. The study may find importance in design and development strategies of nano MRFs for different applications.

We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P(x)$ has a rich behavior in the $(p, \alpha)$-plane. For $p>1$, the distribution has a finite support in $[x_-,x_+]$ and there is a critical line $\alpha_c(p)$ that separates an active-like phase for $\alpha > \alpha_c(p)$ where $P(x)$ diverges at $x_\pm$, from a passive-like phase for $\alpha < \alpha_c(p)$ where $P(x)$ vanishes at $x_\pm$. For $p<1$, the stationary density $P(x)$ collapses to a delta function at the origin, $P(x) = \delta(x)$. In the marginal case $p=1$, we show that, for $\alpha < \alpha_c$, the stationary density $P(x)$ is a symmetric exponential, while for $\alpha > \alpha_c$, it again is a delta function $P(x) = \delta(x)$. For the special cases $p=2$ and $p=1$, we obtain exactly the full time-dependent distribution $P(x,t)$, that allows us to study how the system relaxes to its stationary state. In addition, in these two cases, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions., Comment: 15 pages, 12 figures. Published version

Drying of colloidal droplets on solid, rigid substrates is associated with a capillary pressure developing within the droplet. In due course of time, the capillary pressure builds up due to droplet evaporation resulting in the formation of a colloidal thin film that is prone to crack formation. In this study, we show that introducing a minimal amount of nematic liquid crystal (NLC) can completely suppress the crack formation. The mechanism behind the curbing of the crack formation may be attributed to the capillary stress-absorbing cushion provided by the elastic arrangements of the liquid crystal at the substrate-droplet interface. Cracks and allied surface instabilities are detrimental to the quality of the final product like surface coatings, and therefore, its suppression by an external inert additive is a promising technique that will be of immense importance for several industrial applications. We believe this fundamental investigation of crack suppression will open up an entire avenue of applications for the NLCs in the field of coatings, broadening its already existing wide range of benefits.

A systematically designed study has been conducted to understand and clearly demarcate the degree of contribution by the constituting elements to the surface tension of nanocolloids. The effects of elements such as surfactants, particles and the combined effects of these on the interfacial tension of these complex fluids are studied employing pendant drop shape analysis method by fitting Young Laplace equation. Only particle has shown considerable increase in surface tension with particle concentration in a polar medium like DI water whereas only marginal effect particles on surface tension in weakly polar mediums like glycerol and ethylene glycol. Such behaviour has been attributed to the enhanced desorption of particles to the interface and a mathematical framework has been derived to quantify this. Combined particle and surfactant effect on surface tension of complex nanofluid system showed a decreasing behaviour with respect to the particle and surfactant concentration with a considerably feeble effect of particle concentration. This combined colloidal system recorded a surface tension value below the surface tension of aqueous surfactant system at the same concentration, which is a counterintuitive observation as only particle results in increase in surface tension and only surfactant results in decrease in surface tension. The possible physical mechanism behind such an anomaly happening at the complex fluid air interface has been explained. Detailed analyses based on thermodynamic, mechanical and chemical equilibrium of the constituents and their adsorption-desorption characteristics as extracted from Gibbs adsorption analysis has been provided., Comment: 31 pages 12 figures

Readily synthesizable nano-graphene and poly ethylene glycol based stable gels have been synthesized employing an easy refluxing method and exhaustive rheological and viscoelastic characterizations have been performed to understand the nature of such complex gel systems. The gels exhibit shear thinning response with pronounced yield stress values which is indicative of a microstructure where the graphene nanoflakes intercalate with the polymer chains and form a pseudo spring damper network. Experimentations on the thixotropic behavior of the gels indicate that the presence of the G nanoflakes leads to immensely augmented structural stability capable of withstanding severe impact shears. Further information about the localized interactions of the G nanoflakes with the polymer chains is revealed from the amplitude and frequency sweep analyses in both linear and nonlinear viscoelastic regimes. Massively enhanced cross over amplitude values are recorded and several smart effects such as enhanced elastic behavior at increasing forcing frequencies are registered. Structural resonance induced disruption of the elastic behavior is observed for the gels for a given range of frequency and the proposition of resonance has been justified mathematically. It is observed that post this resonance bandwidth, the gels are able to self-heal and regain their original elastic behavior back without any external intervention. More detailed information on the viscoelastic nature of the gels has been obtained from creep and recovery compliance tests and justifications for the spring damper microstructure has been obtained. Smart features such as enhanced stress relaxation behavior with increasing strain have been observed and the same explained based on the proposed microstructure.

Unprecedentedly massive electrorheology has been reported for dilute graphene nanoflakes based ER fluids that have been engineered as novel, readily synthesizable polymeric gels. Polyethylene glycol based graphene gels have been synthesized and very high ER response, 25,000 percent enhancement in viscosity under influence of electric field, has been observed for low concentration systems 2 wt. percent. The gels overcome several drawbacks innate to ER fluids. The gels exhibit long term stability, high graphene packing ratio which ensures very high ER response and the microstructure of the gels ensure that fibrillation of the graphene nanoflakes under field is undisturbed by thermal fluctuations, further leading to mega ER. The gels exhibit large yield stress handling caliber with yield stress observed as high as 13 kPa at 2 wt. perc. graphene. Detailed investigations on the effects of graphene concentration, electric field strength, imposed shear resistance and transients of electric field actuation on the ER response of the gels have been performed. The gels show nearly negligible hysteresis with respect to electro viscous effects which speak of the stability and responsiveness required in transient situations. Indepth analyses with explanations have been provided for the observations and effects, such as sheet over-crowding induced loss of structural integrity at high concentrations and inter flake lubrication or slip induced augmented ER response. The present gels show great promise as potential ER gels for variant smart applications, such as damping and vibration control in active aircraft and vehicle structures, micronanoscale electroactuation, in suspensions or braking clutching in high performance specialized vehicular systems, etc., Comment: 29 pages 10 figures

Particle-particle interactions in sedimenting systems have been investigated in the present study considering the many-body hydrodynamic and electrodynamic interactions. These interactions primarily occur in two modes: near-field and far-field interactions. The hydrodynamic interactions are modeled employing the Stokesian Dynamics while the electrodynamic interactions are accounted using the grand Capacitance matrix formulation capable of tackling externally applied arbitrary electric field effects. It is seen that the presence of an external electric field and asymmetry in particle positioning greatly modifies the dynamics of the rigid dielectric spherical particles when compared with the sedimenting system without the electric field effects. This is attributed to the induced dipole moment interactions among the particles. A consequence of the alterations in the particle arrangements also changes the net drag force experienced by these sedimenting particles, which is also reported in the present study. Furthermore, we have evaluated the induced background velocity field of the continuous medium due to sedimentation of the particles. A net velocity is observed in the continuous medium due to the sedimentation-induced particle rotation, which is found to vary in presence of an external electric field., Comment: 31 pages

Advent of nematic liquid crystals flows have attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electroosmosis stands as one of the efficient flow actuation method through narrow confinement. In the present study, we explore the electrically actuated flow of a nematic fluid with ionic inclusions taking into account the influences from surface induced elastic and electrical double layer phenomena. Influence of surface effects on the flow characteristics is known to get augmented in micro-confined environment and must be properly addressed. Towards this, we devise the coupled flow governing equations from fundamental free energy analysis considering the contributions from first and second-order elastic, dielectric, flexoelectric, ionic and entropic energies. We have further considered weak anchoring surface conditions with second order elasticity which helps us to more accurately capture the director deformations along the boundaries. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electroosmosis through a slit-type microchannel whose surface are considered to be chemically treated in order to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed especially for higher electric fields wherein the Ericksen number for the dynamic study is restricted to the order of unity.

Study of electrokinetics of nematic liquid crystals (LCs) with dissolved impurities hold utmost importance in understanding director distribution characteristics and modified flow rheology. However, no concrete theory for the non-uniform potential and ionic species distribution, due to an induced electrical double layer (EDL) at the LC-substrate interface, derived from fundamental principles have been put forward in this regard. In this work, we have developed coupled governing equations from fundamental free energy considerations for the potential distribution and the director configuration of the nematic LC within the induced electrical double layer which is generated due to certain physico-chemical interactions at the LC-substrate interface. With these considerations, an electroosmotically-enabled nematodynamics for a particular LC, namely, MBBA, with strong planar anchoring at the boundaries is studied. We obtained multiple solution for director configuration, which is an integral characteristics of nematic flow solutions, and investigated for the most stable solution employing an entropic analysis. We finally proceed to depicts the electroosmotic flow features of the nematic LC wherein we focused on the spontaneous development of the electrorheological effect and the resulting elastic description of the nematic LC for the most stable solution obtained.

Magnetic nanocolloids with synthesized super paramagnetic Fe3O4 nanoparticles (SPION) (5 to 15 nm) dispersed in insitu developed Polyethylene Glycol (PEG 400) and nano silica complex have been synthesized. The PEG nano Silica complex physically encapsulates the SPIONs, ensuring no phase separation under high magnetic fields (1.2 T). Exhaustive magnetorheological investigations have been performed to comprehend the structural behavior and response of the ferrocolloids. Remarkable stability and reversibility have been observed under magnetic field for concentrated systems. The results exhibit the impact of particle concentration, size and encapsulation efficiency on parameters such as shear viscosity, yield stress, viscoelastic moduli, magnetoviscous hysteresis etc. Analytical models to reveal the system mechanism and mathematically predict the magnetoviscosity and magneto yield stress has been theorized. The mechanistic approach based on near field magnetostatics and Neel Brownian interactivities can predict the colloidal properties under the effect of field accurately. The colloid exhibits amplified storage and loss moduli alongside highly augmented linear viscoelastic region under magnetic stimuli. The transition of the colloidal state from fluidic phase to soft condensed phase and its viscoelastic stimuli under the influence of magnetic field has been explained based on the mathematical analysis. The remarkable stability, magnetic properties and accurate physical models reveal good promise for the colloids in transient situations viz. magneto MEMS/ NEMS devices, antiseismic damping, biomedical invasive treatments etc.

Heat and charge transport characteristics of nanocolloids have been bridged from fundamental analysis. The relationship between the two transport phenomena in dielectric nanostructure based polar colloids has been quantitatively presented. An extensional intuitive analogy to the Wiedemann Franz law has been drawn. Derived from the fact that mobile electrons transport both heat and charge within metallic crystal structure, the analogy can be extended to nanocolloids, wherein the dispersed population act as the major transporter. The analogy allows modeling the relationship between the two phenomena and sheds more insight and conclusive evidence that nanoparticle traversal within the fluid domain is the main source of augmented transport phenomena exhibit by nanocolloids. Important factors such as the thermal and dielectric responses of the nanocolloid can be quantified and bridged through the semi analytical formalism. The theoretical analysis has been validated against experimental data and variant scientific literature and good accuracy has been observed.

The dominant modes of charge transport in variant polar liquid based nanoparticulate colloidal dispersions (dilute) have been theorized. Theories formulating electrical characteristics of colloids have often been found to over or under predict charge transport in dilute suspensions of nanoparticles in polar fluids owing to grossly different mechanistic behavior of concentrated systems. Three major interacting modes with independent yet simultaneous existence have been proposed and found to be consistent with analyses of experimental data. Electric Double Layer (EDL) formation at nanoparticle fluid interface conjugated electrophoresis under the influence of the electric field has been determined as one important mode of charge transport. Nanoparticle polarization due to short range field non-uniformity caused by the EDL with consequent particle motion due to interparticle electrostatic interactions acts as another mode of transport. Coupled electrothermal diffusion arising out of Brownian randomization in presence of the electric field has been determined as the third dominant mode. An analytical model based on discrete interactions of the charged particle fluid domains explains the various behavioral aspects of such dispersions, as observed and validated from detailed experimental analysis. The analysis is also predictive of the dominance and behavior of the three modes with important nanocolloid parameters such as temperature and concentration.

Time kinetics of interaction of natural graphite (GR) to colloidal graphene (G) collagen (C) nanocomposites was studied at ambient conditions, and observed that just one day at ambient conditions is enough to form colloidal graphene directly from graphite using the protein collagen. Neither controlled temperature and pressure ambiance nor sonication was needed for the same; thereby rendering the process biomimetic. Detailed spectroscopy, X ray diffraction, electron microscopy as well as fluorescence and luminescence assisted characterization of the colloidal dispersions on day one and day seven reveals graphene and collagen interaction and subsequent rearrangement to form an open structure. Detailed confocal microscopy, in the liquid state, reveals the initial attack at the zigzag edges of GR, the enhancement of auto fluorescence and finally the opening up of graphitic stacks of GR to form near transparent G. Atomic Force Microscopy studies prove the existence of both collagen and graphene and the disruption of periodicity at the atomic level. Thermal conductivity of the colloid shows a 17% enhancement for a volume fraction of less than 0.00005 of G. Time variant increase in thermal conductivity provides qualitative evidence for the transient exfoliation of GR to G. The composite reveals interesting properties that could propel it as a future material for advanced bio applications including therapeutics.

The viscosity of Graphene nano-sheet suspensions (GNS)and its behavior with temperature and concentration have been experimentally determined. A physical mechanism for the enhanced viscosity over the base fluids has been proposed for the poly-dispersed GNSs. Experimental data reveals that enhancement of viscosity for GNSs lie in between that of Carbon Nanotube Suspensions (CNTSs) and nano Alumina suspensions (nAS) , indicating the hybrid mechanism of percolation (like CNTs) and Brownian motion assisted sheet dynamics (like Alumina particles). Sheet dynamics and percolation, along with a proposed percolation Network Dynamicity Factor; have been used to determine a dimensionally consistent analytical model to accurately determine and explain the viscosity of poly-dispersed GNSs. It has been hypothesized that the dynamic sheets behave qualitatively analogous to gas molecules. The model also provides insight into the mechanisms of viscous behavior of different dilute nanoparticle suspensions. The model has been found to be in agreement with the GNS experimental data, and even for CNT and nano Alumina suspensions.

We consider the single-file motion of colloidal particles interacting via short-ranged repulsion and placed in a traveling wave potential, that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed., Comment: published version

We consider the inelastic Maxwell model, which consists of a collection of particles that are characterized by only their velocities, and evolving through binary collisions and external driving. At any instant, a particle is equally likely to collide with any of the remaining particles. The system evolves in continuous time with mutual collisions and driving taken to be point processes with rates $\tau_c^-{1}$ and $\tau_w^{-1}$ respectively. The mutual collisions conserve momentum and are inelastic, with a coefficient of restitution $r$. The velocity change of a particle with velocity $v$, due to driving, is taken to be $\Delta v=-(1+r_w) v+\eta$, mimicking the collision with a vibrating wall, where $r_w$ the coefficient of restitution of the particle with the "wall" and $\eta$ is Gaussian white noise. The Ornstein-Uhlenbeck driving mechanism given by $\frac{dv}{dt}=-\Gamma v+\eta$ is found to be a special case of the driving modeled as a point process. Using both the continuum and discrete versions we show that while the equations for the one-particle and the two-particle velocity distribution functions do not close, the joint evolution equations of the variance and the two-particle velocity correlation functions close. With the exact formula for the variance we find that, for $r_w\ne-1$, the system goes to a steady state. On the other hand, for $r_w=-1$, the system does not have a steady state. Similarly, the system goes to a steady state for the Ornstein-Uhlenbeck driving with $\Gamma\not=0$, whereas for the purely diffusive driving ($\Gamma=0$), the system does not have a steady state., Comment: 9 pages, 4 figures

A model of homogeneously driven dissipative system, consisting of a collection of $N$ particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is randomly selected. They undergo inelastic collision with probability $p$. With probability $(1-p)$, energy of the system is changed by changing the velocities of both the particles independently according to $v\rightarrow -r_w v +\eta$, where $\eta$ is a Gaussian noise drawn independently for each particle as well as at each time steps. For the case $r_w=- 1$, although the energy of the system seems to saturate (indicating a steady state) after time steps of $O(N)$, it grows linearly with time after time steps of $O(N^2)$, indicating the absence of a eventual steady state. For $ -1

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special case where all particles have the same mass, we obtain analytic results for the velocity auto-correlation function in the short time diffusive regime and the long time approach to the saturation value when finite-size effects become relevant. In the case where the masses are unequal, numerical simulations indicate sub-diffusive behaviour with mean square displacement of the tagged particle growing as t/ln(t) with time t. Also various correlation functions, involving the velocity and position of the tagged particle, show damped oscillations at long times that are absent for the equal mass case., Comment: 13 pages, 5 figures, to be submitted to J. Stat. Phys

The Brazil-nut effect is the phenomenon in which a large intruder particle immersed in a vertically shaken bed of smaller particles rises to the top, even when it is much denser. The usual practice, while describing these experiments, has been to use the dimensionless acceleration \Gamma=a \omega^2/g, where a and \omega are respectively the amplitude and the angular frequency of vibration and g is the acceleration due to gravity. Considering a vibrated quasi-two-dimensional bed of mustard seeds, we show here that the peak-to-peak velocity of shaking v= a\omega, rather than \Gamma, is the relevant parameter in the regime where boundary-driven granular convection is the main driving mechanism. We find that the rise-time \tau of an intruder is described by the scaling law \tau ~ (v-v_c)^{-\alpha}, where v_c is identified as the critical vibration velocity for the onset of convective motion of the mustard seeds. This scaling form holds over a wide range of (a,\omega), diameter and density of the intruder., Comment: 4 pages, 5 figures + supplementary information

We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external field. The equilibrium properties of our model are essentially those of the Tonks gas, but at high densities, the orientational degrees of freedom become effectively frozen due to jamming. This is a simple analytically tractable model of glassy phase. Under a cyclic variation of the pressure, hysteresis is observed. Following a pressure quench, the orientational persistence exhibits a two-stage decay characteristic of glassy systems., Comment: 7 pages

We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase relations generate time-averaged directed current of particles. We obtain analytic results for a lattice version of the model using a recently developed perturbative approach. Many interesting features like particle-hole symmetry, current reversal with changing density, and system-size dependence of current are obtained. We propose possible experiments to test our predictions., Comment: 4 pages, 2 figures

We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n=-2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class., Comment: 14 pages,10 figures

We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different ricepile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size $L$, the probabilities that the residence time at a site or the total residence time is greater than $t$, both decay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where $\gamma$ is an exponent $ \ge 1$, and values of $x$ and $\omega$ in the two cases are different. In the Oslo ricepile model we find that the probability that the residence time $T_i$ at a site $i$ being greater than or equal to $t$, is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple scaling. For model in $d$ dimensions, we show that the probability of minimum slope configuration in the steady state, for large $L$, varies as $\exp(-\kappa L^{d+2})$ where $\kappa$ is a constant, and hence $ \gamma = d+2$., Comment: 13 pages, 23 figures, Submitted to Phys. Rev. E

We study the average number A_n per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are characterized by an integer parameter b, b > 1. The fractal dimension varies from $ log_{_2} 3$ to 2 as b is varied from 2 to infinity. We find that for all b > 2, A_n varies as $ \lambda^n exp(b n ^{\psi})$, where $\lambda$ and $b$ are some constants, and $ 0 < \psi <1$. We determine the exponent $\psi$, and the size exponent $\nu$ (average diameter of polymer varies as $n^\nu$), exactly for all b > 2. This generalizes the earlier results of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988]., Comment: 24 pages, 8 figures

We study number density distribution and the behavior of time correlation functions in the density of grains for a quasi-two dimensional system of vibrated grains. We study the system at various packing fractions, from low to high. At low densities we recover usual gas like behavior, reflected in a Poissonian statistics for the number density distribution. At higher densities we notice effects like formation of cages of the kind that are seen in glass transition., Comment: A Technical Report

We compute the distribution of the work done in stretching a Gaussian polymer, made of N monomers, at a finite rate. For a one-dimensional polymer undergoing Rouse dynamics, the work distribution is a Gaussian and we explicitly compute the mean and width. The two cases where the polymer is stretched, either by constraining its end or by constraining the force on it, are examined. We discuss connections to Jarzynski's equality and the fluctuation theorems., Comment: 5 pages, 2 figures

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness for finite chains of length L. We find that the polymer properties obtained in this ensemble are "qualitatively" different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves., Comment: Published version, 4 pages, 5 figures, revtex

We show that in the loop-erased random walk problem, the exponent characterizing probability distribution of areas of erased loops is superuniversal. In d-dimensions, the probability that the erased loop has an area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two-dimensions is consistent with the known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The exponent for the distribution of durations of avalanche in the three-dimensional abelian sandpile model is determined from this by using scaling relations., Comment: 25 pages, 1 table, 8 figures