arXiv subjects

Subhadeep Roy

Publications and source records attributed to Subhadeep Roy.

36 records · Page 2Linked to original sources

arXiv2021

Rheology of immiscible two-phase flow in mixed wet porous media: Dynamic pore network model and capillary fiber bundle model results

Immiscible two-phase flow in porous media with mixed wet conditions was examined using a capillary fiber bundle model, which is analytically solvable, and a dynamic pore network model. The mixed wettability was implemented in the models by allowing each tube or link to have a different wetting angle chosen randomly from a given distribution. Both models showed that mixed wettability can have significant influence on the rheology in terms of the dependence of the global volumetric flow rate on the global pressure drop. In the capillary fiber bundle model, for small pressure drops when only a small fraction of the tubes were open, it was found that the volumetric flow rate depended on the excess pressure drop as a power law with an exponent equal to 3/2 or 2 depending on the minimum pressure drop necessary for flow. When all the tubes were open due to a high pressure drop, the volumetric flow rate depended linearly on the pressure drop, independent of the wettability. In the transition region in between where most of the tubes opened, the volumetric flow depended more sensitively on the wetting angle distribution function and was in general not a simple power law. The dynamic pore network model results also showed a linear dependence of the flow rate on the pressure drop when the pressure drop is large. However, out of this limit the dynamic pore network model demonstrated a more complicated behaviour that depended on the mixed wettability condition and the saturation. In particular, the exponent relating volumetric flow rate to the excess pressure drop could take on values anywhere between 1.0 and 1.8. The values of the exponent were highest for saturations approaching 0.5, also, the exponent generally increased when the difference in wettability of the two fluids were larger and when this difference was present for a larger fraction of the porous network.

physics.flu-dyn↗

arXiv2021

Correlation between avalanches and emitted energies during fracture with variable stress release range

We observe the failure process of a fiber bundle model with a variable stress release range, $γ$, higher the value of $γ$ lower the stress release range. By tuning $γ$ from low to high, it is possible to go from the mean-field (MF) limit of the model to local load sharing (LLS) where local stress concentration plays a crucial role. In the MF limit, the avalanche size $s$ and energy $E$ emitted during the avalanche are highly correlated producing the same distribution for both $P(s)$ and $Q(E)$: a scale-free distribution with a universal exponent -5/2. With increasing $γ$, the model enters the LLS limit. In this limit, due to the presence of local stress concentration such correlation $C(γ)$ between $s$ and $E$ decreases where the nature of the decreases depends highly on the dimension of the bundle. In 1d, the $C(γ)$ stars from a high value for low $γ$ and decreases towards zero when $γ$ is increased. As a result, $Q(E)$ and $P(s)$ are similar at low $γ$, an exponential one, and then $Q(E)$ becomes power-law for high-stress release range though $P(s)$ remains exponential. On the other hand, in 2d, the $C(γ)$ decreases slightly with $γ$ but remains at a high value. Due to such a high correlation, the distribution of both $s$ and $E$ is exponential in the LLS limit independent of how large $γ$ is.

cond-mat.stat-mech↗

arXiv2021

Role of pore-size distribution on effective rheology of two-phase flow in porous media

The flow of immiscible fluids inside a porous medium shows non-linearity in the form of a power law in the rheological properties of the fluids under steady state flow conditions. However, different experimental and numerical studies have reported different values for the exponent related to this power law. Here we explore how the rheological properties of the two-phase flow in porous media depends on the distribution of the pore sizes and how it affects the power-law exponent. The pore-size distribution controls fluctuation in the pore radii and their density in a porous material. We present two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. We observe crossover from a non-linear to linear rheology when increasing the flow rate where the non-linear part is highly affected by the pore-size distribution. We have also carried out the study for different saturations of the two fluids.

physics.flu-dyn↗

arXiv2020

Size distribution of emitted energies in local load sharing fiber bundles

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size ($s$) and the corresponding energy burst ($E$) in this version of the model have a non-linear relation ($E\sim s^γ$). Numerical results indicate that $γ\approx 2.5$ universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of $-(γ+1)$.

cond-mat.dis-nn↗

arXiv2020

Crack Localization and the Interplay between Stress Enhancement and Thermal Noise

We study the competition between thermal fluctuations and stress enhancement in the failure process of a disordered system by using a local load sharing fiber bundle model. The thermal noise is introduced by defining a failure probability that constitutes the temperature and elastic energy of the fibers. We observe that at a finite temperature and low disorder strength, the failure process, which nucleate in the absence of any thermal fluctuation, becomes spatially uncorrelated when the applied stress is sufficiently low. The dynamics of the model in this limit lies closely to the universality class of ordinary percolation. When applied stress is increased beyond a threshold value, localized fractures appear in the system that grow with time. We identify the boundary between the localized and random failure process in the space of temperature and applied stress, and find that the threshold of stress corresponding to the onset of localized crack growth increases with the increase of temperature.

cond-mat.dis-nn↗

arXiv2020

Phase transitions and correlations in fracture processes where disorder and stress compete

We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.

cond-mat.dis-nn↗

arXiv2019

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.

physics.flu-dyn↗

arXiv2019

Creep failure in a threshold activated dynamics: Role of temperature during a sub-critical loading

Creep is a time-dependent deformation of solids at relatively low stresses, leading to the breakdown with time. Here we propose a simple model for creep failure of disordered solids, in which temperature and stress are controllable. Despite its simplicity, this model can reproduce most experimental observations. Time dependence of the strain rate is well fitted with power laws resembling the Omori-Utsu and the inverse Omori laws in the primary and the tertiary creep regimes, respectively. Distribution of the creep lifetime obeys the log-normal distribution, and the average creep lifetime decays in a scale-free manner with the increasing stress. The above results are in good agreement with experiments. Additionally, the mean avalanche size as a function of temperature exhibits a series of jumps, and finite-size scaling implies the existence of phase transitions.

cond-mat.dis-nn↗

arXiv2019

Effective rheology of two-phase flow in a capillary fiber bundle model

We investigate the effective rheology of two-phase flow in a bundle of parallel capillary tubes carrying two immiscible fluids under an external pressure drop. The diameter of each tube varies along its length and the corresponding capillary threshold pressures are considered to be distributed randomly according to a uniform probability distribution. We demonstrate through analytical calculations that a transition from a linear Darcy regime to a non-linear behavior occurs while decreasing the pressure drop $ΔP$, where the total flow rate $\langle Q \rangle$ varies with $ΔP$ with an exponent $2$. This exponent for the non-linear regime changes when a lower cut-off $P_m$ is introduced in the threshold distribution. We demonstrate analytically that, in the limit where $ΔP$ approaches $P_m$, the flow rate scales as $\langle Q \rangle \sim (|ΔP|-P_m)^{3/2}$. We have also provided some numerical results in support to our analytical findings.

physics.flu-dyn↗

arXiv2018

Fiber bundle model under heterogeneous loading

The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.

cond-mat.dis-nn↗

arXiv2018

Modes of failures in disordered solids

The two principal ingredients determining the failure modes of disordered solids are the level of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage, the two extreme failure modes. In this study, using the random fiber bundle model as a prototype for disorder solids, we classify every failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes.

cond-mat.dis-nn↗

arXiv2017

Stability in fiber bundle model : Existence of strong links and the effect of disorder

In this paper I have studied the fiber bundle model with a fraction α of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value α_c . The present work has a twofold purpose: (i) study of failure abruptness, mainly the brittle to quasi-brittle transition point (δ_c ) with varying α and (ii) variation of α_c as we change the disorder introduced in the model. The brittle to quasi-brittle transition is confirmed from the failure abruptness. On the other hand, the α_c is obtained from the knowledge of failure abruptness and statistics of avalanches. It is observed that δ_c scales to lower values, suggesting more quasi-brittle like continuous failure even at low strength of disorder, when α is increased. Also, the critical fraction α_c, required to make the model deviate from the conventional results, increases with decreasing δ values. The analytical expression for α_c shows good agreement with the numerical result. Finally, the findings in the paper are compared with previous results as well as with the real life application of composite materials.

cond-mat.stat-mech↗

arXiv2017

Creep-like behavior in athermal threshold dynamics: Effects of disorder and stress

We study the dynamical aspects of a statistical-mechanical model for fracture of heterogeneous media: the fiber bundle model with various interaction range. Although the model does not include any thermal activation process, the system exhibits creep-like behaviors under a constant load being slightly above the critical value. These creep-like behaviors comprise three stages: in the primary and tertiary stages, the strain rate exhibits power-law behaviors with time, which are well described by the Omori-Utsu and the inverse Omori laws, respectively, although the exponents are larger than those typically observed in experiments. A characteristic time that defines the onset of power-law behavior in the Omori-Utsu law is found to decrease with the strength of disorder in the system. The analytical solution, which agrees with the above numerical results, is obtained for the mean-field limit. Beyond the mean-field limit, the exponent for the Omori-Utsu law tends to be even larger but decreases with the disorder in the system. Increasing the spatial range of interactions, this exponent is found to be independent of disorder and to converge to the mean-field value. In contrast, the inverse Omori law remains independent of the spatial range of interaction and the disorder strength.

cond-mat.stat-mech↗

arXiv2017

Predictability and Strength of a Heterogeneous System : The Role of System Size and Disorder

In this work I have studied the effect of disorder and system size in fiber bundle model with a certain range of stress redistribution. The strength of the bundle as well as the failure abruptness is observed with varying disorder, stress release range and system sizes. With a local stress concentration, the strength of the bundle is observed to decrease with system size. The behavior of such decrement changes drastically as disorder strength is tuned. At moderate disorder, the critical stress scales with system size in an inverse logarithmic manner. In low disorder, where the brittle response is highly expected, the strength decreases in a scale free manner. With increasing system size and stress release range the model approaches thermodynamic limit and the mean field limit respectively. A detail study expresses different limit in the model and the corresponding modes of failure on the plane of above mentioned parameters.

cond-mat.stat-mech↗

arXiv2016

Failure time in heterogeneous systems

We show that the failure time $τ_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $δ$ and the stress release range $R$ in the system. For $R$ beyond a critical value $R_c$ the distribution of $τ_f$ follows Weibull form. In this region, the average $τ_f$ shows the variation $τ_f \sim L^α$ where $L$ is the system size. For $R<R_c$, $τ_f\sim L/R$. We find that the crossover length scale has the scaling form $R_c \sim L^{1-α}$. This scaling has been found to be valid for various disorder distributions. For $δ<δ_c$, $α$ is an increasing function of $δ$. For all $δ\ge δ_c$, $α$=1/3.

cond-mat.dis-nn↗

arXiv2016

A Recipe for Composite Materials: An Approach through Fiber Bundle Model

Strengthening of materials and preventing abrupt fracture are really challenging jobs in the field of engineering and material science. Such problems can be resolved by using composite materials. In this work, we have studied the fracture process of a composite material in light of fiber bundle model with different elastic constants as well as different random threshold breaking strength of fibers. The critical width of the threshold distribution ($δ_c$), for which abrupt failure occurs, is studied both analytically and numerically with increasing number of components $(k)$ in the composite and it is shown that $δ_c$ is inversely related to $k$. Corresponding phase diagram for the model suggests decrease in the tendency of abrupt fracture as number of components in the composite increase.

cond-mat.mtrl-sci↗

arXiv2015

Nucleation versus percolation: Scaling criterion for failure in disordered solids

One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as $R$ scales slower than $L^ζ$, with $ζ=2/3$. For a faster increase in $R$, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

cond-mat.stat-mech↗

arXiv2014

Criticality in Fiber Bundle Model

We report a novel critical behavior in the breakdown of an equal load sharing fiber bundle model at a dispersion $δ_c$ of the breaking threshold of the fibers. For $δ< δ_c$, there is a finite probability $P_b$, that rupturing of the weakest fiber leads to the failure of the entire system. For $δ\geq δ_c$, $P_b = 0$. At $δ_c, P_b \sim L^{-η}$, with $η\approx 1/3$, where $L$ is the size of the system. As $δ\rightarrow δ_c$, the relaxation time $τ$ diverges obeying the finite size scaling law: $τ\sim L^β(|δ-δ_c| L^α)$ with $α, β= 0.33 \pm 0.05$. At $δ_c$, the system fails, at the critical load, in avalanches (of rupturing fibers) of all sizes $s$ following the distribution $P(s) \sim s^{-κ}$, with $κ= 0.50 \pm 0.01$. We relate this critical behavior to brittle to quasi-brittle transition.

cond-mat.stat-mech↗