arXiv subjects

Ram Prakash Bharti

Publications and source records attributed to Ram Prakash Bharti.

16 recordsLinked to original sources

arXiv2026

A Robust Cell-Centered Nodal Integral Method (RCCNIM) for Nonlinear Burgers' Equation: Accurate Formulation, Efficient Implementation, and Validation

An improved formulation of the recently developed cell-centered nodal integral method (MCCNIM) is proposed for the numerical solution of the nonlinear Burgers' equation. The improved scheme, referred to as RCCNIM, reformulates the nonlinear convection term prior to discretization by evaluating the convective velocity using cell-averaged values from the previous time level, rather than the present-time approximation used in the original MCCNIM formulation. This reformulation leads to a fully algebraic system whose coefficients depend only on known quantities and are therefore evaluated once per time step. As a result, the proposed method significantly reduces computational cost while retaining the accuracy of the original MCCNIM. The performance of RCCNIM is assessed through systematic numerical comparisons with MCCNIM for the nonlinear Burgers' equation. The results demonstrate that RCCNIM achieves comparable accuracy with improved computational efficiency, indicating its potential for extension to more complex nonlinear fluid flow problems.

math.NA↗

arXiv2026

Performance Evaluation of RANS-Based Turbulence Models in Predicting Turbulent Non-Premixed Swirling Combustion within a Realistic Can Combustor

This study has presented a comprehensive computational fluid dynamics (CFD) analysis of combustion flow in a realistic can combustor, evaluating the influence of various turbulence models on flow, thermal, and species fields. The non-premixed combustion modeling is performed using a presumed (beta) PDF approach in conjunction with a steady laminar flamelet model employing the San Diego reaction mechanism, and the turbulence is modeled using the RANS approach. The influence of turbulence models (standard $k-ε$, realizable $k-ε$, SST $k-ω$, LPS-RSM) on the velocity field, such as the mean axial velocity, mean transverse velocity, turbulent kinetic energy (TKE) and shear stress, is analyzed, besides their influence on temperature and species (\ce{C3H8}, \ce{CO2}, and \ce{CO}) concentration. Analysis showed that despite the shortcomings of the isotropic turbulent viscosity formulation of the SST $k-ω$ model being evident, it predicted the mean axial velocity, mean transverse velocity, turbulent kinetic energy and shear stress more accurately. Additionally, it predicted the flow features expected in a can combustor, such as the central recirculation zone (CRZ) and central vortex core (CVC), more accurately than other models. Besides, the model predicted a higher temperature in the primary zone, which is supported by a lower prediction of \ce{C3H8}, and elevated TKE, both of which support strong mixing and efficient heat release. Furthermore, the SST $k-ω$ model predicted the most compact stoichiometric mixture fraction bubble, encompassing CRZ and shear layers, indicating that the majority of the combustion occurs in the primary zone. The corresponding progress variables also indicated high values in the primary zone and shear layers, confirming near completion of the reaction, supported by negligible prediction of \ce{C3H8} and \ce{CO} at the outlet.

physics.flu-dyn↗

arXiv2026

Experimental and Computational Analysis of the Hydrodynamics of Droplet Generation in a Cylindrical Microfluidic Device

This study investigates the hydrodynamics of droplet formation in a T-shaped cylindrical microfluidic device using micro-PIV experiments and CFD simulations. Devices of 150 micro-m internal diameter were fabricated from PDMS via a cost-effective embedded templating method. Flow visualization was conducted using immiscible silicone oil and deionized water, forming water-in-oil droplets. A mathematical model coupling the Navier-Stokes and conservative level-set equations was solved using the finite element method. Detailed flow fields (velocity, pressure, and phase distribution) were obtained over a wide range of flow-rate ratios (0.1-10) and capillary numbers (0.001-0.1) to characterize droplet formation mechanisms. Phase evolution revealed distinct breakup stages (lag, filling, necking, and pinch-off) and multiple regimes (squeezing, dripping, sausage flow, and parallel flow with tip streaming). A regime map delineating droplet and non-droplet regions was developed. Droplet size, curvature, and internal flow profiles exhibited strong dependence on Ca and Qr. Scaling analysis showed linear dependence of droplet size on Qr in the squeezing regime, with curvature nearly independent of Qr. In contrast, both size and curvature followed power-law dependence on Ca and Qr in the dripping regime. Velocity fields inside droplets were laminar and parabolic in the core. Fully developed plug-like profiles appeared in squeezing, whereas front and rear regions remained developing in dripping. Correlations for droplet length, curvature, and film thickness, including a novel thin-film model incorporating visco-inertial and capillary effects, enable predictive design within the studied range. These findings advance fundamental understanding of confined droplet dynamics and provide quantitative guidelines for optimizing droplet-based microfluidic systems.

physics.flu-dyn↗

arXiv2025

Electroviscous effects in electrolyte liquid flow through an oppositely-charged contraction-expansion microfluidic slit device

Electrokinetic flows in microchannels with opposite charge asymmetry, i.e., unequal and contrasting surface charges on opposing channel walls, significantly influence microfluidic hydrodynamics and can be exploited for enhanced control of mass transfer, mixing, and heat transport in microfluidic applications. This study numerically investigates electroviscous flow of a liquid electrolyte through an oppositely charged non-uniform microslit. The governing Poisson, Nernst-Planck, and Navier-Stokes equations are solved using the finite element method to determine the coupled electrokinetic fields for a wide range of dimensionless parameters: Reynolds number (Re = 0.01), Schmidt number (Sc = 1000), inverse Debye length (K = 2-20), top-wall surface charge density (St = 4-16), surface charge density ratio (Sr = -2 to 0), and contraction ratio (dc = 0.25). For completeness, results for like-charged devices, where both walls carry surface charges of the same sign (Sr = 0-2), are also included. The results show that maximum enhancement in total electrical potential (|ΔU|) and pressure drop (|ΔP|) reaches 296.82% at K = 20, St = 4, -2 \le Sr \le -1.25, and 14.57% at St = 16, Sr = 0, K = 2-20, respectively. The electroviscous correction factor Y exhibits maximum increases of 14.02% at K = 2, St = 16; 11.81% at K = 2, Sr = 0; and 14.57% at Sr = 0, St = 16, when Sr increases (-0.75 to 0), St increases (4 to 16), and K decreases (20 to 2), respectively. The overall maximum increment in Y is 15.13% at K = 2, Sr = 0, St = 16, relative to the non-electroviscous flow case. These findings demonstrate that opposite charge asymmetry, though weaker than similar asymmetry, still strongly influences electroviscous flow in non-uniform microchannels.

physics.flu-dyn↗

arXiv2025

Unconfined flow of a non-Newtonian power-law fluid past counter-rotating circular cylinders

This study numerically examines the steady unconfined laminar flow of incompressible non-Newtonian power-law fluids past a pair of side-by-side counter-rotating circular cylinders using the finite element method. The cylinders simultaneously rotate at equal angular speeds in opposite directions, with the upper cylinder (UC) rotating clockwise and the lower cylinder (LC) counterclockwise. The numerical simulations are performed over wide parameter ranges: power-law index ($0.2 \le n \le 1.8$), rotational rate ($0 \le α\le 2$), gap ratio ($0.2 \le G \le 1$), and Reynolds number ($1 \le Re \le 40$). The detailed influence of these flow parameters on key flow characteristics, including streamlines, surface pressure, centerline velocity, and individual as well as total drag and lift coefficients, is systematically analyzed. For stationary cylinders ($α= 0$), a twin-vortex structure forms in the wake, which progressively vanishes with increasing rotation ($α= 2$). The surface pressure coefficient attains its maximum values for shear-thickening fluids ($n > 1$) at higher rotational speeds, irrespective of the gap ratio. The total drag coefficient ($C_D$) decreases with increasing $α$ and $n$, whereas the lift coefficient ($C_L$) exhibits a more intricate dependence on the flow parameters. The results provide fundamental insights into the interplay between rotation, non-Newtonian rheology, and geometric confinement in determining the hydrodynamic behavior of rotating cylinder systems.

physics.flu-dyn↗

arXiv2025

Efficient cell-centered nodal integral method for multi-dimensional Burgers equations

An efficient coarse-mesh nodal integral method (NIM), based on cell-centered variables and termed the cell-centered NIM (CCNIM), is developed and applied to solve multi-dimensional, time-dependent, nonlinear Burgers equations, extending the applicability of CCNIM to nonlinear problems. To overcome the existing limitation of CCNIM to linear problems, the convective velocity in the nonlinear convection term is approximated using two different approaches, both demonstrating accuracy comparable to or better than traditional NIM for nonlinear Burgers problems. Unlike traditional NIM, which utilizes surface-averaged variables as discrete unknowns, this innovative approach formulates the final expression of the numerical scheme using discrete unknowns represented by cell-centered (or node-averaged) variables. Using these cell centroids, the proposed CCNIM approach presents several advantages compared to traditional NIM. These include a simplified implementation process in terms of local coordinate systems, enhanced flexibility regarding the higher order of accuracy in time, straightforward formulation for higher-degree temporal derivatives, and offering a viable option for coupling with other physics. The multi-dimensional time-dependent Burgers problems (propagating shock, propagation, and diffusion of an initial sinusoidal wave, shock-like formation) with known analytical solutions are solved in order to validate the developed scheme. Furthermore, a detailed comparison between the proposed CCNIM approach and other traditional NIM schemes is conducted to demonstrate its effectiveness. The proposed approach has shown quadratic convergence in both space and time, i.e., O[$(Δx)^2, (Δt)^2$], for the considered test problems. The simplicity and robustness of the approach provide a strong foundation for its seamless extension to more complex fluid flow problems.

math.NA↗

arXiv2024

CFD analysis of electroviscous effects in electrolyte liquid flow through heterogeneously charged uniform microfluidic device

This study has numerically investigated the charge-heterogeneity effects in the electroviscous flow of symmetric ($1$:$1$) electrolyte liquid through a uniform slit microfluidic device. The Poisson's, Nernst-Planck (N-P), Navier-Stokes (N-S), and continuity equations are solved using the finite element method (FEM) to obtain the flow fields, such as total electrical potential ($U$), excess charge ($n^\ast$), induced electric field strength ($E_\text{x}$), and pressure ($P$) fields for following conditions: inverse Debye length ($2\le K\le 20$), surface charge density ($4\le \mathit{S_\text{1}}\le 16$), and surface charge-heterogeneity ratio ($0\le \mathit{S_\text{rh}}\le 2$). Results have shown that the total potential ($|ΔU|$) and pressure ($|ΔP|$) drop maximally increase by 99.09% (at $K=20$, $\mathit{S_\text{1}}=4$) and 12.77% (at $K=2$, $\mathit{S_\text{1}}=8$), respectively with overall charge-heterogeneity ($0\le \mathit{S_\text{rh}}\le 2$). Electroviscous correction factor (i.e., the ratio of effective to physical viscosity) maximally enhances by 12.77% (at $K=2$, $\mathit{S_\text{1}}=8$), 40.98% (at $\mathit{S_\text{1}}=16$, $\mathit{S_\text{rh}}=1.50$), and 41.35% (at $K=2$, $\mathit{S_\text{rh}}=1.50$), with the variation of $\mathit{S_\text{rh}}$ (from 0 to 2), $K$ (from 20 to 2), and $\mathit{S_\text{1}}$ (from 0 to 16), respectively. Further, a simple pseudo-analytical model is developed to estimate the pressure drop in the electroviscous (EV) flow, accounting for the influence of charge-heterogeneity based on the Poiseuille flow in the uniform channel. This model predicts the pressure drop $\pm$2-4% within the numerical results. The robustness and simplicity of this model enable the present numerical results for engineering and design aspects of microfluidic applications.

physics.flu-dyn↗

arXiv2024

CFD analysis of the influence of solvent viscosity ratio on the creeping flow of viscoelastic fluid over a channel-confined circular cylinder

In this study, the role of solvent viscosity ratio ($β$) on the creeping flow characteristics of Oldroyd-B fluid over a channel-confined circular cylinder has been explored numerically. The hydrodynamic model equations have been solved by RheoTool, an open-source toolbox based on OpenFOAM, employing the finite volume method for extensive ranges of Deborah number ($De = 0.025-1.5$) and solvent viscosity ratio ($β= 0.1-0.9$) for the fixed wall blockage ($B = 0.5$). The present investigation has undergone extensive validation, with available literature under specific limited conditions, before obtaining detailed results for the relevant flow phenomena such as streamline, pressure and stress contour profiles, pressure coefficient ($C_p$), wall shear stress ($τ_w$), normal stress ($τ_{xx}$), first normal stress difference ($N_{1}$), and drag coefficient ($C_{\text{D}}$).The flow profiles have exhibited a distinctive behavior characterized by a loss of symmetry in the presence of pronounced viscoelastic and polymeric effects. The results for low $De$ notably align closely with those for Newtonian fluids, and the drag coefficient ($C_D$) remains relatively constant regardless of $β$, as the viscoelastic influence is somewhat subdued. As $De$ increases, the influence of viscoelasticity becomes more pronounced, while a decrease in $β$ leads to an escalation in polymeric effects; an increase in the $C_D$ value is observed as $β$ increases. Within this parameter range, the prevailing force governing the flow is the pressure drag force.

physics.flu-dyn↗

arXiv2023

CFD analysis of electroviscous effects in electrolyte liquid flow through heterogeneously charged non-uniform microfluidic device

In this work, the pressure-driven flow of symmetric electrolyte liquid through a heterogeneously charged contraction-expansion (4:1:4) microfluidic device has been investigated numerically. Total potential ($U$), ion concentrations ($n_\pm$), velocity (${V}$), and pressure ($P$) fields are obtained after solving the mathematical model consisting of the Poisson's, Nernst-Planck (NP), Navier-Stokes (NS), and continuity equations numerically using the finite element method (FEM). Results are presented for wide ranges of dimensionless parameters such as inverse Debye length ($2\le K\le 20$), surface charge density ($4\le S_\text{1}\le 16$), and surface charge-heterogeneity ratio ($0\le S_\text{rh}\le 2$). Results show that the total potential ($ΔU$) and pressure ($ΔP$) drops change maximally by 3511.45% \add{(0.2127 to 7.6801)} (at $S_1=4$, $K=20$) and 41.4% \add{(1.0941 to 1.5471)} (at $S_1=16$, $K=2$), respectively with overall enhancing charge-heterogeneity ($0\le S_\text{rh}\le 2$), over the ranges of $K$ and $S_1$. Electroviscous correction factor, $Y$ (i.e., ratio of apparent to physical viscosity) increases maximally by 24.39\% \add{(1.1158 to 1.3879)} (at $K=4$, $S_\text{rh}=1.75$), 37.52% \add{(1.0597 to 1.4573)} (at $S_1=16$, $S_\text{rh}=2$), and 41.4% \add{(1.0306 to 1.4573)} (at $S_1=16$, $K=2$) with the variation of $S_1$ from 4 to 16, $K$ from 20 to 2, and $S_\text{rh}$ from 0 to 2, respectively. Further, overall increment in $Y$ is noted as 45.73\% \add{(1 to 1.4573)} (at $K=2$, $S_1=16$, $S_\text{rh}=2$), relative to non-EVF ($S_1=0$ or $K=\infty$). Thus, charge-heterogeneity enhances electroviscous effects in microfluidic devices, which enables the use of present numerical results for designing reliable and essential micro-sized channels for practical microfluidic applications.

physics.flu-dyn↗

arXiv2023

CFD analysis of the influence of contraction size on electroviscous flow through the slit-type non-uniform microfluidic device

The electroviscous effects are relevant in controlling and manipulating the fluid, thermal, and mass transport microfluidic processes. The existing research has mainly focused on the fixed contraction ratio ($d_\text{c}$, i.e., the area ratio of contraction to expansion) concerning the widely used contraction-expansion geometrical arrangement. This study has explored the influence of the contraction ratio ($d_\text{c}$) on the electroviscous flow of electrolyte liquids through the charged non-uniform microfluidic device. The numerical solution of the mathematical model (Poisson's, Nernst-Planck, and Navier-Stokes) using a finite element method (FEM) yields the local flow fields. In general, the contraction ratio significantly affects the hydrodynamic characteristics of microfluidic devices. The total electrical potential and pressure drop maximally increase by {1785\% and 2300\%}, respectively, with an overall contraction ratio ($0.25\le d_\text{c}\le 1$). Further, an electroviscous correction factor ($Y$, i.e., the ratio of apparent to physical viscosity) maximally enhances by 11.24\% (at $K=8$, $S=16$ for $0.25\le d_\text{c}\le 1$), 31.80\% (at $S=16$, $d_\text{c}=0.75$ for $2\le K\le 20$), 22.89\% (at $K=2$, $d_\text{c}=0.5$ for $4\le S\le 16$), and 46.99\% (at $K=2$, $d_\text{c}=0.75$ for $0\le S \le 16$). The present numerical results may provide valuable guidelines for the performance optimization and design of reliable and essential microfluidic devices.

physics.flu-dyn↗

arXiv2023

Evaluation of RANS-based turbulence models for isothermal flow in a realistic can-type gas turbine combustor application

The present study assesses RANS-based turbulence models to simulate isothermal flow in a combustor representing a constituent can combustor of can-annular configuration used in jet engines. Two-equation models (standard $k-ε$, realizable $k-ε$, standard $k-ω$, SST $k-ω$), and Linear Pressure Strain - Reynolds Stress Model (LPS-RSM), are assessed by comparing their predictions of mean axial and transverse velocity, turbulent kinetic energy, and shear stress with the experimental data at the primary and dilution hole planes in combustor. While the two-equation models generally have failed to predict the confined swirling flow at both positions accurately, the SST $k-ω$ model yielded the most accurate, followed by standard $k-ω$ and realizable $k-ε$ models. The discrepancies between the computational and experimental results could be attributed to the isotropic turbulence assumptions, which, however, are invalid for confined swirling flows. Further, the two-equation model formulations cannot capture the intricacies of vortex flow and its interaction with the surroundings in confined swirling flows. LPS-RSM, which considers turbulence anisotropy, showed some promise, although overpredicted results follow the trend with experimental values at the primary holes plane. However, at dilution holes plane, the model overpredicted the velocity field and underestimated turbulence field, including turbulent kinetic energy and shear stress. These observed discrepancies can be ascribed to the pressure-strain correlation in the LPS-RSM, which assumes the pressure is a linear function of the strain-rate tensor. However, for complex flows, this linear assumption is quite simplistic. Hence, this study suggests that more advanced turbulence models such as non-LPS-RSM are needed to accurately predict the confined swirling flow in combustors.

physics.flu-dyn↗

arXiv2023

CFD analysis of electroviscous effects in pressure-driven flow of electrolyte liquid through an asymmetrically charged non-uniform microfluidic device

The electroviscous effects in the pressure-driven flow of electrolyte liquid through an asymmetrically charged contraction-expansion (4:1:4) slit microfluidic device have been investigated numerically. The mathematical model (i.e., Poisson's, Navier-Stokes, and Nernst-Planck equations) is solved using the finite element method to obtain the electrical potential, velocity, pressure, ion concentration fields, excess charge, an induced electric field strength for the following ranges of parameters: Reynolds number (${Re=0.01}$), Schmidt number (${\mathit{Sc}=1000}$), inverse Debye length (${2\le K\le 20}$), top wall surface charge density (${4\le S_t\le 16}$), surface charge ratio (${0\le S_r\le 2}$) and contraction ratio (${d_{\text{c}}=0.25}$). Results show that the charge asymmetry at the different walls of the microfluidic device plays a significant role in the induced electric field development and microfluidic hydrodynamics. The total potential (${|ΔU|}$) and pressure drop (${|ΔP|}$) maximally increase by 197.45\% and 25.46\%, respectively, with asymmetry of the charge. {The electroviscous correction factor (ratio of apparent to physical viscosity) maximally increases by 20.85\% (at ${K=2}$, ${S_t=16}$ for ${0\le S_r\le 2}$), 25.46\% (at ${S_t=16}$, ${S_r=2}$ for ${2\le K\le 20}$), and 39.13\% (at ${K=2}$, ${S_r=2}$ for ${0\le S_t\le16}$).} Further, a simpler analytical model is developed to predict the pressure drop in electroviscous flow considering asymmetrically charged surface, based on the Poiseuille flow in the individual uniform sections and pressure losses due to orifice, estimates the pressure drop 1--2\% within the numerical results. The robustness of this model enables the use of present numerical results for design aspects in microfluidic applications.

physics.flu-dyn↗

arXiv2022

CFD analysis of effects of surface wettability and flow rates on the interface evolution and droplet pinch-off mechanism in the cross-flow microfluidic systems

This study has numerically investigated the effect of surface wettability on two-phase immiscible flow and dynamics of droplet pinch-off in a T-junction microchannel using finite element method. A conservative level set method (CLSM) has been adopted to capture the interface topology in squeezing regime ($Ca_c <10^{-2}$) for wide flow rate ratio ($1/10 \leq Q_r \leq 10$) and contact angle ($120^{\circ} \leq θ\leq 180^{\circ}$). Based on the instantaneous phase profiles, droplet formation stages are classified as initial, filling, squeezing, pinch-off and stable droplet. Wettability effects are insignificant in filling stage. However, hydrophobic effects are more visible in squeezing and pinch-off stages. Engineering parameters have generally shown complex dependence on dimensionless parameters ($Ca_c$, $Q_r$, $θ$). Capturing the instantaneous interface evolution has revealed droplet shape senstivity with the contact angle. Interface profiles transform from convex into concave immediately for hydrophobic ($120^{\circ} \leq θ\leq 135^{\circ}$) whereas slowly for super hydrophobic ($150^{\circ} \leq θ\leq 180^{\circ}$) conditions. In contrast to the literature, pressure in dispersed phase is not constant, but it is an anti-phase with pressure in continuous phase. Comparing the filling and pinch-off time based on the pressure and phase profiles has brought new insights that the droplet pinch-off mechanism can be elucidated by installing the pressure sensors even without the flow visualization and phase profiles. The interface curvature adopts a flattened to a more concave shape when the Laplace pressure varies from a smaller to a higher value. The interface neck width (2r) shows an increasing trend up to a threshold value and then decreases linearly with the contact angle.

physics.flu-dyn↗

arXiv2022

Charge-dependent slip flow of ionic liquids through the non-uniform microfluidic device: pressure drop and electroviscous effects

This work investigates electroviscous effects in presence of charge-dependent slip in steady pressure-driven laminar flow of a symmetric (1:1) electrolyte liquid through a uniformly charged slit contraction - expansion (4:1:4) microfluidic device. The mathematical model comprising Poisson's, Nernst-Planck, Navier-Stokes, and current continuity equations are solved numerically using finite element method (FEM). The flow fields (electrical potential, charge, induced electric field strength, pressure drop, and electroviscous correction factor) have been obtained and presented for a wide range of parameters like inverse Debye length (K=2-20), surface charge density (S=4-16) and slip length ($0\le B_0\le 0.20$) at fixed Schmidt number (Sc=1000) and low Reynolds number (Re=0.01). The flow fields have shown complex dependence on governing parameters. The charge-dependent slip has further enhanced complexity of dependency in comparison to no-slip condition. The total electrical potential ($|ΔU|$) maximally increases by 78.68%, and pressure drop ($|ΔP|$) maximally decreases by 63.42%, relative to no-slip flow, over the ranges of conditions. The electroviscous correction factor ($Y=$ ratio of apparent to physical viscosity) increases by 33.58% under the no-slip ($B_0=0$) condition. It ($Y$) increases maximally by 72.10% for charge-dependent slip than in no-slip flow for considered ranges of the conditions. A simple analytical model to estimate the pressure drop in the electroviscous flow has been developed based on the Poiseuille flow in individual uniform sections and pressure loss due to thin orifice. The model overpredicts pressure drop by 2 - 4% from the numerical values. Finally, the predictive relations, depicting the functional dependence of numerical results on governing parameters, are presented for their practical use in design and engineering of microfluidic devices.

physics.flu-dyn↗

arXiv2022

Computational analysis of interface evolution and droplet pinch-off mechanism in two-phase liquid flow through T-junction microfluidic system

This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element method under the squeezing regime ($Ca_c < 10^{-2}$) for wide range of flow rates ($Qr = 0.1 - 10$) and fixed contact angle ($θ=135^o$). The droplet formation process has been classified into various instantaneous stages as initial, filling, squeezing, pinch-off and stable droplet through microscopic visualization of interface evolution in phase profiles. The dynamics of interface, and point pressure in both phases is further gained and discussed. Maximum pressure in the continuous phase varied linearly with Qr. The droplet pinch-off mechanism has been thoroughly elucidated by determining the local radius of the curvature ($R_{c,min}$) and neck width (2r) during the squeezing and pinch-off stages. At the pinch-off point, both $R_{c,min}$ and 2r are non-linearly related to Qr. Further, the topological dynamics of interface has been explored by analyzing the Laplace pressure ($p_{\text{L}}$), acting on the interface curvature, evaluated using (a) pressure sensors in both phases, (b) local radius of curvature, and (c) minimum radius of curvature. The insights obtained from the present work can reliably be used in designing the model and prototypes of microfluidic devices for generating monodispersed droplets in emulsions, and the droplet breakup mechanism would help accurate prediction of the pinch-off moment. The proposed knowledge provides detailed insights of the interface evolution and droplet pinch-off to a precision of 10 $μ$s and resolution of 10 $μ$m, equivalent to experimental flow visualization with a high-speed ($10^{5}$ fps) and high-resolution (10 $μ$m pixel size) camera.

physics.flu-dyn↗

arXiv2022

Effects of capillary number and flow rates on the hydrodynamics of droplet generation in T-junction microfluidic systems

The hydrodynamics of droplets is significant in wide-ranging applications involving immiscible fluids and emulsions in food and pharmaceutical. The control and manipulation of droplets are primarily a function of flow governing and geometrical parameters. The finite element and level set approaches are used in this work to explore the influences of capillary number (Ca) and flow rate ratio (Qr) of dispersed and continuous phases on hydrodynamics of droplet generation in two-phase flow through T-junction cross-flow microfluidic device. A mathematical model based on a mass continuity, Navier-Stokes, and level set equations are solved computationally using the Eulerian framework for Ca = 1e-4 - 1 and Qr =0.1 - 10. Both immiscible phases, having equal density and unequal viscosity, flow (Re=0.1) through equal-sized channels. In particular, instantaneous phase flow field, droplet size, droplet detachment time and generation frequency are presented and discussed as a function of governing parameters (Ca and Qr). Considered parametric space is characterized as squeezing, first transition, dripping, second transition, parallel, and jet flow regimes. In contrast to threshold Ca ~ 0.01 in earlier studies, squeezing regime exists for all Ca and Qr = 2- 10. Flow regimes are also mapped into droplets and non-droplet zones. Threshold interfacial Ca, defining the boundary between droplet and non-droplet zones, scales quadratically with Qr. Droplet dynamics shows a complex dependence on Ca and Qr. Droplet length varies linearly with Qr in squeezing regime whereas power-law variation with Ca and Qr in dripping regime. Droplet frequency shows a power-law function of Ca and Qr in droplet zone. Present results compare excellently with earlier limited experimental and numerical studies. Finally, present results and predictive correlations can guide engineering and design of droplet microfluidics devices.

physics.flu-dyn↗