Fluid Viscosity Research Articles

Dual-functional adsorptive membranes for PFAS removal: Mechanism, CFD simulation, and selective enrichment

The remediation of emerging water contaminants, particularly per- and polyfluoroalkyl substances (PFAS), presents challenges due to their refractory nature and the presence of competing substances. Dual-functional adsorptive membranes, with hydrophobic backbone and quaternary ammonium moieties, were thereby designed to selectively intercept organic competitors while enrich PFAS. A 96.8 % removal of perfluorooctanoic acid (PFOA) was achieved and this effective removal (>90 %) maintained across five reuse cycles with a total treatment capacity of 650 L m−2. Rather than the rejection mechanism of nanofiltration process, these adsorptive membranes utilize synergistic electrostatic attraction and hydrophobic interactions, leading to a greater enrichment factor of 18.5 (PFOA over humic acid) and a permeability of 34.6 L m-2h−1 bar−1 (1.9- and 4.5-fold higher than reported NF 270 membranes, respectively). Furthermore, computational fluid dynamics (CFD) modeling revealed that the sponge-like matrix effectively prevents channeling flow and enhance access to adsorption sites. Sensitivity analysis and the high Damkohler number indicated that the adsorption process is mass transfer-controlled, with the key parameters ranked in order of significance: residence time > fluid viscosity > intrinsic adsorption rate. With consistent removal performance with co-existing competitors, efficient regeneration, and reusability, the dual-functional adsorptive membranes offer promising practical efficacy for PFAS remediation.

The effect of temperature on asphaltene transformation and agglomeration in oil pressure tank systems under injection of carbon dioxide in a porous structure: A molecular dynamics study

Asphaltene is a complex blend of high-molecular-weight hydrocarbons present in crude oil. It is a solid, insoluble component that precipitates from oil under certain circumstances, such as temperature (Temp), pressure, or composition changes. Despite its problems, asphaltene has potential uses in a variety of sectors, including the manufacture of carbon materials, asphalt, and pharmaceuticals. Specifically, this study investigated the changes in the asphaltene compaction process under carbon dioxide (CO2) injection by examining changes in initial temperature and analyzing influencing parameters such as radial distribution function, radius of gyration, and density changes. In this study, thermodynamic equilibrium in simulated asphaltene samples was achieved within 10 ns, with temperature and kinetic energy stabilizing at 310 K and 0.86 kcal/mol, respectively. The subsequent analysis focused on the agglomeration of asphaltene molecules under varying temperatures. The agglomeration process was completed within 10 ns, with the gyration radius stabilizing at 30.5 Å, providing insights into asphaltene behavior and its impact on petroleum fluid properties. At 300 K, asphaltene agglomeration increased viscosity to 23.3 Pa s by reducing molecular movement, illustrating the complex relationship between aggregation and fluid viscosity. The study also observed that asphaltene agglomeration increased viscosity to approximately 23.3 Pa s at 300 K due to reduced molecular movement. As the temperature was raised from 300 to 400 K, the maximum density profile decreased from 0.0225 to 0.0207 atom/Å3, while the gyration radius of asphaltene molecules decreased from 30.54 to 28.51 Å and viscosity increased from 23.3 to 23.92 Pa s. These results highlight the intricate effects of temperature on asphaltene dynamics and petroleum fluid properties.

Numerical Simulations of Flow and Heat Exchange in Zigzag-Shaped Microchannels

Cooling of electronic components is of great importance currently. One of the most important methods of integrated circuit cooling is the use of microchannel heat sinks. The aim of this work is to analyze the cooling capacity of zigzag shaped microchannels. The heat exchange for four different microchannels was tested depending on the flow rate of the cooling liquid (water) and the temperature of the cooled element. The system of differential equations that describe fluid flow and heat transport is presented in the paper. The equations were solved using the finite volume method. The work showed that both the increase in the number of zigzag sections and the increase in the flow velocity cause an increase in the flow resistance. In contrast, an increase in the temperature of the cooled element causes a decrease in fluid viscosity, which results in a decrease in flow resistance. From the point of heat exchange, both the increase in the number of segments, the flow rate, and the temperature of the cooled element increase the cooling capacity of the microchannel. Research shows that zigzag shaped microchannels are excellent cooling elements, especially for geometrically small heat sources such as electronic components.

Design of a tooth-shaped magnetorheological brake with multiple coils

This research presents an optimized design for a tooth-shaped magnetorheological brake (MRB) with multiple coils. The MRB configuration consists of a disk immersed in magnetorheological fluid (MRF), where four coils act as electromagnets when an electric current is applied. The energized coils induce the alignment of suspended particles in the MRF, forming a chain-like structure that increases the fluid's viscosity. This rapid, strong, and controllable phenomenon enables the MRB to find applications in haptic systems, tension control, and industrial braking systems. To analyze the electromagnetic behavior of the brake, Finite Element Method (FEM) simulations are conducted using ANSYS APDL, and the optimization process is performed utilizing ANSYS Workbench software. The software provides optimized geometries for the brake, resulting in significant improvements in desired performance aspects compared to prior designs, etc.

Influence of mixed particle sizes on shear yield stress of magnetorheological fluid

AbstractThis study investigated the effect of magnetic particle size and volume fraction on the shear yield stress and dynamic viscosity of magnetorheological fluids. Magnetorheological fluids with varying volume fractions of micro‐ and nanoscale magnetic particles were prepared. A plate‐on‐plate shear test bench was constructed to evaluate the fluids under a constant shear rate, with the applied current ranging from 0 A to 1.2 A. Results indicated that the shear yield stress initially increased and then decreased as the volume fraction of magnetic nanoparticles increased, reaching a maximum of 47 kPa at a volume fraction of 7 %. However, the excessive addition of magnetic particles or large‐diameter particles led to settling and reduced stability of the fluids. The findings suggest that optimizing the size and volume fraction of magnetic particles is crucial for maximizing the shear yield stress of magnetorheological fluids.

Modeling proppant transport and settlement in 3D fracture networks in geothermal reservoirs

In this paper, we develop an efficient proppant transport model using the Eulerian-Eulerian approach for simulating proppant transport in fractures and 3D fracture networks in geothermal reservoirs. The proposed model accounts for proppant settling, pack/bed formation, bridging/screenout, proppant concentration effect, fracture wall effect, and the transition from Poiseuille flow (fracture channel) to Darcy flow (proppant pack). Notably, the heat transfer process and its impact on proppant transport are also considered—a facet often overlooked in previous proppant transport models. A three-dimensional displacement discontinuity method (3D DDM) that incorporates the stress shadow effect is employed to generate the fracture geometry. The governing equations for slurry flow, proppant transport, and heat transfer are discretized and solved using the finite volume method (FVM). The model is verified against analytical solutions and published experimental data, demonstrating good agreement with these references. To demonstrate the proposed model, we applied it to both low-temperature (depleted hydrocarbon wells) and high-temperature (dry hot rocks) enhanced geothermal systems (EGS). The simulation results highlight the significant influence of reservoir temperature on proppant transport and settlement in a reservoir environment. Heating of the slurry by higher temperature reservoir rocks reduces fluid viscosity and accelerates proppant settling, thereby shortening the transport distance and reducing the coverage area of the proppant. Both ultra-light and micro-proppant are effective in mitigating proppant settlement in enhanced geothermal systems. However, proppant is susceptible to bridging at fracture intersections, where the fracture widths are narrower due to more pronounced stress shadow effects in these areas. Consequently, the use of micro-proppant could offer substantial benefits over ultra-light proppant in enhancing proppant coverage area in enhanced geothermal systems.

Analysis of Flow Loss Characteristics of a Multistage Pump Based on Entropy Production

To reveal the internal flow loss characteristics of a multi-stage pump, the unsteady calculation of the internal flow field of a seven-stage centrifugal pump was carried out, and the entropy production theory and Q criterion were utilized to analyze the unsteady flow characteristics of each flow component under different flow rates. The research results show that as the flow rate increases, the entropy production value and the energy loss inside the flow components also increase accordingly. The viscous dissipation entropy production caused by fluid viscosity is very small, and the turbulent dissipation entropy production caused by turbulent fluctuations and wall dissipation entropy production are the main sources of energy loss. The impellers, diffusers, and outlet chamber are the main regions of energy loss in the multistage pump. The entropy production value of the first-stage impeller is significantly higher than that of other impellers, while the entropy production value of the first-stage diffuser is significantly lower than that of other diffusers. Through vortex structure analysis, it is found that the high entropy production regions in the impeller are concentrated in the impeller inlet area, the blade suction surface, and the impeller outlet area.

Fluid-filled lattices for responsive orthotic insoles

Abstract Orthotic insoles are essential for alleviating discomfort and preventing injuries in the foot caused by high peak pressures in the plantar tissue. Traditional orthotic insoles, often prescribed to address these issues, are designed based on the static foot shape and pressure measurements, lacking responsiveness to dynamic movements. This study explores the behaviour of fluid-filled lattices for improving the functionality of orthotic insoles, focusing on energy dissipation and pressure redistribution capabilities. Using numerical homogenisation, the research integrates hyperelastic and permeability models to simulate the behaviour of Solid–Liquid Composites. Experimental tests validated these models, examining the influence of fluid viscosity and structural variations on energy dissipation and pressure distribution. Results show that fluid-filled lattices provide enhanced energy dissipation and reduce peak pressures by evening out the pressure distribution compared to non-fluid-filled samples. These findings highlight the potential of fluid-filled lattices to improve the performance and comfort of orthotic insoles.

Multi-Task Learning Network-Based Prediction of Hydraulic Fracturing Effects in Horizontal Wells Within the Ordos Yanchang Formation Tight Reservoir

Accurate prediction of fracture volume and morphology in horizontal wells is essential for optimizing reservoir development. Traditional methods struggle to capture the intricate relationships between fracturing effects, geological variables, and operational factors, leading to reduced prediction accuracy. To address these limitations, this paper introduces a multi-task prediction model designed to forecast fracturing outcomes. The model is based on a comprehensive dataset derived from fracturing simulations within the Long 4 + 5 and Long 6 reservoirs, incorporating both operational and geological factors. Pearson correlation analysis was conducted to assess the relationships between these factors, ranking them according to their influence on fracturing performance. The results reveal that operational variables predominantly affect Stimulated Reservoir Volume (SRV), while geological variables exert a stronger influence on fracture morphology. Key operational parameters impacting fracturing performance include fracturing fluid volume, total fluid volume, pre-fluid volume, construction displacement, fracturing fluid viscosity, and sand ratio. Geological factors affecting fracture morphology include vertical stress, minimum horizontal principal stress, maximum horizontal principal stress, and layer thickness. A multi-task prediction model was developed using random forest (RF) and particle swarm optimization (PSO) methodologies. The model independently predicts SRV and fracture morphology, achieving an R2 value of 0.981 for fracture volume predictions, with an average error reduced to 1.644%. Additionally, the model’s fracture morphology classification accuracy reaches 93.36%, outperforming alternative models and demonstrating strong predictive capabilities. This model offers a valuable tool for improving the precision of fracturing effect predictions, making it a critical asset for reservoir development optimization.

Intelligent neuron based interpretation of carreau trihybrid nanofluid model with streamline analysis: Configuration of distinct geometries

This current attempt develops a more efficient predictive model that can accurately simulate the behavior of Carreau trihybrid nanofluids in non-trivial configurations. This study interprets thermal behavior of Carreau trihybrid nanofluid model with streamline analysis considering the two geometries wedge and cone. Three nanoparticles are involved in base fluid (water) with physical effects of non-uniform heat sink source and nonlinear thermal radiation are assumed for heat transport and Lorentz forces are considered for velocity inspection. Furthermore, this study employs intelligent neural networks to interpret data for streamline and thermal transport analysis, focusing on the specific cases of wedge and cone geometries. Initial data fetched through bvp4c and further, obtained data trained through supervised neural scheme, Levenberg marquardt neural network (LM-NN) is applied and required predictions are made. Higher “Gc” indicates stronger solutal buoyancy forces, which promote upward fluid movement, thereby increasing the velocity gradient. With increasing (M), the velocity profile decreases. Fluid exhibits enhancing the velocity gradient with higher (n). Higher particle concentration enhances the fluid's viscosity and resistance.

A Comparison of 226- and 1000-Hz Probe Tone Tympanometry With Myringotomy Findings in Infants.

This study aimed to verify the diagnostic value of tympanometry with 226- and 1000-Hz probe tones in infants by comparing tympanometry results with the gold standard of the middle ear state assessed by myringotomy. Furthermore, clinically useful predictors for false peaked tympanograms despite the presence of middle ear fluid should be identified. Pre-operative 226- and 1000-Hz tympanograms were retrospectively compared with intraoperative findings of the tympanic cavity after myringotomy in 111 infants (217 ears) aged ≤ 12 months. In addition to the shape of tympanograms, demographic and clinical characteristics, the results of other audiometric measurements, and the viscosity of middle ear fluid, if present, were evaluated in several subgroups. The sensitivity and specificity of 1000-Hz tympanometry for middle ear effusion (MEE) detection were 97%-98% and 71%-84%, respectively, whereas standard tympanometry with a 226-Hz probe tone achieved a poor sensitivity of 43%-61% and a specificity of 81%-97%. Younger age, low viscosity of the middle ear fluid, and female sex were associated with an increased risk of false peaked 226-Hz tympanograms despite MEE. Furthermore, larger equivalent outer ear canal volumes were linked to false peaked 226-Hz tympanograms. The comparison of myringotomy findings and 226- and 1000-Hz tympanometry confirms the superiority of high-frequency tympanometry in infants younger than 12 months. Although this study identified some vague predictors of potentially false peaked 226-Hz tympanograms, the assessment of the middle ear state by 226-Hz tympanometry remains unreliable in young infants.

Nonlinear deterministic dynamic analysis of a GPL micropipe conveying pulsating laminar flow

In several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3 % addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98 % , and critical flow stimulation amplitude fraction by 152.19 % , while declines instability area bandwidth by 36.95 % , and steady state response by 67.17 % relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40 % , 42.59 % , 41.67 % , and 227.28 % in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications.

Numerical Simulation of Hydraulic Fracture Propagation in Unconsolidated Sandstone Reservoirs

In order to comprehensively understand the complex fracture mechanisms in thick and loose sandstone formations, we have carefully developed a coupled finite element numerical model that captures the complex interactions between fluid flow and solid deformation. This model is the cornerstone of our future exploration. Based on this model, the crack propagation problem of hydraulic fracturing under different engineering and geological conditions was studied. In addition, we conducted in-depth research on the key factors that shape the geometry of hydraulic fractures, revealing their subtle differences and complexities. It is worth noting that the sharp contrast between the stress profile and mechanical properties between the production layer and the boundary layer often leads to fascinating phenomena, such as the vertical merging of hydraulic fracture propagation. The convergence of cracks originating from adjacent layers is a recurring theme in these strata. Sensitivity analysis clarified our understanding, revealing that increased elastic modulus promotes longer crack propagation paths. As the elastic modulus increases from 12 GPa to 18 GPa, overall, the maximum crack width slightly decreases, with a less than 10% reduction rate. The increased fluid leakage rate will significantly shorten the length and width of hydraulic fractures (with a maximum decrease of over 70% in fracture width). The increase in viscosity of fracturing fluid causes a change in fracture morphology, with a reduction in length of about 32% and an increase in fracture width of about 25%. It is worth noting that as the leakage rate of fracturing fluid increases, the importance of the viscosity of fracturing fluid decreases relatively. Strategies such as increasing fluid viscosity or adding anti-filtration agents can alleviate these challenges and improve the efficiency of fracturing fluids. In summary, our research findings provide valuable insights that can provide information and optimization for hydraulic fracturing filling and fracturing strategies in loose sandstone formations, promoting more efficient and influential oil and gas extraction work.

Membrane Ruffles: Composition, Function, Formation and Visualization

Membrane ruffles are cell actin-based membrane protrusions that have distinct structural characteristics. Linear ruffles with columnar spike-like and veil-like structures assemble at the leading edge of cell membranes. Circular dorsal ruffles (CDRs) have no supporting columnar structures but their veil-like structures, connecting from end to end, present an enclosed ring-shaped circular outline. Membrane ruffles are involved in multiple cell functions such as cell motility, macropinocytosis, receptor internalization, fluid viscosity sensing in a two-dimensional culture environment, and protecting cells from death in response to physiologically compressive loads. Herein, we review the state-of-the-art knowledge on membrane ruffle structure and function, the growth factor-induced membrane ruffling process, and the growth factor-independent ruffling mode triggered by calcium and other stimulating factors, together with the respective underlying mechanisms. We also summarize the inhibitors used in ruffle formation studies and their specificity. In the last part, an overview is given of the various techniques in which the membrane ruffles have been visualized up to now.

An investigation of the behaviour of polymer fluids in the American Petroleum Institute filter press

The American Petroleum Institute (API) filter press test has been used for decades in the construction industry as part of the quality control regime for bentonite-based excavation support fluids. The industry has carried over the use of this test to polymer fluids despite the lack of published evidence of its suitability for these fluids and the very different mechanisms by which polymer fluids and bentonite slurries achieve excavation support. This paper presents the first systematic investigation of this issue through a combination of laboratory testing and theoretical analysis. The investigation demonstrates the very different behaviours of bentonite slurries and polymer fluids. In contrast to the results for bentonite slurries, API filter press results for polymers are shown to be highly sensitive to the filter paper used. In particular, repeatability testing revealed a substantial variation in the polymer fluid loss rates attributable to three primary factors: (a) the filter paper pore size; (b) filter paper damage resulting from the applied test pressure; (c) apparent ‘clogging’ of the filter paper pore space. Furthermore, the study demonstrates the poor repeatability of the API filter press test for polymer fluids even when filter papers of the same type are used. Interestingly, analysis of polymer flow with respect to filter paper pore size and the applied pressure showed that the filter papers were behaving as porous media rather than a simple bundle of capillaries; their behaviour could not be modelled using a simple capillary bundle model. Importantly, this finding shows that the filter press may provide a rapid method of assessing the apparent viscosity of polymer fluids in porous media at high shear rates – data that cannot be obtained by rotational viscometry, and would otherwise require resort to permeameter testing of coarse soils. The investigation demonstrates that the filter press test is not useful for the on-site quality control of polymer fluids but, given the theory presented in the paper, it can be a useful laboratory tool that provides valuable insight into polymer fluid flow behaviour in soils of high hydraulic conductivity, the most challenging soils for polymer fluid support.

Characterization of Simulated Cytoplasmic Fluids

AbstractMolecularly crowded solutions have been used to simulate cytoplasmic fluids, but little justification is provided in the literature. This work compared three key physical properties of solutions containing polyethylene glycol and sucrose against those in the cytoplasmic fluid from bacteria Escherichia coli: fluid viscosity, relaxation time (T1 and T2) of water, and the diffusion coefficient of water. It was concluded that appropriate mixtures of sucrose and polyethylene glycol 10,000, such as 10% sucrose and 15% PEG10,000 and 7.5% sucrose and 19% PEG10,000, closely mimic these properties of cytoplasmic fluid from E. coli containing around 100 mg/mL of proteins.

Significant Improvement in Magnetorheological Performance by Controlling Micron Interspaces with High Permeability Submicron Particles.

The shear yield strength, sedimentation stability and zero-field viscosity of magnetorheological fluids (MRFs) are crucial for practical vibration damping applications, yet achieving a balanced combination of these performances remains challenging. Developing MRFs with excellent comprehensive performance is key to advancing smart vibration damping technologies further. Theoretically, incorporating a multiscale particle system and leveraging synergistic effects between their can somewhat enhance MRFs' performance. However, this approach often faces issues such as insignificant increases in shear yield strength and excessive rise in zero-field viscosity. In response, this study employs a DC arc plasma method to synthesize a high magnetic permeability, low coercivity submicron FeNi particles, and further develops a novel CIPs-FeNi bidisperse MRFs. The introduction of submicron FeNi particles not only significantly enhances the shear2019 yield strength of MRFs under low magnetic fields but also promotes improvements in sedimentation stability and redispersibility without excessively increasing viscosity. Comprehensive performance analysis is conducted to explore the optimal content ratio, and detailed mechanisms for the enhancement of performance are elucidated through analysis of parameters such as chain-like structure, magnetic flux density and friction coefficient. Most importantly, the superior comprehensive performance combined with straightforward fabrication methods significantly enhances the engineering applicability of the CIPs-FeNi bidisperse MRFs.

Dynamics of particle entrainment for glass particles suspended in various fluids

The frictional properties of two sliding surfaces are often influenced by a fluid lubricant’s ability to separate and facilitate movement. When particles are present, their entrainment between surfaces can alter friction, either increasing or decreasing it compared to fluid lubrication alone. Understanding the frictional regimes and the dynamics driving particle entrainment in suspensions is thus critical. This study investigates the tribological properties of glass particles suspended in various fluid matrices. We examined suspensions with varying particle concentrations, fluid viscosities, fluid hydrophobicity, and particle hydrophobicity. Our findings reveal that particle lubrication dominates under the following conditions: (I) high particle concentrations, (II) high fluid viscosities, (III) strong particle – surface interactions, and (IV) weak fluid – particle interactions. These insights are crucial for applications in food science, biomedical industries, and pharmaceuticals, where controlling particle friction is essential for optimizing consumer satisfaction and ensuring the performance and safety of lubricants in medical devices.

Soret and dufour impacts on radiative power-law fluid flow via continuously stretchable surface with varying viscosity and thermal conductivity

The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

Advancements and future directions in single-cell Hi-C based 3D chromatin modeling

Single-cell Hi-C data provides valuable insights into the three-dimensional organization of chromatin within individual cells, yet modeling this data poses significant challenges due to its inherent sparsity and variability. This review comprehensively explores the predominant approaches to reconstructing 3D chromatin structures from single-cell Hi-C data, positioning these methods within the broader contexts of single-cell Hi-C research and bulk Hi-C data modeling.We categorize the modeling strategies based on their objective functions, which are framed in terms of force fields, potentials, cost functions, or likelihood probabilities. Despite their diverse methodologies, these approaches exhibit deep underlying similarities. We further dissect the basic components of these models, such as attractive restraint forces and repulsive forces, and discuss additional terms like fluid viscosity and variation penalties.The review also critically evaluates the current state of model validation, highlighting the inconsistencies across various studies and emphasizing the need for a comprehensive validation framework. We detail common validation techniques, including the comparison of distance matrices and the assessment of contact violations.We argue that the future of single-cell Hi-C modeling lies in integrating multiple data modalities and incorporating cell cycle trajectory information. Such integration could significantly advance our understanding of chromatin conformation dynamics during cell cycle progression and cell differentiation. We also foresee the continued growth of optimization-based and molecular dynamics approaches, supported by general molecular dynamics toolkits.