Interface Motion Research Articles

Nonlinear stability of two superimposed electrified dusty fluids of type Rivlin-Ericksen: Non-perturbative approach

The nonlinear instability of a planar interface between two overlapping Rivlin-Ericksen viscoelastic liquids, in the occurrence of fine dust and vertical electric fields throughout permeable media, and the influence of surface tension is studied. The prototype structure is assumed to be a two-dimensional groundwork for the sake of simplicity. The growing approval of several disciplines of practical physics and technology serves as motivation for analyzing this problem. Using viscous potential theory, the mathematical procedure is condensed. To properly control electro convection in liquid crystals, which is widely used in various displays technologies, it was crucial to have a thorough comprehension of stability. Gaining understanding of the behavior of viscoelastic fluids at interfaces was crucial in polymer manufacturing industries. Employing the linear equations of movement with the suitable nonlinear bounder circumstances forms the basis of the considered nonlinear technique. A nonlinear partial differential equation that evaluates the interface movement is the objective of the process. Since linear stability has frequently been investigated, the present situation will be constructed only in the nonlinear sense, where a number of dimensionless physical numerals are achieved. The non-perturbative methodology is used to accomplish the nonlinear standards. The main idea behind the novel performance is to convert an ordinary nonlinear ordinary differential equation into a linear one. The new technique differs from the conventional perturbation methods in that it may be used to exactly and correctly analyze the behavior of the strong nonlinear aspects of the interface displacement. This innovative method is established by using He's frequency formula. Using the nonlinear distinguishing equation, the special situation of the real and the complex coefficients is accomplished. It was observed that the instability zone expands as the electric field, porosity of porous medium, and density ratio of two fluids rise. The stability configuration is enhanced by the viscoelasticity parameter, Bond number, and ratio of kinematic viscoelasticity.

An Enhanced Mapping Interpolation ISPH–FVM Coupling Method for Simulating Two-Phase Flows with Complex Interfaces

In this paper, an enhanced mapping interpolation ISPH–FVM coupling method is developed to improve the accuracy and stability of two-phase flows simulation. Similar to the original ISPH–FVM coupling method, the coupling framework between the numerical schemes of ISPH and FVM is established at the overlapping region of the ISPH particles and the FVM grids. Although the original ISPH–FVM coupling method can effectively predict movement and deformation of the two-phase interface, it is difficult to ensure the mass conservation in the flow domain during the information transfer between ISPH particles and FVM grids, thus weakening the numerical accuracy of interaction between different fluid phases. To improve the mapping interpolation accuracy and ensure the mass conservation, a volume fraction correction scheme combined with the particle approximate interpolation technique is introduced to form an enhanced mapping interpolation ISPH–FVM coupling method. The effect of surface tension is assessed by the continuum surface force (CSF) model. Several 2D/3D numerical cases are given to verify the efficiency and robustness of the present ISPH–FVM coupling method. Numerical results demonstrate that the enhanced mapping interpolation developed in the ISPH–FVM coupling method can reproduce the two-phase flow with complex interfaces effectively.

Divergent Richtmyer–Meshkov instability under different shock strengths

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.

Damage accumulation and its effect during thermal- and stress-induced cycling martensite transformation of laser powder bed fused (LPBF) NiTi alloy

Nitinol (NiTi) alloys produced via laser powder bed fusion (LPBF) exhibit promising potential across diverse applications, yet their suitability for devices necessitating repetitive actuation confronts uncertainties regarding microstructural evolution and functional fatigue behavior during cyclic operation. Our investigation unveils that damage accumulation during thermal cycling stems from geometrically necessary dislocations formed through finite-scale incoherent interface motion, contrasting earlier hypotheses attributing LPBF-induced dislocation activity as the primary contributor. Damage accumulation during mechanical cycling is characterized by notable multiplication of cyclic dislocations via dislocation twinning interactions, rather than severe martensitic plasticity. These newborn cycling dislocations inherit martensite's crystallographic characteristics, exerting a distinct influence mechanism on martensite transformation and deformation behavior, diverging from conventional studies on function fatigue in traditional NiTi alloys. This study sheds light on the distinctive damage accumulation traits observed during thermal/mechanical cycling of LPBF-fabricated NiTi alloys, offering valuable insights for probing their functional fatigue mechanisms.

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

A high order generalized finite difference method for solving the anisotropic elliptic interface problem in static and moving systems

In this paper, a high order meshless numerical scheme based on the Generalized Finite Difference Method (GFDM) is proposed to analyze the anisotropic elliptic interface problem. The GFDM has an advantage in dealing with some anisotropic elliptic problems with complex interfaces, interface conditions with the jump of derivatives. Four problems with eight examples are provided to verify the existence of the good performance of the GFDM for anisotropic elliptic interface problems, including that the simplicity, accuracy, and stability in static and moving systems. Especially, GFDM has the tolerance of the complexity of interface shape, the interface movement and the large jump.

Multi-Objective Topology Optimization of Conjugate Heat Transfer Using Level Sets and Anisotropic Mesh Adaptation

This study proposes a new computational framework for the multi-objective topology optimization of conjugate heat transfer systems using a continuous adjoint approach. It relies on a monolithic solver for the coupled steady-state Navier–Stokes and heat equations, which combines finite elements stabilized by the variational multi-scale method, level set representations of the fluid–solid interfaces and immersed modeling of heterogeneous materials (fluid–solid) to ensure that the proper amount of heat is exchanged to the ambient fluid by solid objects in arbitrary geometry. At each optimization iteration, anisotropic mesh adaptation is applied in near-wall regions automatically captured by the level set. This considerably cuts the computational effort associated with calling the finite element solver, in comparison to traditional topology optimization algorithms operating on isotropic grids with a comparable refinement level. Given that we operate within the constraint of a specified number of nodes in the mesh, this allows not only to improve the accuracy of interface representation and motion but also to retain the high fidelity of the numerical solutions at the grid points just adjacent to the interface. Finally, the remeshing and resolution steps both run within a highly parallel environment, which makes it possible for the proposed algorithm to tackle large-scale problems in three dimensions with several tens of millions of state degrees of freedom. The developed solver is validated first by minimizing dissipation in a flow splitter device, for which the method delivers relevant optimal designs over a wide range of volume constraints and flow rate distributions over the multiple outlet orifices but yields better accuracy compared to reference data from literature obtained using uniform meshes (in the sense that the layouts are more smooth, and the solutions are better resolved). The scheme is then applied to a two-dimensional heat transfer problem, using bi-objective cost functionals combining flow resistance and thermal recoverable power. A comprehensive parametric study reveals a complex arrangement of optimal solutions on the Pareto front, with multiple branches of symmetric and asymmetric designs, some of them previously unreported. Finally, the algorithmic developments are substantiated with several three-dimensional numerical examples tackled under fixed weights for heat transfer and flow resistance, for which we show that the optimal layouts computed at low Reynolds number, that are intrinsically relevant to a broad range of microfluidic application, can also serve as smooth solutions to high-Reynolds-number engineering problems of practical interest.

The Effect of Spatially Varying Collision Frequency on the Development of the Rayleigh–Taylor Instability

The Rayleigh–Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic models to completely capture dynamics in certain collisional regimes. Where previous kinetic simulations used spatially and temporally constant collision frequency, this work presents five-dimensional (two spatial, three velocity dimensions) continuum-kinetic simulations of the RT instability using a more realistic spatially varying collision frequency. Three cases of collisional variation are explored for two Atwood numbers: low to intermediate, intermediate to high, and low to high. The low-to-intermediate case exhibits no RT instability growth, while the intermediate-to-high case is similar to a fluid-limit kinetic case with interface widening biased toward the lower-collisionality region. A novel contribution of this work is the low-to-high collisionality case that shows significantly altered instability growth through an upward movement of the interface and damped spike growth due to increased free-streaming particle diffusion in the lower region. Contributions to the energy flux from the non-Maxwellian portions of the distribution function are not accessible to fluid models and are greatest in magnitude in the spike and regions of low collisionality. Increasing the Atwood number results in greater RT instability growth and reduced upward interface movement. Deviation of the distribution function from Maxwellian is inversely proportional to collision frequency and concentrated around the fluid interface. The linear phase of RT instability growth is well described by theoretical linear growth rates accounting for viscosity and diffusion.

Mechanism of improving solidification structure of super austenitic stainless steel by feeding strip into molten steel

Feeding steel strip into molten steel is an effective technique for refining the solidification structure of steel, especially for high-alloy steel. This study experimentally and numerically investigated the effects of feeding strip on the solidification structure of super austenitic stainless steel S32654. The results revealed that feeding strip noticeably increased the proportion of equiaxed grains, refined the dendritic structure, and improved Mo segregation and the precipitation of σ phase. The relevant mechanism was clarified as follows. Firstly, feeding strip promoted the formation and survival of a large number of floating dendrites by cooling the molten steel. As the temperature decreased, these floating dendrites sharply increased their quantity by repeated splitting and then acted as nucleation particles. Numerous equiaxed grains grew around these floating dendrites, significantly refining the central dendritic structure. Meanwhile, the doubling of the equiaxed grains has two effects on Mo segregation. First, it prevented the growth of columnar grains and the movement of Mo segregation interface towards the center, thus reducing the Mo macrosegregation. On the other hand, it dispersed and refined the residual liquid phase (Mo segregation regions), thereby reducing the Mo microsegregation. Additionally, the reduced Mo segregation lowered the σ phase precipitation temperature, allowing it to form in solid austenite with a shortened growth duration. The lighter Mo segregation and slower Mo diffusion in solid austenite led to insufficient Mo supply for the σ phase growth. Moreover, dendritic refinement limited the growth space of the σ phase. Finally, less and finer σ phase particles precipitated in the S32654 steel fed with strip. The improvement of feeding strip on the solidification structure will reduce the temperature and time required for high-temperature homogenization, which is beneficial for the subsequent hot working.

Crystalline Microstructure, Microsegregations, and Mechanical Properties of Inconel 718 Alloy Samples Processed in Electromagnetic Levitation Facility

The solidification of Inconel 718 alloy (IN718) from undercooled liquid is studied. The solidification kinetics is evaluated in melted and undercooled droplets processed using the electromagnetic levitation (EML) technique by the temperature–time profiles and solid/liquid (S/L) interface movement during recalescence. The kinetics is monitored in real time by special pyrometrical measurements and high-speed digital camera. It is shown that the growth velocity of γ-phase (the primary phase in IN718), the final crystalline microstructure (dendritic and grained), and the mechanical properties (microhardness) are strongly dependent on the initial undercooling ΔT at which the samples started to solidify with the originating γ-phase. Particularly, with the increase in undercooling, the secondary dendrite arm spacing decreases from 28 μm to 5 μm. At small and intermediate ranges of undercooling, the solidified droplets have a dendritic crystalline microstructure. At higher undercooling values reached in the experiment, ΔT>160 K (namely, for samples solidified with ΔT=170 K and ΔT=263 K), fine crystalline grains are observed instead of the dendritic structure of solidified drops. Such change in the crystalline morphology is qualitatively consistent with the behavior of crystal growth kinetics which exhibits the change from the power law to linear law at ΔT≈160 K in the velocity–undercooling relationship (measured by the advancement of the recalescence front in solidifying droplets). Study of the local mechanical properties shows that the microhardness increases with the increase in the γ″-phase within interdendritic spacing. The obtained data are the basis for testing the theoretical and computational of multicomponent alloy samples.

ALTERNATE SLIDING FRICTION FORMULATIONS OF ELASTO - HYDRODYNAMIC OF SPUR GEARS

In this paper, several sliding friction formulations used in spur gear dynamics are examined and compared in terms of the predictions of interfacial friction forces and off-line-of-action. Computing friction formulations include Coulomb models with time-varying friction coefficients and empirical expressions based on elasto - hydrodynamic and/or boundary lubrication regime principles. Predicted results compare well with friction force measurements and appeared completely conformed with specific objectives of this paper are established as follows: (1) propose an improved MDOF spur gear pair model with time-varying coefficient of' friction, µ(t), given realistic mesh stiffness profiles.(2) comparatively evaluate alternate sliding friction models and predict the interfacial friction forces and motions in the off-line-of-action (OLOA) direction: and (3) validate one particular model (III) by comparing predictions to the benchmark gear friction force measurements

Features of numerical modeling electrical coalescence in a droplet-layer system using the arbitrary Lagrangian-Eulerian method

The electrocoalescence of a water drop at the water-oil interface was numerically analyzed using the finite element method by solving a set of equations including hydrodynamics and electrostatics. The simulation was performed using COMSOL Multiphysics software, the interface movement was implemented using an arbitrary Lagrangian-Eulerian method (also called the moving-mesh method). The influence of the initial distance from the drop to the layer, as well as the size of the entire domain on the outcome of the process was studied. The electrical coalescence and non-coalescence of a single uncharged droplet with a layer under the action of the DC field were calculated in a wide range of electric field strength. The created computer model makes it possible to calculate the voltage dependence of the detached droplet volume and charge. Also, it can help to determine features of non-coalescence, including the stretching of the droplet along the interelectrode gap and spraying.

A New Calculation Model for Equivalent Circulating Density Considering Interface Effect between Various Fluids during Cementing Process

Summary Equivalent circulating density (ECD) is an essential parameter in the construction of oil and gas wells, which can be used to control the downhole pressure and prevent serious incidents such as well leakage or blowouts. Different engineering tasks will lead to changes in the ECD calculation model; the classical pipe flow theory can be used to calculate the ECD of circulating drilling fluid, but it is not suitable for the cementing displacement because it does not consider the interface effect between various fluids. In this paper, a new ECD calculation model has been developed that accounts for the changes in fluid interface morphology between displacing fluid and displaced fluid during the cementing process. Moreover, a simulation of the effects of borehole radius, casing eccentricity, displaced fluid density, and flow rate on the ECD were analyzed and quantified by a numerical approach to solve the fluid dynamics equilibrium equations that describe the flow in the eccentric annuli based on the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. The results show that the calculated ECD predicted by the proposed model is larger than the traditional model with the reduction in the borehole radius, and the maximum deviation at the inlet position can reach 0.03 g·cm−3. Variation in the length of the interface transition zone is the main reason for the deviation in ECD prediction accuracy. In the case of constant casing outer diameter, fluid rheology, and displaced fluid density, the ECD decreases with increasing borehole radius. Meanwhile, it increases with higher displaced fluid density, eccentricity, and annular velocity. It is also shown that the length of the mixing zone can reach up to 40% of the pipe length under the conditions of eccentricity and displacement described in the paper. The proposed model predicts the ECD in the annulus by considering the influence of different engineering parameters on the movement of displacement interface, which can effectively ensure the safety of the cementing operation.

Real-time hybrid model test to replicate high-rise building resonant vibration under wind loads

In May 2021, the 72-story Shenzhen Saige building experienced abnormal vibration that was strongly felt on many floors and triggered social panic. The tower was therefore closed for more than 2 months resulting in huge economic losses. A preliminary study consisting of field resonant excitation tests and a series of numerical simulations were carried out. It was concluded that the wind loads provoked the higher modes of the building vibration. Specifically, the vibration of the mast, which is located at the building top, induced this abnormal vibration. To validate this conclusion, real-time hybrid model (RTHM) tests was developed to reproduce this building vibration incident. This paper presents the details of the validation RTHM tests including testing design and result discussions. Structural vibration parameters obtained from the field tests were used in the numerical substructure building model, and the experimental substructures were the two scaled down mast models (the cantilever beam section of the masts). During RTHM test, the restoring force of the experimental substructure due to real wind loads induced by an air fan was measured and used in the numerical simulation to compute interface motions. A shaking table was then used to impose the interface motion back to the bottom of the mast model to reproduce the abnormal vibration incident. The demonstrated ability of the developed RTHM testing method to reproduce the resonant phenomenon of the wind-induced tower vibration provides an alternative experimental method to study vibration responses of high-rise buildings in future.

The Sharp Interface Limit of an Ising Game

The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods. We introduce and explore an Ising game, a variant of the Ising model that features competing agents influencing the behavior of the spins. With long-range interactions, we consider a mean-field limit resulting in a nonlocal potential game at the mesoscopic scale. This game exhibits a phase transition and multiple constant Nash-equilibria in the supercritical regime. Our analysis focuses on a sharp interface limit for which potential minimizing solutions to the Ising game concentrate on two of the constant Nash-equilibria. We show that the mesoscopic problem can be recast as a mixed local/nonlocal space-time Allen-Cahn type minimization problem. We prove, using a Γ-convergence argument, that the limiting interface minimizes a space-time anisotropic perimeter type energy functional. This macroscopic scale problem could also be viewed as a problem of optimal control of interface motion. Sharp interface limits of Allen-Cahn type functionals have been well studied. We build on that literature with new techniques to handle a mixture of local derivative terms and nonlocal interactions. The boundary conditions imposed by the game theoretic considerations also appear as novel terms and require special treatment.

Quantitative characterization of the pseudo-boiling contribution to supercritical heat transfer

This paper explores the supercritical heat transfer mechanism by characterizing the boiling contribution ratio qb/q, where qb is the boiling heat flux and q is the applied heat flux. Experiments are performed using nickel–chromium wire in 15 °C liquid carbon dioxide at 5.2, 7.6, 9.0, and 11.0 MPa. The evaporation heat flux qe is the amount of heat used for vapor generation, while qb is the heat transfer in the bulk liquid due to the disturbance of the flow/temperature field by vapor–liquid interface motion. A data processing procedure is developed to measure qb/q from the captured images. Similar trends appear for both supercritical pseudo-boiling and subcritical boiling. The evaporation-like regime at supercritical pressures reaches qb/q = 0.21–0.43, while the film boiling (evaporation) regime achieves qb/q = 0.08. In the supercritical-boiling-like regime, qb/q increases sharply from 0.19 to 0.65, whereas in the subcritical-nucleate-boiling regime, qb/q maintains a value of 0.30 followed by a rapid rise to 0.68 under a vigorous bubble merging and departing mechanism. At both subcritical and supercritical pressures, the heat transfer deteriorates in the evaporation regime, but is significantly enhanced by phase-change-induced flow/temperature field perturbations. The boiling curves differ in the two pressure domains. At supercritical pressures, natural convection transitions smoothly to the evaporation-like regime, then to the boiling-like regime. At subcritical pressures, a steep transition from natural convection to nucleate boiling occurs, and then, film boiling is induced through the action of surface tension. The above findings complete the inverse boiling curves in the two pressure domains.

Optical tracking of the heterogeneous solvent diffusion dynamics and swelling kinetics of single polymer microspheres.

The diffusion dynamics of small molecules into polymer entities is crucial for driving their morphology and function, which can be applied to research fields such as optical identification, medical implantation and intelligent sensing platforms. Herein, we demonstrate a nondestructive bright-field imaging strategy to monitor and control the morphology of polymer microspheres by varying the interfacial interaction and diffusion in a penetrant bath. The nanoscale interface movement of single polymer microspheres was tracked and converted into the diameter variation during the swelling event with sub-pixel accuracy, which is consistent with the calculation using Li-Tanaka's kinetic equations. More interestingly, the solvent diffusion dynamics along different directions of one particle are heterogeneous, indicating the non-uniform internal structure of a soft confined assembly. The swelling characteristics of single polymer microspheres can be quantified by this simple imaging strategy, and the transient intermediate swelling states are captured. To model the lifetime and stabilization times of microplastic entities, solvent selectivity and thermodynamic regulation were introduced to obtain the activation energy down to the single micro-entity level. This optical methodology shows capability for decoding the complex diffusion mechanism in polymer entities and provides guidance for the design of drug delivery systems, sensor platforms, and optical responsive materials.

Critical Percolation in the Ordering Kinetics of Twisted Nematic Phases.

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds toward a broken Z_{2}-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale t_{p}. At this time, exact formulas for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.

Weak solutions for a degenerate phase‐field model via Galerkin approximation

This paper is concerned with a phase‐field model driven by interface diffusion, which is an elliptic and nonlinear degenerate parabolic coupled system arising in a theory of interface motion in the elastically deformable materials. Spinodal decomposition is a typical example for this motion. We shall study the global existence of weak solutions to this model with a general polynomial potential function via the Galerkin method. Moreover, we perform the numerical simulations to investigate the spinodal decomposition process of binary alloy by applying this model.

White Light Reflectance Spectroscopy as a novel and noninvasive method for in situ wetting monitoring in membrane distillation

Wetting, in membrane distillation (MD), is a major drawback appearing as a dynamic mechanism consisting of multiple stages. Normally, the liquid-air interface is placed on top of the membrane surface and pores are only occupied with vapor. If liquid starts to penetrate, surface wetting is followed by partial wetting that develops until the fully wetted state occurs, compromising the operation. Usually, only the fully wetted state is assumed, indirectly, as liquid from the feedwater stream, containing soluble salts, passes through the pores and contaminates the permeate, thus increasing its conductivity. In this work, we present White Light Reflectance Spectroscopy (WLRS) as a novel method for in-situ wetting monitoring in MD. In WLRS, light incidents vertically onto the membrane and reflectance is continuously recorded. Thus, it is possible to observe any movement of the liquid-vapor interface in real-time, via changes in the reflectance spectrum, without compromising the structural integrity of the membrane nor the module. Notably, the proposed method is applicable to all standard MD modes, without operating limitations and restrictions. With this noninvasive technique we can predict and observe all wetting stages, not only in the presence of surfactants in the feed stream, but also due to hydraulic pressure increase.