# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

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### Numerical simulation of a drop impact on a superhydrophobic surface with a wire

Physics of Fluids, Volume 31, Issue 11, November 2019.

Superhydrophobic surfaces patterned with macroscale (≈1 mm) structures have gained increasing interest in the past years because of their potential in reducing the contact time between impacting liquid drops and the solid surface. The reduced wettability of these surfaces is of interest in numerous technical applications, as, for example, in anti-icing on airplane wings. Several experimental studies have been carried out on this topic in the literature; on the other hand, only very limited numerical investigations are available in the literature. In this paper, we present a numerical study based on a volume of fluid code for direct numerical simulation of incompressible multiphase flows. A necessary condition for the realization of this study was the implementation of arbitrary-shaped boundaries using a Cartesian grid system. Our implementation of embedded boundaries is based on a volume fraction representation of the boundaries and on a piecewise linear approximation of their surface. The discretized boundaries are then cut off from the computational domain, leading to an altered formulation of the discretized governing equations. To validate the method, we show simulation results for different impact velocities for the case of a droplet impacting on a wire, which has been investigated experimentally in the literature. The simulations show good agreement in terms of contact time and impact morphology, thus, showing the validity of the implementation. Moreover, an extensive analysis of the velocity field for this setup is presented, helping us to better understand the underlying physical phenomena.

Superhydrophobic surfaces patterned with macroscale (≈1 mm) structures have gained increasing interest in the past years because of their potential in reducing the contact time between impacting liquid drops and the solid surface. The reduced wettability of these surfaces is of interest in numerous technical applications, as, for example, in anti-icing on airplane wings. Several experimental studies have been carried out on this topic in the literature; on the other hand, only very limited numerical investigations are available in the literature. In this paper, we present a numerical study based on a volume of fluid code for direct numerical simulation of incompressible multiphase flows. A necessary condition for the realization of this study was the implementation of arbitrary-shaped boundaries using a Cartesian grid system. Our implementation of embedded boundaries is based on a volume fraction representation of the boundaries and on a piecewise linear approximation of their surface. The discretized boundaries are then cut off from the computational domain, leading to an altered formulation of the discretized governing equations. To validate the method, we show simulation results for different impact velocities for the case of a droplet impacting on a wire, which has been investigated experimentally in the literature. The simulations show good agreement in terms of contact time and impact morphology, thus, showing the validity of the implementation. Moreover, an extensive analysis of the velocity field for this setup is presented, helping us to better understand the underlying physical phenomena.

Categories: Latest papers in fluid mechanics

### A fundamental rule: Determining the importance of flow prior to polymer crystallization

Physics of Fluids, Volume 31, Issue 11, November 2019.

A continuum-level model for nonisothermal polymer crystallization following a complex flow is presented, along with a fundamental rule that may be employed to determine if the flow will influence the ensuing crystallization dynamics. This rule is based on two dimensionless parameters: the (Rouse) Weissenberg number and an inverse Deborah number defined by the ratio between the time taken to cool and the melting point vs the stretch relaxation time, which determines the time available for flow-enhanced crystallization. Moreover, we show how the time to reach the melting point can be derived semianalytically and expressed in terms of the processing conditions in the case of pipe flow—ubiquitous in polymer processing. While the full numerical model is required to quantitatively predict induction times and spherulite-size distributions, the proposed fundamental rule may be used practically to ensure, or eliminate, flow-enhanced structures by controlling the processing conditions or material properties. We discuss how flow-enhanced structures may be revealed only after postprocessing annealing and finally examine previous works that have successfully applied the model to extrusion-based three-dimensional printing.

A continuum-level model for nonisothermal polymer crystallization following a complex flow is presented, along with a fundamental rule that may be employed to determine if the flow will influence the ensuing crystallization dynamics. This rule is based on two dimensionless parameters: the (Rouse) Weissenberg number and an inverse Deborah number defined by the ratio between the time taken to cool and the melting point vs the stretch relaxation time, which determines the time available for flow-enhanced crystallization. Moreover, we show how the time to reach the melting point can be derived semianalytically and expressed in terms of the processing conditions in the case of pipe flow—ubiquitous in polymer processing. While the full numerical model is required to quantitatively predict induction times and spherulite-size distributions, the proposed fundamental rule may be used practically to ensure, or eliminate, flow-enhanced structures by controlling the processing conditions or material properties. We discuss how flow-enhanced structures may be revealed only after postprocessing annealing and finally examine previous works that have successfully applied the model to extrusion-based three-dimensional printing.

Categories: Latest papers in fluid mechanics

### Effect of bolus viscosity on carbohydrate digestion and glucose absorption processes: An in vitro study

Physics of Fluids, Volume 31, Issue 11, November 2019.

Digestion is the process of breaking down food into smaller nutrient components which can be easily absorbed in the intestinal tract. The aim of this study was to experimentally investigate the influence of bolus (gastric content) viscosity on digestion and nutrient absorption processes, using an in vitro gastrointestinal model, the TIM-1 system. Two types of simple carbohydrates, namely, glucose and maltodextrin, were used as model foods. The initial bolus viscosity was varied (∼1 mPa·s, ∼15 mPa·s, and ∼100 mPa·s) using different glycerol-water proportions. A fluorescent molecular rotor compound (Fast Green For Coloring Food) was used to monitor viscosity changing patterns of the gastrointestinal content during digestion in the in vitro stomach and small intestinal sections. The digested-nutrient absorption data indicated that the initial bolus viscosity did not significantly affect the glucose absorption process in the small intestine. However, an increase in the initial bolus viscosity from ∼1 mPa·s to ∼15 mPa·s reduced the maltodextrin to glucose conversion by 35%. A further increase in the initial bolus viscosity from ∼15 mPa·s to ∼100 mPa·s did not significantly reduce the maltodextrin to glucose conversion.

Digestion is the process of breaking down food into smaller nutrient components which can be easily absorbed in the intestinal tract. The aim of this study was to experimentally investigate the influence of bolus (gastric content) viscosity on digestion and nutrient absorption processes, using an in vitro gastrointestinal model, the TIM-1 system. Two types of simple carbohydrates, namely, glucose and maltodextrin, were used as model foods. The initial bolus viscosity was varied (∼1 mPa·s, ∼15 mPa·s, and ∼100 mPa·s) using different glycerol-water proportions. A fluorescent molecular rotor compound (Fast Green For Coloring Food) was used to monitor viscosity changing patterns of the gastrointestinal content during digestion in the in vitro stomach and small intestinal sections. The digested-nutrient absorption data indicated that the initial bolus viscosity did not significantly affect the glucose absorption process in the small intestine. However, an increase in the initial bolus viscosity from ∼1 mPa·s to ∼15 mPa·s reduced the maltodextrin to glucose conversion by 35%. A further increase in the initial bolus viscosity from ∼15 mPa·s to ∼100 mPa·s did not significantly reduce the maltodextrin to glucose conversion.

Categories: Latest papers in fluid mechanics

### Numerical study on wide gap Taylor Couette flow with flow transition

Physics of Fluids, Volume 31, Issue 11, November 2019.

This study aims to investigate the possible sources of nonaxisymmetric disturbances and their propagation mechanism in Taylor Couette flow for wide gap problems using a direct numerical simulation with a radius ratio of 0.5 and the Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of nonaxisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Above Re = 425, transition from axisymmetric to nonaxisymmetric flow is observed up to Re = 575 before the emergence of wavy-vortex flow. From the variation of VL thickness with Re, the VL does not experience any significant changes in the flow separation region of the inner wall, as well as jet impingement region of both the inner and outer walls. However, a sudden increase in VL thickness in the flow separation region of the outer wall reveals possible sources of nonaxisymmetric disturbances in the flow separation region of the outer wall. These disturbances develop into the periodic secondary flow as the axisymmetric flow transforms into nonaxisymmetric flow, and this leads to the emergence of the azimuthal wave. The periodic secondary flow contributes to a sudden increase in the natural wavelength and rapid reduction in the strength of two counter-rotating Taylor vortices. This in turn leads to a substantial reduction of torque in the transition flow vis-à-vis axisymmetric Taylor-vortex flow.

This study aims to investigate the possible sources of nonaxisymmetric disturbances and their propagation mechanism in Taylor Couette flow for wide gap problems using a direct numerical simulation with a radius ratio of 0.5 and the Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of nonaxisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Above Re = 425, transition from axisymmetric to nonaxisymmetric flow is observed up to Re = 575 before the emergence of wavy-vortex flow. From the variation of VL thickness with Re, the VL does not experience any significant changes in the flow separation region of the inner wall, as well as jet impingement region of both the inner and outer walls. However, a sudden increase in VL thickness in the flow separation region of the outer wall reveals possible sources of nonaxisymmetric disturbances in the flow separation region of the outer wall. These disturbances develop into the periodic secondary flow as the axisymmetric flow transforms into nonaxisymmetric flow, and this leads to the emergence of the azimuthal wave. The periodic secondary flow contributes to a sudden increase in the natural wavelength and rapid reduction in the strength of two counter-rotating Taylor vortices. This in turn leads to a substantial reduction of torque in the transition flow vis-à-vis axisymmetric Taylor-vortex flow.

Categories: Latest papers in fluid mechanics

### Allotropic transformation instigated thermal diffusivity of soot nanofluid: Thermal lens study

Physics of Fluids, Volume 31, Issue 11, November 2019.

This paper employs the sensitive single-beam thermal lens technique for analyzing the thermal behavior of gasoline soot containing allotropes of carbon by preparing its nanofluid (NF). The soot, annealed at different temperatures up to 400 °C (the samples), used for preparing the NF, is found to enhance the thermal diffusivity (α) up to 95% without changing the solid volume fraction, suggesting its possible use in coolants. The thermal induced modifications are understood from the field emission scanning electron microscopic, X-ray diffraction (XRD), thermogravimetric, and Raman spectroscopic analyses. The variation of α of the sample is found to exhibit similar variations observed in XRD and Raman spectroscopic analyses. The study stresses the significance of the optimum temperature (300 °C) for the soot NF above which morphological and structural modifications may lead to thermal energy trapping rather than dissipation or cooling.

This paper employs the sensitive single-beam thermal lens technique for analyzing the thermal behavior of gasoline soot containing allotropes of carbon by preparing its nanofluid (NF). The soot, annealed at different temperatures up to 400 °C (the samples), used for preparing the NF, is found to enhance the thermal diffusivity (α) up to 95% without changing the solid volume fraction, suggesting its possible use in coolants. The thermal induced modifications are understood from the field emission scanning electron microscopic, X-ray diffraction (XRD), thermogravimetric, and Raman spectroscopic analyses. The variation of α of the sample is found to exhibit similar variations observed in XRD and Raman spectroscopic analyses. The study stresses the significance of the optimum temperature (300 °C) for the soot NF above which morphological and structural modifications may lead to thermal energy trapping rather than dissipation or cooling.

Categories: Latest papers in fluid mechanics

### Numerical study of total temperature effect on hypersonic boundary layer transition

Physics of Fluids, Volume 31, Issue 11, November 2019.

The total temperature in the hypersonic wind tunnel test can be significantly different from that in real flight conditions, and this leads to a large discrepancy in the measurement of the boundary layer transition between ground experiment measurements and flight tests. Even at the same Mach number and Reynolds number, different wind tunnels may yield different transition data for the same model due to the total temperature effect. In this paper, the boundary layer transition on a 7° half-angle sharp cone (at a 0° angle of attack) with four freestream total temperatures is investigated using both the simulations of a local correlation-based transition model and linear stability analysis. The results show that as the freestream total temperature increases, the starting point of the transition on the sharp cone gradually moves backward and the length of the transition region decreases. The N factor of the unstable wave gradually decreases with increasing freestream total temperature, causing the transition onset to move backward. The total temperature effects on boundary transition as determined by both methods of analysis were in good agreement.

The total temperature in the hypersonic wind tunnel test can be significantly different from that in real flight conditions, and this leads to a large discrepancy in the measurement of the boundary layer transition between ground experiment measurements and flight tests. Even at the same Mach number and Reynolds number, different wind tunnels may yield different transition data for the same model due to the total temperature effect. In this paper, the boundary layer transition on a 7° half-angle sharp cone (at a 0° angle of attack) with four freestream total temperatures is investigated using both the simulations of a local correlation-based transition model and linear stability analysis. The results show that as the freestream total temperature increases, the starting point of the transition on the sharp cone gradually moves backward and the length of the transition region decreases. The N factor of the unstable wave gradually decreases with increasing freestream total temperature, causing the transition onset to move backward. The total temperature effects on boundary transition as determined by both methods of analysis were in good agreement.

Categories: Latest papers in fluid mechanics

### Quantitative analysis for the effects of internal flow on mass transfer processes inside rising bubbles

Physics of Fluids, Volume 31, Issue 11, November 2019.

The mass transfer process inside bubbles is an important, but easily overlooked, component of the global mass transfer process. Bubble deformation influences the internal flow pattern and the mass transfer area. Furthermore, the internal flow impacts on the concentration distribution. This paper presents the results of a study on the mass transfer process inside bubbles and the interactions among the above factors using a computational fluid dynamics model. The accuracy of the model is verified by an experiment with a chromogenic reaction. Gas–interface mass transfer processes with and without internal flow are compared to show the positive effects of the shape change and the flow. A mass transfer enhancement factor, which is related to the concentration gradient and the mass transfer area, is presented to quantitatively analyze the effects. The results show that various internal flow patterns and concentration distributions can occur in different bubbles. The change in the average mass fraction and the average mass transfer coefficient of the process including internal flow are 2.8 times and 28.0% higher than those of the process without any internal flow. The enhancement factors are greater than 1.0, which indicates that a stronger internal flow intensifies the mass transfer process.

The mass transfer process inside bubbles is an important, but easily overlooked, component of the global mass transfer process. Bubble deformation influences the internal flow pattern and the mass transfer area. Furthermore, the internal flow impacts on the concentration distribution. This paper presents the results of a study on the mass transfer process inside bubbles and the interactions among the above factors using a computational fluid dynamics model. The accuracy of the model is verified by an experiment with a chromogenic reaction. Gas–interface mass transfer processes with and without internal flow are compared to show the positive effects of the shape change and the flow. A mass transfer enhancement factor, which is related to the concentration gradient and the mass transfer area, is presented to quantitatively analyze the effects. The results show that various internal flow patterns and concentration distributions can occur in different bubbles. The change in the average mass fraction and the average mass transfer coefficient of the process including internal flow are 2.8 times and 28.0% higher than those of the process without any internal flow. The enhancement factors are greater than 1.0, which indicates that a stronger internal flow intensifies the mass transfer process.

Categories: Latest papers in fluid mechanics

### Retention and infiltration of bacteria on a plant leaf driven by surface water evaporation

Physics of Fluids, Volume 31, Issue 11, November 2019.

Evaporation-driven internal flows within a sessile droplet can transport microorganisms close to the leaf surface and facilitate their infiltration into the available openings, such as stomata. Here, using microfabricated surfaces out of polydimethylsiloxane, the sole effects of evaporation of sessile droplets in contamination of plant leaves was studied. These surfaces were patterned with stomata, trichomes, and grooves that are common surface microstructures on plant leaves. Evaporation of sessile droplets, containing bacterial suspensions, on real leaves and fabricated surfaces was studied using confocal microscopy. To provide insight about the effects of leaf hydrophobicity and surface roughness on the bacterial retention and infiltration, variations of contact angle of sessile droplets at these surfaces were measured during evaporation. The results showed that evaporation-driven flow transported bacteria close to the surface of spinach leaves and fabricated surfaces, leading to distinct infiltration into the stomata. Larger size and wider spacing of the micropores, and a more hydrophilic surface, led bacteria to spread more at the droplet base area and infiltrate into more stomata. Evaporation-driven movement of contact line, which can sweep bacteria over the leaf surface, was shown to lead to bacterial infiltration into the stomatal pores. Findings should help improve microbial safety of leafy greens.

Evaporation-driven internal flows within a sessile droplet can transport microorganisms close to the leaf surface and facilitate their infiltration into the available openings, such as stomata. Here, using microfabricated surfaces out of polydimethylsiloxane, the sole effects of evaporation of sessile droplets in contamination of plant leaves was studied. These surfaces were patterned with stomata, trichomes, and grooves that are common surface microstructures on plant leaves. Evaporation of sessile droplets, containing bacterial suspensions, on real leaves and fabricated surfaces was studied using confocal microscopy. To provide insight about the effects of leaf hydrophobicity and surface roughness on the bacterial retention and infiltration, variations of contact angle of sessile droplets at these surfaces were measured during evaporation. The results showed that evaporation-driven flow transported bacteria close to the surface of spinach leaves and fabricated surfaces, leading to distinct infiltration into the stomata. Larger size and wider spacing of the micropores, and a more hydrophilic surface, led bacteria to spread more at the droplet base area and infiltrate into more stomata. Evaporation-driven movement of contact line, which can sweep bacteria over the leaf surface, was shown to lead to bacterial infiltration into the stomatal pores. Findings should help improve microbial safety of leafy greens.

Categories: Latest papers in fluid mechanics

### Self-propulsion of a sticky sphere partially covered with a surface slip velocity

Physics of Fluids, Volume 31, Issue 11, November 2019.

Microorganisms follow various strategies to swim in a viscous medium. In an attempt to understand the swimming of ciliated microorganisms, we study low Reynolds number locomotion of a rigid slip-stick swimmer where the propulsive slip velocity is concentrated around an annular patch, which imitates the distinctive surface activity of the microorganisms. In addition, we assume the Navier slip condition at the rigid-fluid interface, which contributes to the hydrodynamic slip or stickiness across the surface. We solve for the locomotion speed and the corresponding flow fields of the swimmer in an axisymmetric unbounded medium. Our analysis reveals insights into how the choice of active slip influences the swimming velocity and the other relevant swimming characteristics. Interestingly, we find that for an optimal active slip in the annular range [π/4, 3π/4], the locomotion speed of the partially covered swimmer is enhanced by a factor of [math] compared to the standard fully covered squirmer. In addition, the corresponding swimming efficiency is enhanced by ∼2.4 times. We independently treat the influence of stickiness of the swimmer on the swimming characteristics. We find that the stickiness reduces the hydrodynamic resistance for the partially covered swimmer and further enhances the swimming speed and efficiency. These findings will be helpful to design efficient artificial swimmers in terms of higher mobility and lower power dissipation.

Microorganisms follow various strategies to swim in a viscous medium. In an attempt to understand the swimming of ciliated microorganisms, we study low Reynolds number locomotion of a rigid slip-stick swimmer where the propulsive slip velocity is concentrated around an annular patch, which imitates the distinctive surface activity of the microorganisms. In addition, we assume the Navier slip condition at the rigid-fluid interface, which contributes to the hydrodynamic slip or stickiness across the surface. We solve for the locomotion speed and the corresponding flow fields of the swimmer in an axisymmetric unbounded medium. Our analysis reveals insights into how the choice of active slip influences the swimming velocity and the other relevant swimming characteristics. Interestingly, we find that for an optimal active slip in the annular range [π/4, 3π/4], the locomotion speed of the partially covered swimmer is enhanced by a factor of [math] compared to the standard fully covered squirmer. In addition, the corresponding swimming efficiency is enhanced by ∼2.4 times. We independently treat the influence of stickiness of the swimmer on the swimming characteristics. We find that the stickiness reduces the hydrodynamic resistance for the partially covered swimmer and further enhances the swimming speed and efficiency. These findings will be helpful to design efficient artificial swimmers in terms of higher mobility and lower power dissipation.

Categories: Latest papers in fluid mechanics

### Effect of the magnetic field on the ferrofluid flow in a curved cylindrical annular duct

Physics of Fluids, Volume 31, Issue 11, November 2019.

The laminar fully developed ferrofluid flow of an otherwise magnetic fluid into a curved annular duct of circular cross section, subjected to a transverse external magnetic field, is studied in the present work. The specific geometry is chosen as it is encountered in heat exchangers and mixers where compactness is a priority. Results are obtained for different values of curvature, field strength, and particles’ volumetric concentration. A computational algorithm is used which couples the continuity, Navier Stokes, and magnetization equations using a nonuniform grid. The velocity–pressure coupling is achieved using the so-called continuity-vorticity-pressure variational equation method, adapted to the toroidal-poloidal coordinate system. The results confirm the ability of the method to produce accurate results in curvilinear coordinates and stretched grids, which is important for the standardization of the method’s application to generalized coordinate systems. Concerning the micropolar flow characteristics, the results reveal the effect of the magnetic field on the ferrofluid flow. It is shown that the axial velocity distribution is highly affected by the field strength and the volumetric concentration, that the axial pressure drop depends almost linearly on the field strength, and that a secondary flow is generated due to the combined effect of the external magnetic field and the curvature. The present analysis provides important insight into the effect of the three main parameters, revealing cases where a straight annular pipe might be preferable to a curved one and specific parts of the pipe that could be susceptible to enhanced loads, giving information that is crucial for design optimization.

The laminar fully developed ferrofluid flow of an otherwise magnetic fluid into a curved annular duct of circular cross section, subjected to a transverse external magnetic field, is studied in the present work. The specific geometry is chosen as it is encountered in heat exchangers and mixers where compactness is a priority. Results are obtained for different values of curvature, field strength, and particles’ volumetric concentration. A computational algorithm is used which couples the continuity, Navier Stokes, and magnetization equations using a nonuniform grid. The velocity–pressure coupling is achieved using the so-called continuity-vorticity-pressure variational equation method, adapted to the toroidal-poloidal coordinate system. The results confirm the ability of the method to produce accurate results in curvilinear coordinates and stretched grids, which is important for the standardization of the method’s application to generalized coordinate systems. Concerning the micropolar flow characteristics, the results reveal the effect of the magnetic field on the ferrofluid flow. It is shown that the axial velocity distribution is highly affected by the field strength and the volumetric concentration, that the axial pressure drop depends almost linearly on the field strength, and that a secondary flow is generated due to the combined effect of the external magnetic field and the curvature. The present analysis provides important insight into the effect of the three main parameters, revealing cases where a straight annular pipe might be preferable to a curved one and specific parts of the pipe that could be susceptible to enhanced loads, giving information that is crucial for design optimization.

Categories: Latest papers in fluid mechanics

### A new liquid transport model considering complex influencing factors for nano- to micro-sized circular tubes and porous media

Physics of Fluids, Volume 31, Issue 11, November 2019.

A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz–van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.

A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz–van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.

Categories: Latest papers in fluid mechanics

### A self-similarity mathematical model of carbon isotopic flow fractionation during shale gas desorption

Physics of Fluids, Volume 31, Issue 11, November 2019.

The existence of nanosized pore systems differentiates isotopic gas transport inside a shale matrix from conventional continuum flow. In this study, a novel self-similarity mathematical model was developed to investigate the effects of gas flow transport (both slip flow and free molecular diffusion flow) on isotopic gas fractionation for four different shale samples (S1 and S2 from north Germany and S3 and S4 from Xiashiwan Field, Ordos Basin, China). In this model, the nonlinear permeability and diffusion coefficients were developed for the isotopologues (12CH4 and 13CH4), respectively. By selecting appropriate exponents of the pressure gradient for 12CH4 and 13CH4, respectively, the estimated isotopic methane concentration and production rate showed a good agreement with experimental data. The developed model shows that the gas concentration of the isotopologues in samples S1 and S2 increases with time following a power law. Similarly, the gas production rates of the isotopologues in samples S3 and S4 decay with time following a power law. Moreover, the exponents of the pressure gradient for the isotopologues are close to 4 for samples S1 and S2, indicating that the effect of slip flow on isotopic gas fractionation cannot be ignored. For samples S3 and S4, the exponents of the pressure gradient for the isotopologues increase with temperature rising, which shows the promotion of isotopic gas fractionation under higher heating temperatures. The slight difference between the exponents of the pressure gradient for the isotopologues for the same shale sample reveals that the isotopic gas fractionation of carbon is a slow process.

The existence of nanosized pore systems differentiates isotopic gas transport inside a shale matrix from conventional continuum flow. In this study, a novel self-similarity mathematical model was developed to investigate the effects of gas flow transport (both slip flow and free molecular diffusion flow) on isotopic gas fractionation for four different shale samples (S1 and S2 from north Germany and S3 and S4 from Xiashiwan Field, Ordos Basin, China). In this model, the nonlinear permeability and diffusion coefficients were developed for the isotopologues (12CH4 and 13CH4), respectively. By selecting appropriate exponents of the pressure gradient for 12CH4 and 13CH4, respectively, the estimated isotopic methane concentration and production rate showed a good agreement with experimental data. The developed model shows that the gas concentration of the isotopologues in samples S1 and S2 increases with time following a power law. Similarly, the gas production rates of the isotopologues in samples S3 and S4 decay with time following a power law. Moreover, the exponents of the pressure gradient for the isotopologues are close to 4 for samples S1 and S2, indicating that the effect of slip flow on isotopic gas fractionation cannot be ignored. For samples S3 and S4, the exponents of the pressure gradient for the isotopologues increase with temperature rising, which shows the promotion of isotopic gas fractionation under higher heating temperatures. The slight difference between the exponents of the pressure gradient for the isotopologues for the same shale sample reveals that the isotopic gas fractionation of carbon is a slow process.

Categories: Latest papers in fluid mechanics

### Vortex shedding patterns in flow past a streamwise oscillating square cylinder at low Reynolds number using dynamic meshing

Physics of Fluids, Volume 31, Issue 11, November 2019.

We present a two-dimensional numerical study for uniform flow past a streamwise oscillating square cylinder at a Reynolds number of 200. To overcome the limitations with an oscillating inlet flow as used in earlier studies, a dynamic meshing feature is used to oscillate the cylinder. A parametric study is carried out by varying amplitude and frequency of cylinder oscillation. Two symmetric modes, named here as S-II-I and S-IV-D, have been found. In S-II-I mode, a pair of vortices are shed symmetrically on each side of the cylinder in one cycle (S-II mode), and in S-IV-D mode, two pairs of vortices of opposite sense are shed on each side of the cylinder. A vortex flapping mode has also been obtained for low to moderate amplitude and frequency ratios. A new mode of vortex shedding termed the “vortex dipole” mode is found and involves the alternate arrangement of vortex pairs unlike the zigzag arrangement of single vortices in a Kármán vortex street. As in most nonlinear oscillators, vortex shedding becomes chaotic when forced sufficiently strongly and is usually associated with nonlinear interactions between competing frequencies. Many modes observed in the current study become chaotic when the peak cylinder velocity becomes comparable with the inlet velocity. The 0-1 test for chaos is applied to the time series of lift coefficient to show that the signals are truly chaotic. We also observe chaos due to mode competition when shedding transitions from an antisymmetric to symmetric modes.

We present a two-dimensional numerical study for uniform flow past a streamwise oscillating square cylinder at a Reynolds number of 200. To overcome the limitations with an oscillating inlet flow as used in earlier studies, a dynamic meshing feature is used to oscillate the cylinder. A parametric study is carried out by varying amplitude and frequency of cylinder oscillation. Two symmetric modes, named here as S-II-I and S-IV-D, have been found. In S-II-I mode, a pair of vortices are shed symmetrically on each side of the cylinder in one cycle (S-II mode), and in S-IV-D mode, two pairs of vortices of opposite sense are shed on each side of the cylinder. A vortex flapping mode has also been obtained for low to moderate amplitude and frequency ratios. A new mode of vortex shedding termed the “vortex dipole” mode is found and involves the alternate arrangement of vortex pairs unlike the zigzag arrangement of single vortices in a Kármán vortex street. As in most nonlinear oscillators, vortex shedding becomes chaotic when forced sufficiently strongly and is usually associated with nonlinear interactions between competing frequencies. Many modes observed in the current study become chaotic when the peak cylinder velocity becomes comparable with the inlet velocity. The 0-1 test for chaos is applied to the time series of lift coefficient to show that the signals are truly chaotic. We also observe chaos due to mode competition when shedding transitions from an antisymmetric to symmetric modes.

Categories: Latest papers in fluid mechanics

### Experimental and theoretical study of swept-wing boundary-layer instabilities. Three-dimensional Tollmien-Schlichting instability

Physics of Fluids, Volume 31, Issue 11, November 2019.

Extensive combined experimental and theoretical investigations of the linear evolution of three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. The flow under consideration is the boundary layer over an airfoil at 35° sweep and an angle of attack of +1.5°. At these conditions, TS instability is found to be the predominant one. Perturbations with different frequencies and spanwise wavenumbers are generated in a controlled way using a row of elastic membranes. All experimental results are deeply processed and compared with results of calculations based on theoretical approaches. Very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved.

Extensive combined experimental and theoretical investigations of the linear evolution of three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. The flow under consideration is the boundary layer over an airfoil at 35° sweep and an angle of attack of +1.5°. At these conditions, TS instability is found to be the predominant one. Perturbations with different frequencies and spanwise wavenumbers are generated in a controlled way using a row of elastic membranes. All experimental results are deeply processed and compared with results of calculations based on theoretical approaches. Very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved.

Categories: Latest papers in fluid mechanics

### Flow structures in transitional and turbulent boundary layers

Physics of Fluids, Volume 31, Issue 11, November 2019.

The basic problems of transition in both incompressible and compressible boundary layers are reviewed. Flow structures in low-speed transitional and developed turbulent boundary layers are presented, together with almost all of the physical mechanisms that have been proposed for their formation. Comparisons of different descriptions of the same flow structures are discussed as objectively as possible. The importance of basic structure such as solitonlike coherent structure is addressed. For compressible flows, the receptivity and instability of boundary layer are reviewed, including the effect of different parameters on the transition. Finally, the principle of aerodynamic heating of hypersonic boundary layer is presented.

The basic problems of transition in both incompressible and compressible boundary layers are reviewed. Flow structures in low-speed transitional and developed turbulent boundary layers are presented, together with almost all of the physical mechanisms that have been proposed for their formation. Comparisons of different descriptions of the same flow structures are discussed as objectively as possible. The importance of basic structure such as solitonlike coherent structure is addressed. For compressible flows, the receptivity and instability of boundary layer are reviewed, including the effect of different parameters on the transition. Finally, the principle of aerodynamic heating of hypersonic boundary layer is presented.

Categories: Latest papers in fluid mechanics

### Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory

Physics of Fluids, Volume 31, Issue 11, November 2019.

With general rigid bead-rod modeling, we recreate shapes of complex macromolecular structures with beads, by rigidly fixing bead positions relative to one another. General rigid-bead rod theory then attributes the elasticity of polymeric liquids to the orientation that their macromolecules develop during flow. For linear viscoelastic behaviors, this theory has been evaluated for just a few very simple structures: rigid rings, the rigid tridumbbell, and three quadrafunctional branched structures. For oscillatory shear flow, the frequency dependencies of both parts of the complex viscosity are, at least qualitatively, predicted correctly. In this paper, we use general rigid-bead rod theory for the most complex macromolecular architectures to date. We thus explore the role of helix geometry on the complex viscosity of a helical polymeric liquid. Specifically, for both singly and doubly helical structures, we investigate the effects of helix radius, flight length, helix length, and the number of beads per flight on the complex viscosity function, the fluid relaxation time, and the zero-shear values of the steady shear viscosity and of the first normal stress coefficient. As a worked example, we examine specifically deoxyribonucleic acid (DNA). Using general rigid bead-rod theory, we dissect the DNA to see how the first helix, second helix, and then the base pairs each contribute to the complex viscosity. We next explore the rheological implications of gene replication to find that the unzipping of DNA into a pair of single strands is viscostatic.

With general rigid bead-rod modeling, we recreate shapes of complex macromolecular structures with beads, by rigidly fixing bead positions relative to one another. General rigid-bead rod theory then attributes the elasticity of polymeric liquids to the orientation that their macromolecules develop during flow. For linear viscoelastic behaviors, this theory has been evaluated for just a few very simple structures: rigid rings, the rigid tridumbbell, and three quadrafunctional branched structures. For oscillatory shear flow, the frequency dependencies of both parts of the complex viscosity are, at least qualitatively, predicted correctly. In this paper, we use general rigid-bead rod theory for the most complex macromolecular architectures to date. We thus explore the role of helix geometry on the complex viscosity of a helical polymeric liquid. Specifically, for both singly and doubly helical structures, we investigate the effects of helix radius, flight length, helix length, and the number of beads per flight on the complex viscosity function, the fluid relaxation time, and the zero-shear values of the steady shear viscosity and of the first normal stress coefficient. As a worked example, we examine specifically deoxyribonucleic acid (DNA). Using general rigid bead-rod theory, we dissect the DNA to see how the first helix, second helix, and then the base pairs each contribute to the complex viscosity. We next explore the rheological implications of gene replication to find that the unzipping of DNA into a pair of single strands is viscostatic.

Categories: Latest papers in fluid mechanics

### Three-dimensional simulation of tracer transport dynamics in formations with high-permeability channels or fractures: Estimation of oil saturation

Physics of Fluids, Volume 31, Issue 11, November 2019.

We simulate flow and dispersion of tracers in three-dimensional fractured geometries obtained with Voronoi tessellations. “Fractures” are generated and discretized using a parallel in-house code. These “fractures” can also be regarded as the high-permeability flow paths through the rock or a network of the “super-k” channels. The generated geometry contains multiply-connected matrix and fracture regions. The matrix region represents a porous rock filled with solid, water, and oil. Tracers diffuse in both regions, but advection is limited only to the fractures. The lattice-Boltzmann and random-walk particle-tracking methods are employed in flow and transport simulations. Mass-transfer across the matrix–fracture interface is implemented using the specular reflection boundary condition. Tracer partitioning coefficients can vary among the tracer compounds and in space. We use our model to match a field tracer injection test designed to determine remaining oil saturation. By analyzing the time-dependent behavior of the fully resolved, three-dimensional “fracture”–matrix geometry, we show that the industry-standard approach may consistently overestimate remaining oil saturation. For a highly heterogeneous reservoir system, the relative error of the field-based remaining oil estimates may exceed 50%.

We simulate flow and dispersion of tracers in three-dimensional fractured geometries obtained with Voronoi tessellations. “Fractures” are generated and discretized using a parallel in-house code. These “fractures” can also be regarded as the high-permeability flow paths through the rock or a network of the “super-k” channels. The generated geometry contains multiply-connected matrix and fracture regions. The matrix region represents a porous rock filled with solid, water, and oil. Tracers diffuse in both regions, but advection is limited only to the fractures. The lattice-Boltzmann and random-walk particle-tracking methods are employed in flow and transport simulations. Mass-transfer across the matrix–fracture interface is implemented using the specular reflection boundary condition. Tracer partitioning coefficients can vary among the tracer compounds and in space. We use our model to match a field tracer injection test designed to determine remaining oil saturation. By analyzing the time-dependent behavior of the fully resolved, three-dimensional “fracture”–matrix geometry, we show that the industry-standard approach may consistently overestimate remaining oil saturation. For a highly heterogeneous reservoir system, the relative error of the field-based remaining oil estimates may exceed 50%.

Categories: Latest papers in fluid mechanics

### Onset of transition in the flow of polymer solutions through deformable tubes

Physics of Fluids, Volume 31, Issue 11, November 2019.

Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR2)/η2, where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη0)/R2ρ, where λ is the zero-shear relaxation time, η0 is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Ret ∼ 700, which is much lower than Ret ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Ret for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Ret ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Ret is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Ret following a scaling relation of Ret ∼ Σ0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.

Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR2)/η2, where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη0)/R2ρ, where λ is the zero-shear relaxation time, η0 is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Ret ∼ 700, which is much lower than Ret ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Ret for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Ret ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Ret is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Ret following a scaling relation of Ret ∼ Σ0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.

Categories: Latest papers in fluid mechanics

### Space-time correlations of velocity in a Mach 0.9 turbulent round jet

Physics of Fluids, Volume 31, Issue 11, November 2019.

In a turbulent jet, the numerical investigation of space-time correlations C(r, τ) at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach 0.9 turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e., x = 0.71, 7.03, and 34.47r0, corresponding to different stages of jet development, where r0 is the radius of the nozzle. Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing. The isocorrelation contours of C(r, τ) show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [G.-W. He and J.-B. Zhang, “Elliptic model for space-time correlations in turbulent shear flows,” Phys. Rev. E 73, 055303 (2006)]. According to the EA model, C(r, τ) has a scaling form of C(rE, 0) with two characteristic velocities U and V, i.e., rE = (r − Uτ)2 + V2τ2. By examining LES data, it is found that the characteristic velocity U determined in LES is in general consistent with the theoretical Ut in the EA model, while the trend of V in LES also matches with that of the theoretical Vt. Additionally, it is interesting that the ratio of V to Vt is approximately a constant V/Vt ≃ 1.3 in the turbulent jet.

In a turbulent jet, the numerical investigation of space-time correlations C(r, τ) at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach 0.9 turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e., x = 0.71, 7.03, and 34.47r0, corresponding to different stages of jet development, where r0 is the radius of the nozzle. Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing. The isocorrelation contours of C(r, τ) show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [G.-W. He and J.-B. Zhang, “Elliptic model for space-time correlations in turbulent shear flows,” Phys. Rev. E 73, 055303 (2006)]. According to the EA model, C(r, τ) has a scaling form of C(rE, 0) with two characteristic velocities U and V, i.e., rE = (r − Uτ)2 + V2τ2. By examining LES data, it is found that the characteristic velocity U determined in LES is in general consistent with the theoretical Ut in the EA model, while the trend of V in LES also matches with that of the theoretical Vt. Additionally, it is interesting that the ratio of V to Vt is approximately a constant V/Vt ≃ 1.3 in the turbulent jet.

Categories: Latest papers in fluid mechanics

### Statistical behaviors of conditioned two-point second-order structure functions in turbulent premixed flames in different combustion regimes

Physics of Fluids, Volume 31, Issue 11, November 2019.

The second-order structure functions and their components conditioned upon various events have been analyzed for unweighted and density-weighted velocities using a Direct Numerical Simulation database. The heat release due to combustion has been shown to have significant influences on the structure functions and their components conditioned on different mixture states. The use of density-weighted velocities changes the relative magnitudes of differently conditioned structure functions but does not reduce the scatter of these magnitudes. The structure functions conditioned to constant-density unburned reactants at both points and normalized using the root-mean-square velocity conditioned to the reactants are larger at higher values of mean reaction progress variables [math] (deeper within the flame brush), with this trend being not weakened with increasing turbulence intensity u′/SL. These results indicate that, contrary to a common belief, combustion-induced thermal expansion can significantly affect the incoming constant-density turbulent flow of unburned reactants even at u′/SL and Karlovitz number Ka as large as 10 and 18, respectively. The statistical behaviors of the structure functions reveal that the magnitude of the flame normal gradient of the velocity component tangential to the local flame can be significant, and it increases with increasing turbulence intensity. Moreover, the structure functions conditioned on both points in the heat release zone bear the signature of the anisotropic effects induced by the baroclinic torque for the flames belonging to the wrinkled flamelet and corrugated flamelet regimes. These anisotropic effects weaken with increasing turbulence intensity in the thin reaction zone regime.

The second-order structure functions and their components conditioned upon various events have been analyzed for unweighted and density-weighted velocities using a Direct Numerical Simulation database. The heat release due to combustion has been shown to have significant influences on the structure functions and their components conditioned on different mixture states. The use of density-weighted velocities changes the relative magnitudes of differently conditioned structure functions but does not reduce the scatter of these magnitudes. The structure functions conditioned to constant-density unburned reactants at both points and normalized using the root-mean-square velocity conditioned to the reactants are larger at higher values of mean reaction progress variables [math] (deeper within the flame brush), with this trend being not weakened with increasing turbulence intensity u′/SL. These results indicate that, contrary to a common belief, combustion-induced thermal expansion can significantly affect the incoming constant-density turbulent flow of unburned reactants even at u′/SL and Karlovitz number Ka as large as 10 and 18, respectively. The statistical behaviors of the structure functions reveal that the magnitude of the flame normal gradient of the velocity component tangential to the local flame can be significant, and it increases with increasing turbulence intensity. Moreover, the structure functions conditioned on both points in the heat release zone bear the signature of the anisotropic effects induced by the baroclinic torque for the flames belonging to the wrinkled flamelet and corrugated flamelet regimes. These anisotropic effects weaken with increasing turbulence intensity in the thin reaction zone regime.

Categories: Latest papers in fluid mechanics