scholarly journals Drops and bubbles in wedges

2014 ◽  
Vol 748 ◽  
pp. 641-662 ◽  
Author(s):  
Etienne Reyssat
Keyword(s):  
Driving Force ◽  
Viscous Friction ◽  
Equation Of Motion ◽  
Relative Strength ◽  
Parallel Plates ◽  
Contact Lines ◽  
Viscous Forces ◽  
Dimensionless Equation ◽  
Physical Mechanisms ◽  
Spontaneous Migration

AbstractWe investigate experimentally the spontaneous motion of drops and bubbles confined between two plates forming a narrow wedge. Such discoidal objects migrate under the gradient in interfacial energy induced by the non-homogeneous confinement. The resulting capillary driving force is balanced by viscous resistance. The viscous friction on a drop bridging parallel plates is estimated by measuring its sliding velocity under gravity. The viscous forces are the sum of two contributions, from the bulk of the liquid and from contact lines, the relative strength of which depends on the drop size and velocity and the physical properties of the liquid. The balance of capillarity and viscosity quantitatively explains the dynamics of spontaneous migration of a drop in a wedge. Close the tip of the wedge, bulk dissipation dominates and the migrating velocity of drops is constant and independent of drop volume. The distance between the drop and the tip of the wedge is thus linear with time $t$, $x(t) \sim t_0-t$, where $t_0$ is the time at which the drop reaches the tip of the wedge. Far away from the apex, contact lines dominate the friction, the motion is accelerated toward the tip of the wedge and velocities are higher for larger drops. In this regime, it is shown that $x(t) \sim (t_0-t)^{4/13}$. The position and time of the crossover between the two dissipation regimes are used to write a dimensionless equation of motion. Plotted in rescaled variables, all experimental trajectories collapse to the prediction of our model. In contrast to drops, gas bubbles in a liquid-filled wedge behave as non-wetting objects. They thus escape the confinement of the wedge to reduce their surface area. The physical mechanisms involved are similar for drops and bubbles, so that the forces acting have the same mathematical structures in both cases, except for the sign of the capillary driving force and a numerical factor. We thus predict and show experimentally that the trajectories of drops and bubbles obey the same equation of motion, except for a change in the sign of $t_0-t$.

scholarly journals Measurements of periodically perturbed dewetting force fields and their consequences on the symmetry of the resulting patterns

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Konstantinos Roumpos ◽  
Sarah Fontaine ◽  
Thomas Pfohl ◽  
Oswald Prucker ◽  
Jürgen Rühe ◽  
...  
Keyword(s):  
Force Field ◽  
Driving Force ◽  
Force Fields ◽  
Contact Lines ◽  
Polymer Flow ◽  
Circular Symmetry ◽  
Pillar Array ◽  
Restoring Forces ◽  
Micro Pillars ◽  
Circular Contact

AbstractWe studied the origin of breaking the symmetry for moving circular contact lines of dewetting polymer films suspended on a periodic array of pillars. There, dewetting force fields driving polymer flow were perturbed by elastic micro-pillars arranged in a regular square pattern. Elastic restoring forces of deformed pillars locally balance driving capillary forces and broke the circular symmetry of expanding dewetting holes. The observed envelope of the dewetting holes reflected the symmetry of the underlying pattern, even at sizes much larger than the characteristic period of the pillar array, demonstrating that periodic perturbations in a driving force field can establish a well-defined pattern of lower symmetry. For the presented system, we succeeded in squaring the circle.

Respiratory Mechanics

2017 ◽  
Author(s):  
John W. Kreit
Keyword(s):  
Mechanical Ventilation ◽  
Respiratory System ◽  
Respiratory Mechanics ◽  
Pressure Change ◽  
Equation Of Motion ◽  
Positive End Expiratory Pressure ◽  
Elastic Recoil ◽  
Viscous Forces ◽  
Equilibrium Volume ◽  
Complex Process

Ventilation can occur only when the respiratory system expands above and then returns to its resting or equilibrium volume. This is just another way of saying that ventilation depends on our ability to breathe. Although breathing requires very little effort and even less thought, it’s nevertheless a fairly complex process. Respiratory Mechanics reviews the interaction between applied and opposing forces during spontaneous and mechanical ventilation. It discusses elastic recoil, viscous forces, compliance, resistance, and the equation of motion and the time constant of the respiratory system. It also describes how and why pleural, alveolar, lung transmural, intra-abdominal, and airway pressure change during spontaneous and mechanical ventilation, and the effect of applied positive end-expiratory pressure (PEEP).

Flow through porous media: limits of fractal patterns

1989 ◽  
Vol 423 (1864) ◽  
pp. 159-168 ◽  
Keyword(s):  
Computer Simulations ◽  
Diffusion Limited Aggregation ◽  
Flow Equations ◽  
Viscous Forces ◽  
Opposite Case ◽  
Physical Mechanisms ◽  
Diffusion Limited ◽  
Fractal Patterns ◽  
Flow Through ◽  
Wetting Fluid

By using experiments on micromodels and computer simulations, we have demonstrated the existence of three types of basic displacements when a non-wetting fluid invades a two-dimensional porous medium: capillary fingering when capillary forces are very strong compared to viscous forces, viscous fingering when a less viscous fluid is displacing a more viscous one, and stable displacement in the opposite case. These displacements are described by statistical models: invasion percolation, diffusion-limited aggregation (DLA) and anti-DLA. The domains of validity of the basic displacements are mapped onto the plane with axes Ca (capillary number) and M (viscosity ratio). The boundaries of these domains are calculated either by using theoretical laws describing transport properties of fractal patterns or by the interpretation of physical mechanisms at the pore scale. In addition, the prefactors that are not available from scaling theories are obtained by computer simulations on a network of capillaries, in which the flow equations are solved at each node.

scholarly journals Parametric oscillation of the prismatic beam with heredity of material

1983 ◽  
Vol 5 (4) ◽  
pp. 7-13
Author(s):  
Hoang Van Da
Keyword(s):  
Parametric Excitation ◽  
Asymptotic Method ◽  
Viscous Friction ◽  
Equation Of Motion ◽  
Parametric Oscillation ◽  
Prismatic Beam ◽  
Set Up

In this work the method set up the equation of motion of the prismatic beam under parametric excitation with regard to the heredity of material. The solution of this problem were constructed by means of average and asymptotic method. It is shown that heredity of material exerts its it influence on the amplitude of the oscillation as does viscous friction for a system with soft characteristics.

scholarly journals DISSIPATIVE OSCILLATORS’ POWER CHARACTERISTIC NON-SYMMETRY DYNAMIC EFFECT

2021 ◽  
pp. 65-75
Author(s):  
Vasiliy Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Differential Equation ◽  
Dry Friction ◽  
Elastic Characteristic ◽  
Approximation Error ◽  
Dynamic Effect ◽  
Viscous Friction ◽  
Equation Of Motion ◽  
Lambert Function ◽  
Coulomb Dry Friction ◽  
Non Linear Oscillator

The features of motion of a non-linear oscillator under the instantaneous force pulse loading are studied. The elastic characteristic of the oscillator is given by a polygonal chain consisting of two linear segments. The focus of the paper is on the influence of the dissipative forces on the possibility of occurrence of the elastic characteristic non-symmetry dynamic effect, studied previously without taking into account the influence of these forces. Four types of drag forces are considered, namely linear viscous friction, Coulomb dry friction, position friction, and quadratic viscous resistance. For the cases of linear viscous friction and Coulomb dry friction the analytical solutions of the differential equation of oscillations are found by the fitting method and the formulae for computing the swings are derived. The conditions on the parameters of the problem are determined for which the elastic characteristic non-symmetry dynamic effect occurs in the system. The conditions for the effect to occur in the system with the position friction are derived from the energy relations without solving the differential equation of motion. In the case of quadratic viscous friction the first integral of the differential equation of motion is given by the Lambert function of either positive or negative argument depending on the value of the initial velocity. The elastic characteristic non-symmetry dynamic effect is shown to occur for small initial velocities, whereas it is absent from the system when the initial velocities are sufficiently large. The values of the Lambert function are proposed to be computed by either linear interpolation of the known data or approximation of the Lambert function by elementary functions using asymptotic formulae which approximation error is less than 1%. The theoretical study presented in the paper is followed up by computational examples. The results of the computations by the formulae proposed in the paper are shown to be in perfect agreement with the results of numerical integration of the differential equation of motion of the oscillator using a computer.

scholarly journals An analytical study on the entropy generation in flow of a generalized Newtonian fluid

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1959-1969
Author(s):  
Yigit Aksoy ◽  
Necmi Gurkan ◽  
Ayse Aksoy ◽  
Derya Durgun ◽  
Ali Yurddas
Keyword(s):  
Heat Transfer ◽  
Viscous Friction ◽  
Analytical Investigation ◽  
Heat Fluxes ◽  
Variable Step Size ◽  
Parallel Plates ◽  
Step Size ◽  
Generalized Newtonian Fluid ◽  
Dissipation Term ◽  
Pressure Driven Flow

In this study, an analytical investigation on pressure driven flow of Powell-Eyring fluid is conducted to understand the irreversibilities due to heat transfer and viscous heating. The flow between infinitely long parallel plates is considered as fully developed and laminar with constant properties and subjected to symmetrical heat fluxes from solid boundaries. The internal heating due to viscous friction accompanies external heat transfer, that is, viscous dissipation term is to be involved in the energy equation. As a cross-check, accuracy of analytical solutions is confirmed by a predictor-corrector numerical scheme with variable step size.

Why did life emerge?

2008 ◽  
Vol 7 (3-4) ◽  
pp. 293-300 ◽  
Author(s):  
Arto Annila ◽  
Erkki Annila
Keyword(s):  
Driving Force ◽  
Second Law Of Thermodynamics ◽  
Equation Of Motion ◽  
Energy Transduction ◽  
External Energy ◽  
Demarcation Line ◽  
Theory Of Evolution ◽  
Transduction Mechanisms ◽  
Fitness Criterion ◽  
Evolution By Natural Selection

AbstractMany mechanisms, functions and structures of life have been unraveled. However, the fundamental driving force that propelled chemical evolution and led to life has remained obscure. The second law of thermodynamics, written as an equation of motion, reveals that elemental abiotic matter evolves from the equilibrium via chemical reactions that couple to external energy towards complex biotic non-equilibrium systems. Each time a new mechanism of energy transduction emerges, e.g., by random variation in syntheses, evolution prompts by punctuation and settles to a stasis when the accessed free energy has been consumed. The evolutionary course towards an increasingly larger energy transduction system accumulates a diversity of energy transduction mechanisms, i.e. species. The rate of entropy increase is identified as the fitness criterion among the diverse mechanisms, which places the theory of evolution by natural selection on the fundamental thermodynamic principle with no demarcation line between inanimate and animate.

A Note on Flow Regimes and Churning Loss Modelling

2011 ◽  
Author(s):  
C. Changenet ◽  
G. Leprince ◽  
F. Ville ◽  
P. Velex
Keyword(s):  
Critical Reynolds Number ◽  
Flow Regimes ◽  
Operating Conditions ◽  
Power Losses ◽  
Secondary Importance ◽  
Helical Gears ◽  
Viscous Forces ◽  
Physical Mechanisms ◽  
Loss Modelling ◽  
Fluid Flow Regimes

The purpose of this study is to investigate the various fluid flow regimes generated by a pinion running partly immersed in an oil bath and the corresponding churning power losses. In a series of papers, the authors have established several loss formulae whose validity depends on two different flow regimes characterized via a critical Reynolds number. Based on some new measurements for transient operating conditions, it has been found that the separation in two regimes may be not accurate enough for wide-faced gears and high temperatures. An extended formulation is therefore proposed which, apart from viscous forces, introduces the influence of centrifugal effects. The corresponding results agree well with the experimental measurements from a number of gears and operating conditions (speed, temperature). Finally, the link between churning and windage losses is examined and it is concluded that the physical mechanisms are different thus making it difficult to establish a general correlation between the two phenomena. In particular, it is shown that tooth geometry is of secondary importance on churning whereas, the air-lubricant circulation being different for spur and helical gears, it substantially impacts windage.

Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows

1999 ◽  
Vol 383 ◽  
pp. 29-54 ◽  
Author(s):  
ANTHONY D. SCHLEIZER ◽  
ROGER T. BONNECAZE
Keyword(s):  
Capillary Number ◽  
Contact Angles ◽  
Fluid Viscosity ◽  
Diffusive Transport ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Contact Lines ◽  
Critical Capillary Number ◽  
Pressure Driven Flow ◽  
Pressure Driven

The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Péclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

The elastocapillary Landau–Levich problem

2013 ◽  
Vol 735 ◽  
pp. 1-28 ◽  
Author(s):  
Harish N. Dixit ◽  
G. M. Homsy
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Functional Dependence ◽  
Dip Coating ◽  
Relative Strength ◽  
Capillary Length ◽  
Viscous Forces ◽  
Flow Speeds ◽  
Numerical Coefficient ◽  
Image Position

AbstractWe study the classical Landau–Levich dip-coating problem for the case in which the interface possesses both elasticity and surface tension. The aim of the study is to develop a complete asymptotic theory of the elastocapillary Landau–Levich problem in the limit of small flow speeds. As such, the paper also extends our previous study on purely elastic Landau–Levich flow (Dixit & Homsy J. Fluid Mech., vol. 732, 2013, pp. 5–28) to include the effect of surface tension. The elasticity of the interface is described by the Helfrich model and surface tension is modelled in the usual way. We define an elastocapillary number, $\epsilon $, which represents the relative strength of elasticity to surface tension. Based on the size of $\epsilon $, we can define three different regimes of interest. In each of these regimes, we carry out asymptotic expansions in the small capillary (or elasticity) numbers, which represents the balance of viscous forces to surface tension (or elasticity).In the weak elasticity regime, the film thickness is a small correction to the classical Landau–Levich law and can be written as $$\begin{eqnarray*}{\tilde {h} }_{\infty , c} = (0. 9458- 0. 0839~\mathscr{E}){l}_{c} C{a}^{2/ 3} , \quad \epsilon \ll 1,\end{eqnarray*}$$ where ${l}_{c} $ is the capillary length, $Ca$ is the capillary number and $\mathscr{E}= \epsilon / C{a}^{2/ 3} $. In the elastocapillary regime, the film thickness is a function of $\epsilon $ through the power-law relationship $$\begin{eqnarray*}{\tilde {h} }_{\infty , ec} = {\bar {h} }_{\infty , e} L\hspace{0.167em} f(\epsilon )C{a}^{4/ 7} , \quad \epsilon \sim O(1),\end{eqnarray*}$$ where ${\bar {h} }_{\infty , e} $ is a numerical coefficient obtained in our previous study, $L$ is the elastocapillary length, and $f(\epsilon )$ represents the functional dependence of film thickness on the elastocapillary parameter.

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