Dynamics Of Capillary Rise Research Articles

Visualized study and performance evaluation on a micro-grooved vapor chamber

The evaporation resistance and capillary flow both dominates the heat transfer performance of aluminum vapor chamber (VC) with micro-grooved wicks (MGW). This study presents the visualization experiments for three MGW VC samples with different cross-sectional shapes, including semicircular (MGW-S), V-shaped (MGW-V) and trapezoidal (MGW-T). The characterization of capillary rise dynamics is evaluated and compared by depicting the transient liquid front in vertical installation while the thermal spreading capability is examined horizontally at the quasi-steady state. Results show that the MGW-T exhibits the highest capillary pressure, and higher capillary rise rate can be obtained when applying acetone as working medium. As the groove shape impacting on the rate of bubble generation and detachment during evaporation process, the MGW-S obtains the lowest average thermal resistance. However, compared to the uniformly generated bubbles of acetone, it is revealed that ethanol might result in the slug or puddle at the evaporation area, which shortens the flow length of vapor and increases the average thermal resistance. When conducting under incremental heat loads, the boiling phenomenon of the working liquid becomes increasingly turbulent, and the average thermal resistance can be minimized from 2.6 K/W to the level lower than 1 K/W. As the result, when using acetone with filling ratio of 30%, the average thermal resistance of the MGW-T reaches 0.92 K/W under heat load of 60 W.

Polymer Imbibition Through Paper Strips.

Liquid wicking and imbibition through porous strips are fundamental to paper microfluidics. In this study, we outline these processes via capillary rise dynamics (CRD) experiments by employing deionized water as a reference fluid and comparing its dynamics with those of aqueous polymer solutions. Replacing the working fluid with polymer solutions led to the occurrence of an intermediate viscous-dominated regime, followed by the gravity-dominated regime at a long-time scale. This transition from viscous-dominated to gravity-dominated was found to be a function of the porous substrate pore diameter. The delay in CRD from the viscous-dominated to gravity-dominated regime is explained by the presence of the prewetting front (PWF). To address it, PWF dynamics has also been quantified, along with the characterization of its morphological differences.

An analytical study of capillary rise dynamics: Critical conditions and hidden oscillations

The rise of a liquid column inside a thin capillary against the action of gravity is a prototypical example of a dynamic wetting process and plays an important role for applications but also for fundamental research in the area of multiphase fluid dynamics. Since the pioneering work by Lucas and Washburn, many research articles have been published which aim at a simplified description of the capillary rise dynamics using complexity-reduced models formulated as ordinary differential equations. Despite the fact that these models are based on profound simplifications, they may still be able to describe the essential physical mechanisms and their interplay. In this study, we focus on the phenomenon of oscillations of the liquid column. The latter has been observed experimentally for liquids with sufficiently small viscosity leading to comparably small viscous dissipation. Back in 1999, Quéré et al. formulated a condition for the appearance of rise height oscillations for an ODE model introduced by Bosanquet in 1923. This model has later been extended to include further dissipative mechanisms. In this work, we extend the mathematical analysis to a larger class of models including additional channels of dissipation. We show that Quéré’s critical condition is generalized to Ω+β<2, where Ω was introduced earlier and β is an additional non-dimensional parameter describing, e.g., contact line friction. A quantitative prediction of the oscillation dynamics is achieved from a linearization of the governing equations. We apply the theory to experimental data by Quéré et al. and, in particular, reveal the oscillatory behavior of dynamics for the nearly critically damped case of ethanol.

Analytical, experimental, and numerical study of capillary rise dynamics from inertial to viscous flow

Fundamental understanding of capillary rise dynamics and precise evaluation of imbibition processes should be considered in many natural and industrial phenomena. In the presence of the capillary rise dynamics, it is obligatory to know the dominant forces. The assumptions considered to solve the capillary rise motion usually neglect specific forces, which limit the reliability of the derived solutions. In the present study, the dominant forces and regimes involved in the initial moments of the capillary rise imbibition process in a tube were investigated analytically, experimentally, and numerically. Analytical solutions available in the literature were discussed, and then, their validity was verified by comparing them to experimental observations and numerical results. Comparing the capillary rise behavior at the initial stages revealed significant differences between the theoretical models and the numerical lattice Boltzmann method. This behavior is attributed to simplify assumptions and ignore the entrance effect, dynamic contact angle, and the inertial term in the theoretical model. By removing these assumptions in numerical formulations, closer results to the experimental records were observed. In the present study, for the first time, capillary rise dynamics were divided into five steps: (1) a transition regime with h ∼ t2, (2) purely inertial (stage one) with h ∼ t, (3) viscous-inertial or crossover (stage two) with h ∼ log10(t), (4) purely viscous (stage three) with h ∼ t1/2, and (5) gravitational-viscous with constant h. It was known that stage one was purely dominated by the inertial forces, then the influence of viscosity increased (viscous-inertial flow), and finally, the effect of inertia faded and the flow became purely viscous and approached the Lucas–Washburn law.

Conflicting Effects of Extreme Nanoconfinement on the Translational and Segmental Motion of Entangled Polymers

Physically confining polymers into nanoscale pores induces significant changes in their dynamics. Although different results on the effect of confinement on the dynamics of polymers have been reported, changes in the segmental mobility of polymers typically are correlated with changes in their chain mobility due to increased monomeric relaxation times. In this study, we show that translational and segmental dynamics of polymers confined in disordered packings of nanoparticles can exhibit completely opposite behavior. We monitor the capillary rise dynamics of entangled polystyrene (PS) in disordered packings of silica nanoparticles (NPs) of 7 and 27 nm diameter. The effective viscosity of PS in 27 nm $SiO_2$ NP packings, inferred based on the Lucas-Washburn equation, is significantly smaller than the bulk viscosity, and the extent of reduction in the translational motion due to confinement increases with the molecular weight of PS, reaching 4 orders of magnitude reduction for PS with a molecular weight of 4M g/mol. The glass transition temperature of entangled PS in the packings of 27 nm $SiO_2$ NPs, however, increases by 45 K, indicating significant slowdown of segmental motion. Interestingly, confinement of the polymers into packings made of 7 nm $SiO_2$ NPs results in molecular weight-independent effective viscosity. The segmental dynamics of PS in 7 nm $SiO_2$ NP packings are slowed down even further as evidenced by 65 K increase in glass transition temperature. These seemingly disparate effects are explained by the microscopic reptation-like transport controlling the translational motion and the physical confinement affecting the segmental dynamics under extreme nanoconfinement.

Analytical and numerical study of capillary rise in sinusoidal wavy channel: Unveiling the role of interfacial wobbling

Capillary rise is ubiquitous in engineering applications and natural phenomena. In straight channels, the dynamics of capillary rise have been thoroughly investigated and are well understood. However, for nonuniform channels of varying radius, the dynamics remain largely unclear. In this study, the capillary rise in a sinusoidal wavy channel is investigated both analytically and numerically. Specifically, the capillary rate-of-rise of water in sinusoidal channels with different contraction frequencies and amplitudes is derived based on the principle of energy conservation. The change in capillary velocity and height over time is further validated by two-phase flow simulations based on the conservative level-set method. The results reveal a strong viscous dissipation in the interfacial region resulting from the wave-like wobbling motion of the liquid–air interface, constituting more than 50% of the total viscous dissipation when the channel profile changes rapidly. Failing to account for this interfacial effect will result in significant overestimations of the capillary velocity and erroneous predictions of the capillary rise curve, typically more than 4 times difference in the capillary velocity and more than 2.5 times difference in the time taken to arrive at the maximum height.

Evaporative capillary rise

We investigate the rise dynamics of a volatile liquid within an open vertical channel, which requires us to consider the effects of capillarity, gravity, viscosity, and evaporation together. Upon quantifying the enhanced evaporation near the solid-liquid-gas contact line and setting up a theoretical model for the rise height, we show how to find an optimal channel dimension that maximizes the equilibrium rise height. This work can lay a foundation for understanding the evaporative capillary rise dynamics occurring in porous media.

Liquid-liquid capillary rise

We study the dynamics of capillary rise of a liquid-liquid interface using two immiscible liquids. By adjusting the height of the less dense fluid column, we measure the rise of the ensemble in the tube. A theoretical model is proposed that captures the time dependence of the position of the interface. Particular attention is given to the dynamics of the oil-water interface. Different types of flow regimes are identified and compared with previous theoretical and experimental findings. The theoretical model was found to be in good qualitative agreement, even though the contact angles of the two interfaces do not remain constant during the elevation of the fluid.

Effects of Tube Radius and Surface Tension on Capillary Rise Dynamics of Water/Butanol Mixtures

Capillary-driven action is an important phenomenon which aids the development of high-performance heat transfer devices, such as microscale heat pipes. This study examines the capillary rise dynamics of n-butanol/water mixture in a single vertical capillary tube with different radii (0.4, 0.6, and 0.85 mm). For liquids, distilled water, n-butanol, and their blends with varying concentrations of butanol (0.3, 0.5, and 0.7 wt.%) were used. The results show that the height and velocity of the capillary rise were dependent on the tube radius and liquid surface tension. The larger the radius and the higher the surface tension, the lower was the equilibrium height (he) and the velocity of rise. The process of capillary rise was segregated into three characteristic regions: purely inertial, inertial + viscous, and purely viscous regions. The early stages (purely inertial and inertial + viscous) represented the characteristic heights h1 and h2, which were dominant in the capillary rise process. There were linear correlations between the characteristic heights (h1, h2, and he), tube radius, and surface tension. Based on these correlations, a linear function was established between each of the three characteristic heights and the consolidated value of tube radius and surface tension (σL/2πr2).

Surfactant Effects on the Dynamics of Capillary Rise and Finger Formation in Square Capillaries.

We investigate the influence of surfactants on capillary rise and corner flow in angular pores. We therefore study capillary rise for simple fluids and surfactant solutions, comparing square to cylindrical capillaries. We show that fingers start to form in the corners of the square capillaries when the capillary rise slows down before reaching the equilibrium height. The corner flow scales as t1/3 and its quantitative understanding necessitates that the surface wettability is taken into account in terms of the liquid's advancing contact angle on the capillary walls inside the corner. Adding surfactants to water greatly influences the corner flow in square capillaries: depending on the nature of the surfactant, the corner flow can be either suppressed completely due to autophobic effects or enhanced due to the presence of Marangoni stresses caused by a surface tension gradient inside the liquid fingers.

Effects of Time‐Dependent Contact Angle on Wettability of Subcritically Water‐Repellent Soils

AbstractRecent studies have indicated that under certain conditions, most soils are water repellent to some degree, which impacts agricultural fields, pastures, forests, grasslands, and turf areas. Soil water repellency originates from amphiphilic molecules that reorient during contact with water. However, models to describe the flow in soils affected by time‐dependent contact angle (CA(t)) are still lacking. The current study aims to close this gap. The measured CA(t) for an oleic acid‐coated glass surface and a uniform capillary tube indicated that the initial CA was substantially higher for the latter. However, the rate of CA decrease was similar for both cases in spite of the fact that the contact area between the water and the tube wall continuously increases by the capillary rise. This indicates that the amphiphilic molecules reorientation at the vicinity of the contact line rather than at the wetted tube area controls the CA dynamics. A mathematical model for flow in a uniform and sinusoidal capillary tube with CA(t) &lt; 90° that includes model for the reorientation of the amphiphilic molecules was introduced. The model for uniform case was successfully verified by comparison with measured capillary rise in a coated uniform tube. The simulations indicated that nonuniform pore geometry amplifies the effect of CA(t) on the capillary rise dynamics. The stepwise meniscus propagation in the sinusoidal capillary tubes is driven by the time for the meniscus to reach the converging section of the tube. The retardation in capillary rise increases with tube waviness.

Dynamics of poroelastocapillary rise

A wetting liquid is driven through a thin gap due to surface tension and when the gap boundaries are elastic, the liquid deforms the gap as it rises. But when the fluid boundaries are also permeable (or poroelastic), the liquid can permeate the boundaries and change their properties, for example by swelling and softening, thereby altering the dynamics of the rise. In this paper, we study the dynamics of capillary rise between two poroelastic paper sheets to understand the effects of boundary permeability and softening. Using theoretical and numerical approaches, we find that if the bending rigidity of sheets is reduced, due to liquid permeation, the sheets coalesce faster compared to the case of impermeable sheets. We show that as a direct consequence of this faster coalescence, the volume of fluid captured between the sheets can be significantly lower. Finally, we compare our model predictions for the equilibrium states with some experimental observations.

Numerical study of capillary-driven flow in square micro-channel by lattice Boltzmann method

This paper presents an investigation into capillary rise dynamics in a vertical square micro-channel based on the lattice Boltzmann method with the Shan-Chen multiphase model. Several different numerical test problems are carried out to validate the model and to provide parameter information, which is then used to simulate the wetting fluid rise in a square tube. The numerical simulation results depict fast flow and accumulation of liquid in the capillary corners. The dynamics of the liquid penetration into a square capillary is also illustrated, which reveals the occurrence of oscillations at the initial time before the liquid reaches a stable regime. Furthermore, the streamlines inside the square capillary as well as the density profiles are obtained by the numerical simulations. The results show the existence of recirculation zones in the cross section and in the inlet region of the micro-channel. The dynamic contact angle was clearly observed via the numerical simulations. Finally, the dynamics of capillary rise were also studied for the micro-channel in which a thin vertical plate was integrated.

Singularity-free approximate analytical solution of capillary rise dynamics

Capillary rise is one of the most well-known capillarity; however, no single and complete analytic solution has ever been obtained yet. This paper used the singularity-free equation, and successfully obtained its Taylor's series solution. The solution revealed that capillary rise dynamics is mainly controlled by the Bond number and the Galileo number, while the Bond number is a key parameter within the solution. To avoid the poor rate of convergence of Taylor's series solution, an approximate analytic solution was proposed, which was verified numerically.

Evaluation of Dynamics of Capillary Rise of Water in Various Papers

Evaluation of Dynamics of Capillary Rise of Water in Various Papers

Finite volume solution for two-phase flow in a straight capillary

The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successful in predicting the complex dynamics of both capillary rise in round capillaries and imbibition along the corners of polygonal capillaries. The model can form the basis for more realistic network models which capture the effect of capillary, viscous and inertial forces on pore-scale interfacial dynamics and consequent macroscopic flow properties.

Infiltration of MHD liquid into a deformable porous material

Abstract We analyze the capillary rise dynamics for magnetohydrodynamics (MHD) fluid flow through deformable porous material in the presence of gravity effects. The modeling is performed using mixture theory approach and mathematical manipulation yields a nonlinear free boundary problem. Due to the capillary rise action, the pressure gradient in the liquid generates a stress gradient that results in the deformation of porous substrate. The capillary rise process for MHD fluid slows down as compared to Newtonian fluid case. Numerical solutions are obtained using a method of lines approach. The graphical results are presented for important physical parameters, and comparison is presented with Newtonian fluid case.

Capillary rise of non-aqueous liquids in cellulose sponges

A cellulose sponge is a mundane porous medium composed of numerous microporous cellulose sheets surrounding macroscale voids. Here, we quantify the capillary rise dynamics of non-aqueous liquids in a sponge using a combination of experiment and theory. Although the classical law of Washburn is obeyed in the early stages, the wet front propagation is no longer diffusive in the late stages and follows a power law, $h\sim t^{1/4}$, with $h$ and $t$ being the capillary rise height and time respectively. The transition of the power law is a consequence of the peculiar heterogeneous pore structure of cellulose sponges. The permeability and driving pressure change at the rise height above which the macro voids can no longer be filled completely due to significant effects of gravity. We rationalize the $t^{1/4}$ law by considering liquid flows along the corners of macro voids driven by capillary pressure of microscale wall pores.

Complex dynamics of capillary imbibition of poly(ethylene oxide) melts in nanoporous alumina

Capillary penetration of a series of entangled poly(ethylene oxide) melts within nanopores of self-ordered alumina follows an approximate t1/2 behavior according to the Lucas-Washburn equation; t is the time. However, the dependence on the capillary diameter deviates from the predicted proportionality to d1/2; d is the pore diameter. We observed a reversal in the dynamics of capillary rise with polymer molecular weight. Chains with 50 entanglements (Mw ≤ 100 kg/mol) or less show a slower capillary rise than theoretically predicted as opposed to chains with more entanglements (Mw ≥ 500 kg/mol) that display a faster capillary rise. Although a faster capillary rise has been predicted by theory and observed experimentally, it is the first time to our knowledge that a slower capillary rise is observed for an entangled polymer melt under conditions of strong confinement (with 2Rg/d = 1). These results are discussed in the light of theoretical predictions for the existence of a critical length scale that depends on the molecular weight and separates the microscopic (d < d*) from the macroscopic (d > d*) regime.

Capillary dynamics driven by molecular self-layering

Capillary dynamics is a ubiquitous everyday phenomenon. It has practical applications in diverse fields, including ink-jet printing, lab-on-a-chip, biotechnology, and coating. Understanding capillary dynamics requires essential knowledge on the molecular level of how fluid molecules interact with a solid substrate (the wall). Recent studies conducted with the surface force apparatus (SFA), atomic force microscope (AFM), and statistical mechanics simulation revealed that molecules/nanoparticles confined into the film/wall surfaces tend to self-layer into 2D layer/s and even 2D in-layer with increased confinement and fluid volume fraction. Here, the capillary rise dynamics of simple molecular fluids in cylindrical capillary is explained by the molecular self-layering model. The proposed model considers the role of the molecular shape on self-layering and its effect on the molecularly thin film viscosity in regards to the advancing (dynamic) contact angle. The model was tested to explain the capillary rise dynamics of fluids of spherical, cylindrical, and disk shape molecules in borosilicate glass capillaries. The good agreement between the capillary rise data and SFA data from the literature for simple fluid self-layering shows the validity of the present model. The present model provides new insights into the design of many applications where dynamic wetting is important because it reveals the significant impact of molecular self-layering close to the wall on dynamic wetting.