Modelling and analysis of meniscus roll coating

Separation of electrically neutral, mutually noninteracting passive solutes via AC electroosmotic slit channel flows is investigated for general asymmetric wall surface zeta potentials and apparent hydrodynamic slip lengths. We consider the nontrivial coupling between the surface potentials (or charge densities) and the apparent slip lengths, and focus our attention on the occurrence of a so called "crossover phenomenon" for separating out the slow diffusers when both slow and fast diffusers are present. Results show that regardless of the potential-slip coupling, wider bandwidths become available for crossover phenomenon to occur when the electroosmotic velocity gradient (magnitude) is greater. Contrarily, plug-like velocity profiles inhibit crossover phenomenon, and the potential-slip parametric combinations leading to such profiles can be easily identified by the conditions for minimal transport enhancement reported in recent literature. When separating out the slow diffuser or crossover phenomenon is desired, we recommend incorporating significant asymmetry in the surface potential and apparent slip boundary conditions such that the operating frequency and flow oscillation amplitude may be lowered to more practical values. Our results also agree with and strengthen the physical picture for explaining crossover phenomenon in macroscopic pressure-driven oscillatory flows.

Hydrated soft tissues of the human musculoskeletal system, such as articular cartilage in diarthrodial joints or the annulus fibrosis of the inter vertebral disk, are accurately represented by a biphasic continuum model consisting of an incompressible solid phase (collagen and proteoglycan) and incompressible, inviscid fluid (interstitial fluid) and derive from the continuum theory of mixtures. These tissues exhibit a viscoelastic‐type response which is caused by the diffusive drag of the fluid phase as it flows past the solid phase. In this study an automated, adaptive, finite element solution of the governing biphasic equations is presented. The finite element formulation is based on a mixed‐penalty approach in which the penalty form of the continuity equation for the mixture is included in the weak form. Pressure, solid and fluid velocities are interpolated independently, and the coefficients of the C−1 pressure field are eliminated at the element level. The resulting matrix form is a system of first order differential equations which is solved via standard finite difference methods. Mesh generation and updating, including both refinement and coarsening, for the two‐dimensional examples examined in this study are performed using Finite Quadtree. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. Rezoning is accomplished by transferring the finite element solution for the primary variables onto the locally updated mesh using a projected field. These projected values allow the finite difference algorithm to proceed in time using the updated mesh. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using two‐dimensional axisymmetric problems corresponding to the uncomined compression of a cylindrical disk of soft tissue and the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients in both problems and to produce solutions in good agreement with independent, converged, numerical solutions.

The influence of geometry on the pressure field within the confined, water-filled annulus between a central, vibrating cylinder and an outer, rigid enclosure is determined. A two dimensional model is constructed using the finite element (FE) method and parameters are identified to characterize the eccentricity of the nominal cylinder position, the size of the annulus relative to the inner cylinder and the degree to which the annulus is not circular (i.e. it is elliptic). The FE solution is verified using a closed form solution for the special case of a concentric cylinder and annulus. It is shown that the system acts as a force multiplier. Analyses of the asymmetrical geometries indicate that while the pressure field on the surface of the cylinder and enclosure can be highly asymmetric, the system is relatively insensitive to minor variations in annulus shape except when the vibrating cylinder is not centrally located within the fluid region or the annulus size itself is small.

Capsule equilibrium positions near channel center in Poiseuille flow

Velocity slip in electroosmotic flows (EOF) is investigated using an analytical solution of Poisson–Boltzmann and Stokes (PB-S) equations with slip correction, and the results are compared with the predictions from molecular dynamics (MD) simulations. Particularly, EOFs of NaCl solution in silicon nanochannels are simulated, and channel dimensions are picked to exhibit plug flow behavior in the bulk region. Electrochemical conditions are specified within the validity region of PB theory to avoid charge inversion and flow reversal effects. The analytical model shows normalization of the slip length (an interfacial property) with the Debye length determined by the ionic concentration, implying that the slip enhancement in EOFs is independent of the channel height. MD results are compared with the analytical solution using the apparent viscosity and slip lengths determined by force-driven flow simulations in charged silicon nanochannels. Onset of slip velocity within the electrical double layer and its effects on EOF are investigated as a function of the liquid–wall interaction strength. Good agreements between the analytical solutions and MD results validate PB-S equations in nanochannels as small as 3.5 nm. Results validate that slip enhancement in EOFs is independent of the channel height, which constitutes a theoretical basis for the slip-length measurements on hydrophobic dielectric surfaces using EOFs.

Dynamic wetting characteristics during droplet formation in a microfluidic T-junction

The motion of a long gas bubble in a continuous liquid phase in a small diameter channel results in a thin liquid film between the bubble and the channel wall. Generally, a free-slip (zero shear) boundary condition is applied at the gas–liquid interphase boundary which is applicable only at low gas velocities. However, at increased flow rates of gas phase, shear stress at the gas–liquid interface is non-negligible. Applying non-zero shear at the interface requires knowledge of velocity profile in the gas phase. In this work, we circumvent this problem by using a slip length like parameter to take into account the velocity gradient in the gas phase. The slip length is infinite for the free-slip condition at the interface and zero for the no-slip condition. An expression is derived for the film thickness in terms of slip length and capillary number and is compared with the experimental data and other correlations available in the literature.

Wax deposition during crude oil transmission can cause a series of negative effects and lead to problems associated with pipeline safety. A considerable number of previous works have investigated the wax deposition mechanism, inhibition technology, and remediation methods. However, studies on the shearing mechanism of wax deposition have focused largely on the characterization of this phenomena. The role of the shearing mechanism on wax deposition has not been completely clarified. This mechanism can be divided into the shearing dispersion effect caused by radial migration of wax particles and the shearing stripping effect caused by hydrodynamic scouring. From the perspective of energy analysis, a novel wax deposition model was proposed that considered the flow parameters of waxy crude oil in pipelines instead of its rheological parameters. Considering the two effects of shearing dispersion and shearing stripping coexist, with either one of them being the dominant mechanism, a shearing dispersion flux model and a shearing stripping model were established. Furthermore, a quantitative method to distinguish between the roles of shearing dispersion and shearing stripping in wax deposition was developed. The results indicated that the shearing mechanism can contribute an average of approximately 10% and a maximum of nearly 30% to the wax deposition process. With an increase in the oil flow rate, the effect of the shearing mechanism on wax deposition is enhanced, and its contribution was demonstrated to be negative; shear stripping was observed to be the dominant mechanism. A critical flow rate was observed when the dominant effect changes. When the oil flow rate is lower than the critical flow rate, the shearing dispersion effect is the dominant effect; its contribution rate increases with an increase in the oil flow temperature. When the oil flow rate is higher than the critical flow rate, the shearing stripping effect is the dominant effect; its contribution rate increases with an increase in the oil flow temperature. This understanding can be used to design operational parameters of the actual crude oil pipelines and address the potential flow assurance problems. The results of this study are of great significance for understanding the wax deposition theory of crude oil and accelerating the development of petroleum industry pipelines.

We study the origins of the dynamic contact angle in a two-dimensional lattice-Boltzmann model of immiscible fluids. We show that the dynamic contact angle changes as a function of capillary number as observed in laboratory experiments and explain how this dependence arises in the lattice-Boltzmann model. We also explain how the fluid-fluid interface can move while retaining its shape. The interface has an apparent slip length. The apparent slip follows the classical Navier slipping rule where the velocity of the fluid at the wall is proportional to the viscous stress at the wall. This apparent slip length is proportional to the viscous length scale associated with the spurious flow induced by uncompensated stress at the three-phase contact point.

A dynamic network model for imbibition based on a physically realistic and mathematically rigorous treatment of the complex dynamics of frontal displacements, film swelling, snap-off and snap-off nucleated displacements is described. Many of the previously reported observations in micro-model displacements, X-ray CT measured saturation profiles in core floods and the competition between frontal displacements and snap-off all arise as a natural consequence of the dynamics of the model. The model is used to study the effect of displacement rate on imbibition patterns, relative permeabilities and residual saturations. The model shows that at very low displacement rates the displacement is dominated by film swelling and snap-off with a displacement pattern similar to bond percolation. Trapping is extensive and relative permeabilities are low. At high displacement rates snap-off is completely suppressed and the displacement pattern is similar to invasion percolation. Trapping is low and relative permeabilities are high. Introduction Quasi-static network models based on realistic rock topology, geometry and pore-scale physics have been used to predict relative permeabilities and residual saturations for displacements in simple porous media1,2,3,4,5. A major limitation of these models in imbibition displacements is the treatment of wetting film or corner flow and snap-off. In imbibition the wetting fluid advances by piston- like displacements of pores and throats from a connected invasion front and by film swelling and snap-off ahead of the connected front. Snap-off is the dominant trapping mechanism and the competition between snap-off and frontal piston-like pore displacements determines the displacement pattern, residual saturation and relative permeability. Quasi-static models assume that the displacement is dominated by capillary forces and neglect viscous pressure gradients in bulk fluid and in films. Neglecting viscous losses in bulk fluid is a reasonable assumption for capillary numbers Ca<10−3-10−4 (Dullien6), where the capillary number is defined asEquation 1 and µ is the viscosity of the displacing fluid, v is the displacement velocity and s is the interfacial tension. However, this is not true for film flow where the small conductivity of films can result in significant rate effects at capillary numbers as low as 10−6-10−8 (Blunt and Scher7 and Hughes and Blunt8). Displacement rate has a profound effect on the competition between piston-like displacements and snap-off and therefore on the displacement pattern, residual saturation and relative permeability. A number of dynamic network models have been proposed to account for rate effects in imbibition7,8,9,10,11,12,13,14,15. All of these models involve the computation of pressure fields based on simplifying assumptions regarding the nature of wetting films and film flow (constant film conductivity, steady-state flow, lumped hydraulic resistances for film and bulk flow). The computed pressure fields are used to modify the order of pore and throat displacements. None of the models fully capture the complex spatial and temporal dependence of film swelling, snap-off and snap-off nucleated pore and throat displacements ahead of the connected front.

The paper presents an investigation of the isothermal steady flow of a viscous incompressible fluid in an extended flat layer using hydrodynamic equations. The bottom of the layer under consideration is limited by a stationary solid hydrophilic surface. At the upper boundary of the layer, the pressure field, which is inhomogeneous in both horizontal coordinates, and the velocity field are specified. These boundary conditions allow one to generalize the classical Poiseuille flow. The exact solution, satisfying the set boundary value problem, is described by a series of polynomials of different orders. The highest (fifth) degree of the polynomials corresponds to a homogeneous component of the horizontal velocity. Here, the pressure field depends only on the horizontal coordinates; the dependence is linear. The detailed analysis of the velocity field is carried out. The obtained results confirm that the determined exact solution can describe multiple stratification of the velocity field and the corresponding field of tangent stresses. The analysis of spectral properties of the velocity field is performed for a general case without specifying the values of physical constants that unambiguously identify the studied fluid. Therefore, the presented results are applicable to viscous fluids of various nature.

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a^{*}), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation.

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles toward the center of the Poiseuille flow. This is in a marked contrast with a result [L. G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation toward its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.

Electroviscous effects in charge-dependent slip flow of liquid electrolytes through a charged microfluidic device

Accurate models for predicting drop dynamics, such as maximum drop departure sizes, are crucial for estimating heat transfer rates during condensation on superhydrophobic (SH) surfaces. Previous studies have focused on examining the heat transfer rates for SH surfaces under the influence of gravity or vapor flowing over the surface. This study investigates the impact of surface solid fraction and texture scale on drop mobility in a condensing environment with a humid air flow. Experiments recorded condensation with varying surface feature sizes from micro- to nano scale under different flow rates. Video analysis detected the drop-size distribution and maximum drop departure sizes. Particle image velocimetry (PIV) provided accurate shear force representations. Results showed that the maximum drop departure sizes decreased with lower surface solid fractions and higher flow rates. A force balance analysis revealed that coalescence-induced drop jumping aids drop departure. Different drop behaviors due to coalescence were linked to surface characteristics. The study quantified drop jump distances under shear force during condensation on SH surfaces, and found that jump distances increased when coalescing drop sizes were similar. Based on these findings, a method for tuning SH surfaces to control drop size at coalescence and departure was suggested. Drop mobility was measured in terms of Bond and Capillary numbers, showing a dependence on surface solid fraction and pitch size. By combining these into surface slip length, it was shown that drop mobility increases with increasing slip length.