1,720,971 research outputs found
Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci
No full textThis paper presents new asymptotic formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.</jats:p
Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles
Full text linkA common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope , we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width is small compared with the array period . The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation wherein is the applied-gradient magnitude, is the liquid viscosity and , a non-monotonic function of the protrusion angle , is provided by the quadrature, \begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s
On spreading resistance for an isothermal source on a compound flux channel
No full textRecently, Jain [ASME J. Heat Mass Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our complimentary approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached
Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries
Full text linkIn the lithium-ion battery literature, discharges followed by a relaxation to
equilibrium are frequently used to validate models and their parametrizations.
Good agreement with experiment during discharge is easily attained with a
pseudo-two-dimensional model such as the Doyle-Fuller-Newman (DFN) model. The
relaxation portion, however, is typically not well-reproduced, with the
relaxation in experiments occurring much more slowly than in models. In this
study, using a model that includes a size distribution of the active material
particles, we give a physical explanation for the slow relaxation phenomenon.
This model, the Many-Particle-DFN (MP-DFN), is compared against discharge and
relaxation data from the literature, and optimal fits of the size distribution
parameters (mean and variance), as well as solid-state diffusivities, are found
using numerical optimization. The voltage after relaxation is captured by
careful choice of the current cut-off time, allowing a single set of physical
parameters to be used for all C-rates, in contrast to previous studies. We find
that the MP-DFN can accurately reproduce the slow relaxation, across a range of
C-rates, whereas the DFN cannot. Size distributions allow for greater internal
heterogeneities, giving a natural origin of slower relaxation timescales that
may be relevant in other, as yet explained, battery behavior
Stability of a photosurfactant-laden viscous liquid thread under illumination
No full textThis paper investigates the effects of a light-actuated photosurfactant on the canonical problem of the linear stability of a viscous thread surrounded by a dynamically passive fluid. A model consisting of the Navier-Stokes equations and a set of molar concentration equations is presented that capture light-induced switching between two stable surfactant isomer states, trans and cis. These two states display significantly different interfacial properties, allowing for some external control of the stability behaviour of the thread via incident light. Normal modes are used to generate a generalized eigenvalue problem for the growth rate which is solved with a hybrid analytical and numerical method. The results are validated with appropriate analytical solutions of increasing complexity, beginning with a solution to a clean interface, then analytical solutions for one insoluble surfactant, one soluble surfactant and a special case of two photosurfactants with a spatially uniform undisturbed state. Presenting each of these cases allows for a holistic discussion of the effect of surfactants in general on the stability of a liquid thread. Finally, the numerical solutions in the presence of two photosurfactants that display radially non-uniform undisturbed states are presented, and details of the impact of the illumination on the linear stability of the thread are discussed.</p
Asymptotic Nusselt numbers for internal flow in the Cassie state
No full textWe consider laminar, fully developed, Poiseuille flows of liquid in the Cassie state through diabatic, parallel-plate microchannels symmetrically textured with isoflux ridges. Via matched asymptotic expansions, we develop expressions for (apparent hydrodynamic) slip lengths and Nusselt numbers. Our small parameter is the pitch of the ridges divided by the height of the microchannel. When the ridges are oriented parallel to the flow, we quantify the error in the Nusselt number expressions in the literature and provide a new closed-form result. It is accurate to and valid for any solid (ridge) fraction, whereas previous ones are accurate to and breakdown in the important limit when the solid fraction approaches zero. When the ridges are oriented transverse to the (periodically fully developed) flow, the error associated with neglecting inertial effects in the slip length is shown to be, where is the channel-scale Reynolds number based on its hydraulic diameter. The corresponding Nusselt number expressions' accuracies are shown to depend on the Reynolds number, Péclet number and Prandtl number in addition to. Manipulating the solution to the inner temperature problem encountered in the vicinity of the ridges shows that classic results for the thermal spreading resistance are better expressed in terms of polylogarithm functions.</p
Mechanical power from thermocapillarity on superhydrophobic surfaces
No full textCrowdy et al. (2023 Phys. Rev. Fluids, vol. 8, 094201), recently showed that liquid suspended in the Cassie state over an asymmetrically spaced periodic array of alternating cold and hot ridges such that the menisci spanning the ridges are of unequal length will be pumped in the direction of the thermocapillary stress along the longer menisci. Their solution, applicable in the Stokes flow limit for a vanishingly small thermal Péclet number, provides the steady-state temperature and velocity fields in a semi-infinite domain above the superhydrophobic surface, including the uniform far-field velocity, i.e. pumping speed, the key engineering parameter. Here, a related problem in a finite domain is considered where, opposing the superhydrophobic surface, a flow of liquid through a microchannel is bounded by a horizontally mobile smooth wall of finite mass subjected to an external load. A key assumption underlying the analysis is that, on a unit area basis, the mass of the liquid is small compared with that of the wall. Thus, as shown, rather than the heat equation and the transient Stokes equations governing the temperature and flow fields, respectively, they are quasi-steady and, as a result, governed by the Laplace and Stokes equations, respectively. Under the further assumption that the ridge period is small compared with the height of the microchannel, these equations are resolved using matched asymptotic expansions which yield solutions with exponentially small asymptotic errors. Consequently, the transient problem of determining the velocity of the smooth wall is reduced to an ordinary differential equation. This approach is used to provide a theoretical demonstration of the conversion of thermal energy to mechanical work via the thermocapillary stresses along the menisci.</p
Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature
No full textWe investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid-gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.</p
Effect of thermocapillary stress on slip length for a channel textured with parallel ridges
No full textWe compute the apparent hydrodynamic slip length for (laminar and fully developed) Poiseuille flow of liquid through a heated parallel-plate channel. One side of the channel is textured with parallel (streamwise) ridges and the opposite one is smooth. On the textured side of the channel, the liquid is in the Cassie state. No-slip and constant heat flux boundary conditions are imposed at the solid–liquid interfaces along the tips of the ridges, and the menisci between ridges are considered to be flat and adiabatic. The smooth side of the channel is subjected to no-slip and adiabatic boundary conditions. We account for the streamwise and transverse thermocapillary stresses along menisci. When the latter is sufficiently small, Stokes flow may be assumed. Then, our solution is based upon a conformal map. When, additionally, the ratio of channel height to half of the ridge pitch is of order 1 or larger, an accurate but less cumbersome solution follows from a matched asymptotic expansion. When inertial effects are relevant, the slip length is numerically computed. Setting the thermocapillary stress equal to zero yields the slip length for an adiabatic flow.</jats:p
Fully developed flow through shrouded-fin arrays: exact and asymptotic solutions
No full textThe flow resistance, i.e. friction factor times Reynolds number , of longitudinal-fin heat sinks with or without clearance between a shroud and the tips of the fins is an important parameter in thermal design. This is because it dictates the caloric resistance of the heat sink, i.e. change in bulk temperature of the fluid flowing through it. When there is no clearance and the common and oft-valid assumption of negligible fin thickness is invoked, corresponds to simply that of a rectangular duct. However, with clearance, only numerical results are available as per the well-known study by Sparrow, Baliga and Patankar (ASME J. Heat Transfer, vol. 100, 1978). We develop analytical formulae for for fully developed flow with clearance. The exact solution is provided by an integral formula derived via conformal mappings. Additionally, simple formulae are derived via asymptotic expansions in three cases: (1) the fin spacing is small compared to the fin height and clearance; (2) the clearance is small compared to the fin spacing, which is small compared to the fin height; (3) the same as case (2) but valid for larger clearances. The different asymptotic formulae are compared to the exact formula, and together cover almost the entire relevant parameter range (for fin spacing and clearance) with errors of less than 15 %. A formula for the limiting case of no clearance is shown to be more accurate, for any fin spacing, than a widely used correlation from the literature.</p
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