## Publications

21 results found

Kirk TL, Lewis-Douglas A, Howey D,
et al., 2023, Nonlinear Electrochemical Impedance Spectroscopy for Lithium-Ion Battery Model Parameterization, *JOURNAL OF THE ELECTROCHEMICAL SOCIETY*, Vol: 170, ISSN: 0013-4651

Tomlin RJJ, Roy T, Kirk TLL,
et al., 2022, Impedance Response of Ionic Liquids in Long Slit Pores, *JOURNAL OF THE ELECTROCHEMICAL SOCIETY*, Vol: 169, ISSN: 0013-4651

Kane D, Hodes M, Bazant MZ, et al., 2022, Asymptotic Nusselt numbers for internal flow in the Cassie state

We consider laminar, fully-developed, Poiseuille flows of liquid in theCassie state through diabatic, parallel-plate microchannels symmetricallytextured with isoflux ridges. Through the use of matched asymptotic expansionswe analytically develop expressions for (apparent hydrodynamic) slip lengthsand variously-defined Nusselt numbers. Our small parameter ($\epsilon$) is thepitch of the ridges divided by the height of the microchannel. When the ridgesare oriented parallel to the flow, we quantify the error in the Nusselt numberexpressions in the literature and provide a new closed-form result. The latteris accurate to $O\left(\epsilon^2\right)$ and valid for any solid (ridge)fraction, whereas those in the current literature are accurate to$O\left(\epsilon^1\right)$ and breakdown in the important limit when solidfraction approaches zero. When the ridges are oriented transverse to the(periodically fully-developed) flow, the error associated with neglectinginertial effects in the slip length is shown to be$O\left(\epsilon^3\mathrm{Re}\right)$, where $\mathrm{Re}$ is the channel-scaleReynolds number based on its hydraulic diameter. The corresponding Nusseltnumber expressions are new and their accuracy is shown to be dependent onReynolds number, Peclet number and Prandtl number in addition to $\epsilon$.Manipulating the solution to the inner temperature problem encountered in thevicinity of the ridges shows that classic results for thermal spreadingresistance are better expressed in terms of polylogarithm functions.

Couto LD, Drummond R, Zhang D, et al., 2022, Identifiability of Lithium-Ion Battery Electrolyte Dynamics, Pages: 1087-1093, ISSN: 0743-1619

The growing need for improved battery fast charging algorithms and management systems is pushing forward the development of high-fidelity electrochemical models of cells. Critical to the accuracy of these models is their parameterisation, however this challenge remains unresolved, both in terms of theoretical analysis and practical implementation. This paper develops a framework to analyse from impedance measurements the identifiability of electrolyte dynamics-a subcomponent of a general Li-ion model that is key to enabling accurate fast charging simulations. By assuming that the electrolyte volume fractions in the electrode and separator regions are equal, an analytic expression for the impedance function of the electrolyte dynamics is obtained, and this can be tested for structural identifiability. It is shown that the only parameters of the electrolyte model that may be identified are the diffusion time scale and a geometric coupling parameter. Simulations highlight the identifiability issues of electrolyte dynamics (relating to symmetric cells) and explain how the electrolyte parameters might be identified.

Kirk TL, Evans J, Please CP,
et al., 2022, MODELING ELECTRODE HETEROGENEITY IN LITHIUM-ION BATTERIES: UNIMODAL AND BIMODAL PARTICLE-SIZE DISTRIBUTIONS, *SIAM Journal on Applied Mathematics*, Vol: 82, Pages: 625-653, ISSN: 0036-1399

In mathematical models of lithium-ion batteries, the highly heterogeneous porous electrodes are frequently approximated as comprising spherical particles of uniform size, leading to the commonly used single-particle model (SPM) when transport in the electrolyte is assumed to be fast. Here electrode heterogeneity is modeled by extending this to a distribution of particle sizes. Unimodal and bimodal particle-size distributions (PSD) are considered. For a unimodal PSD, the effect of the spread of the distribution on the cell dynamics is investigated, and choice of effective particle radius when approximating by an SPM assessed. Asymptotic techniques are used to derive a correction to the SPM valid for narrow, but realistic, PSDs. In addition, it is shown that the heterogeneous internal states of all particles (relevant when modeling degradation, for example) can be efficiently computed after the fact. For a bimodal PSD, the results are well approximated by a double-particle model (DPM), with one size representing each mode. Results for lithium iron phosphate with a bimodal PSD show that the DPM captures an experimentally observed double plateau in the discharge curve, suggesting it is entirely due to bimodality.

Kirk TL, Please CP, Jon Chapman S, 2021, Physical Modelling of the Slow Voltage Relaxation Phenomenon in Lithium-Ion Batteries, *JOURNAL OF THE ELECTROCHEMICAL SOCIETY*, Vol: 168, ISSN: 0013-4651

- Author Web Link
- Cite
- Citations: 7

Yariv E, Kirk TL, 2021, Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles, *IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*, Vol: 86, Pages: 490-501, ISSN: 0272-4960

A 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 \sigma T, 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 2c is small compared with the array period 2l. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation \begin{align} \pi \frac{G\sigmaT c^2}{\mu l} I(\alpha), \end{align∗}wherein G is the applied-gradient magnitude, \mu is the liquid viscosity and I(\alpha) , a non-monotonic function of the protrusion angle \alpha , 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. \end{align}

Alexander JP, Kirk TL, Papageorgiou DT, 2020, Stability of falling liquid films on flexible substrates, *Journal of Fluid Mechanics*, Vol: 900, Pages: A40-1-A40-33, ISSN: 0022-1120

The linear stability of a liquid film falling down an inclined flexible plane under the influence of gravity is investigated using analytical and computational techniques. A general model for the flexible substrate is used leading to a modified Orr–Sommerfeld problem addressed numerically using a Chebyshev tau decomposition. Asymptotic limits of long waves and small Reynolds numbers are addressed analytically and linked to the computations. For long waves, the flexibility has a destabilising effect, where the critical Reynolds number decreases with decreasing stiffness, even destabilising Stokes flow for sufficiently small stiffness. To pursue this further, a Stokes flow approximation was considered, which confirmed the long-wave results, but also revealed a short wave instability not captured by the long-wave expansions. Increasing the surface tension has little effect on these instabilities and so they were characterised as wall modes. Wider exploration revealed mode switching in the dispersion relation, with the wall and surface mode swapping characteristics for higher wavenumbers. The zero-Reynolds-number results demonstrate that the long-wave limit is not sufficient to determine instabilities so the numerical solution for arbitrary wavenumbers was sought. A Chebyshev tau spectral method was implemented and verified against analytical solutions. Short wave wall instabilities persist at larger Reynolds numbers and destabilisation of all Reynolds numbers is achievable by increasing the wall flexibility, however increasing the stiffness reverts back to the rigid wall limit. An energy decomposition analysis is presented and used to identify the salient instability mechanisms and link them to their physical origin.

Kirk T, Karamanis G, Crowdy D,
et al., 2020, Thermocapillary stress and meniscus curvature effects on slip lengths in ridged microchannels, *Journal of Fluid Mechanics*, Vol: 894, ISSN: 0022-1120

Pressure-driven flow in the presence of heat transfer through a microchannel patterned with parallel ridges is considered. The coupled effects of curvature and thermocapillary stress along the menisci are captured. Streamwise and transverse thermocapillary stresses along menisci cause the flow to be three-dimensional, but when the Reynolds number based on the transverse flow is small the streamwise and transverse flows decouple. In this limit, we solve the streamwise flow problem, i.e. that in the direction parallel to the ridges, using a suite of asymptotic limits and techniques – each previously shown to have wide ranges of validity thereby extending results by Hodes et al. (J. Fluid Mech., vol. 814, 2017, pp. 301–324) for a flat meniscus. First, we take the small-ridge-period limit, and then we account for the curvature of the menisci with two further complementary limits: (i) small meniscus curvature using boundary perturbation; (ii) arbitrary meniscus curvature but for small slip (or cavity) fractions using conformal mapping and the Poisson integral formula. Heating and cooling the liquid always degrade and enhance (apparent) slip, respectively, but their effect is greatest for large meniscus protrusions, with positive protrusion (into the liquid) being the most sensitive. For strong enough heating the solutions become complex, suggesting instability, with large positive protrusions transitioning first.

Mayer M, Hodes M, Kirk T,
et al., 2019, Effect of surface curvature on contact resistance between cylinders, *Journal of Heat Transfer*, Vol: 141, ISSN: 0022-1481

Due to the microscopic roughness of contacting materials, an additional thermal resistance arises from the constriction and spreading of heat near contact spots. Predictive models for contact resistance typically consider abutting semi-infinite cylinders subjected to an adiabatic boundary condition along their outer radius. At the nominal plane of contact, an isothermal and circular contact spot is surrounded by an adiabatic annulus and the far-field boundary condition is one of constant heat flux. However, cylinders with flat bases do not mimic the geometry of contacts. To remedy this, we perturb the geometry of the problem such that, in cross section, the circular contact is surrounded by an adiabatic arc. When the curvature of this arc is small, we employ a series solution for the leading-order (flat base) problem. Then, Green's second identity is used to compute the increase in spreading resistance in a single cylinder, and thus the contact resistance for abutting ones, without fully resolving the temperature field. Complementary numerical results for contact resistance span the full range of contact fraction and protrusion angle of the arc. The results suggest as much as a 10–15% increase in contact resistance for realistic contact fraction and asperity slopes. When the protrusion angle is negative, the decrease in spreading resistance for a single cylinder is also provided.

Game S, Hodes M, Kirk T,
et al., 2018, Nusselt Numbers for Poiseuille Flow Over Isoflux Parallel Ridges for Arbitrary Meniscus Curvature, *JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME*, Vol: 140, ISSN: 0022-1481

- Author Web Link
- Cite
- Citations: 9

Crowdy D, Hodes M, Kirk T, 2018, Spreading and contact resistance formulae capturing boundary curvature and contact distribution effects, *Journal of Heat Transfer*, Vol: 140, ISSN: 0022-1481

There is a substantial and growing body of literature which solves Laplace's equation governing the velocity field for a linear-shear flow of liquid in the unwetted (Cassie) state over a superhydrophobic surface. Usually, no-slip and shear-free boundary conditions are applied at liquid–solid interfaces and liquid–gas ones (menisci), respectively. When the menisci are curved, the liquid is said to flow over a “bubble mattress.” We show that the dimensionless apparent hydrodynamic slip length available from studies of such surfaces is equivalent to (i) the dimensionless spreading resistance for a flat, isothermal heat source flanked by arc-shaped adiabatic boundaries and (ii) the dimensionless thermal contact resistance between symmetric mating surfaces with flat contacts flanked by arc-shaped adiabatic boundaries. This is important because real surfaces are rough rather than smooth. Furthermore, we demonstrate that this observation provides a significant source of new and explicit results on spreading and contact resistances. Significantly, the results presented accommodate arbitrary solid-to-solid contact fraction and arc geometry in the contact resistance problem for the first time. We also provide formulae for the case when each period window includes a finite number of no-slip (or isothermal) and shear free (or adiabatic) regions and extend them to the case when the latter are weakly curved. Finally, we discuss other areas of mathematical physics to which our results are directly relevant.

Karamanis G, Hodes M, Kirk T,
et al., 2018, Solution of the Extended Graetz-Nusselt Problem for Liquid Flow Over Isothermal Parallel Ridges, *JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME*, Vol: 140, ISSN: 0022-1481

Kirk TL, 2018, Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci, *Journal of Fluid Mechanics*, Vol: 839, Pages: R31-R312, ISSN: 0022-1120

This 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.

Kadoko J, Karamanis G, Kirk T,
et al., 2017, One-Dimensional Analysis of Gas Diffusion-Induced Cassie to Wenzel State Transition, *JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME*, Vol: 139, ISSN: 0022-1481

- Author Web Link
- Cite
- Citations: 5

Karamanis G, Hodes M, Kirk T,
et al., 2017, Solution of the Graetz-Nusselt Problem for Liquid Flow Over Isothermal Parallel Ridges, *JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME*, Vol: 139, ISSN: 0022-1481

- Author Web Link
- Cite
- Citations: 4

Hodes M, Kirk TL, Karamanis G,
et al., 2017, Effect of thermocapillary stress on slip length for a channel textured with parallel ridges, *JOURNAL OF FLUID MECHANICS*, Vol: 814, Pages: 301-324, ISSN: 0022-1120

- Author Web Link
- Cite
- Citations: 12

Kirk TL, Hodes M, Papageorgiou DT, 2016, Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature, *Journal of Fluid Mechanics*, Vol: 811, Pages: 315-349, ISSN: 1469-7645

We 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.

Lam LS, Hodes M, Karamanis G,
et al., 2016, Effect of Meniscus Curvature on Apparent Thermal Slip, *JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME*, Vol: 138, ISSN: 0022-1481

- Author Web Link
- Cite
- Citations: 10

Karamanis G, Hodes M, Kirk T, et al., 2016, Nusselt Numbers for Fully-Developed Flow Between Parallel Plates with One Plate Textured with Isothermal Parallel Ridges, ASME Summer Heat Transfer Conference, Publisher: AMER SOC MECHANICAL ENGINEERS

Kadoko J, Karamanis G, Kirk T, et al., 2016, ANALYSIS OF GAS DIFFUSION-INDUCED CASSIE TO WENZEL STATE TRANSITION ON A STRUCTURED SURFACE, ASME Summer Heat Transfer Conference, Publisher: AMER SOC MECHANICAL ENGINEERS

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.