skip to main content

Title: Ultrahigh evaporative heat transfer measured locally in submicron water films

Thin film evaporation is a widely-used thermal management solution for micro/nano-devices with high energy densities. Local measurements of the evaporation rate at a liquid-vapor interface, however, are limited. We present a continuous profile of the evaporation heat transfer coefficient ($$h_{\text {evap}}$$hevap) in the submicron thin film region of a water meniscus obtained through local measurements interpreted by a machine learned surrogate of the physical system. Frequency domain thermoreflectance (FDTR), a non-contact laser-based method with micrometer lateral resolution, is used to induce and measure the meniscus evaporation. A neural network is then trained using finite element simulations to extract the$$h_{\text {evap}}$$hevapprofile from the FDTR data. For a substrate superheat of 20 K, the maximum$$h_{\text {evap}}$$hevapis$$1.0_{-0.3}^{+0.5}$$1.0-0.3+0.5 MW/$$\text {m}^2$$m2-K at a film thickness of$$15_{-3}^{+29}$$15-3+29 nm. This ultrahigh$$h_{\text {evap}}$$hevapvalue is two orders of magnitude larger than the heat transfer coefficient for single-phase forced convection or evaporation from a bulk liquid. Under the assumption of constant wall temperature, our profiles of$$h_{\text {evap}}$$hevapand meniscus thickness suggest that 62% of the heat transfer comes from the region lying 0.1–1 μm from the meniscus edge, whereas just 29% comes from the next 100 μm.

; ; ; ;
Publication Date:
Journal Name:
Scientific Reports
Nature Publishing Group
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$(107Re103). Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$Re=v0x0ν, wherev0corresponds to the maximum wetting speed on a flat, dry surface andx0is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv0andx0measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v02m/s,25µmx028µm), viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v00.3m/s,18.6µmx038.6µm)and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v01.2m/s,11.8µmx033.3µm).

  2. Abstract

    We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu $$BDνat nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$Nf=2+1flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$a0.15fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$|Vcb|. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$Vcb=(38.40±0.68th±0.34exp±0.18EM)×10-3. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$χ2/dof=126/84, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is inmore »agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict$$R(D^*) = 0.265 \pm 0.013$$R(D)=0.265±0.013, which confirms the current tension between theory and experiment.

    « less
  3. Abstract

    It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.arXiv:2010.09793) that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scenarios such Green function estimates are equivalent to the uniform rectifiability of a set. The present paper tackles a strong analogue of these results, starting with the “flagship degenerate operators on sets with lower dimensional boundaries. We consider the elliptic operators$$L_{\beta ,\gamma } =- {\text {div}}D^{d+1+\gamma -n} \nabla $$Lβ,γ=-divDd+1+γ-nassociated to a domain$$\Omega \subset {\mathbb {R}}^n$$ΩRnwith a uniformly rectifiable boundary$$\Gamma $$Γof dimension$$d < n-1$$d<n-1, the now usual distance to the boundary$$D = D_\beta $$D=Dβgiven by$$D_\beta (X)^{-\beta } = \int _{\Gamma } |X-y|^{-d-\beta } d\sigma (y)$$Dβ(X)-β=Γ|X-y|-d-βdσ(y)for$$X \in \Omega $$XΩ, where$$\beta >0$$β>0and$$\gamma \in (-1,1)$$γ(-1,1). In this paper we show that the Green functionGfor$$L_{\beta ,\gamma }$$Lβ,γ, with pole at infinity, is well approximated by multiples of$$D^{1-\gamma }$$D1-γ, in the sense that the function$$\big | D\nabla \big (\ln \big ( \frac{G}{D^{1-\gamma }} \big )\big )\big |^2$$|D(ln(GD1-γ))|2satisfies a Carleson measure estimate on$$\Omega $$Ω. We underline that the strong and the weak results are different in nature and, of course, at the levelmore »of the proofs: the latter extensively used compactness arguments, while the present paper relies on some intricate integration by parts and the properties of the “magical distance function from David et al. (Duke Math J, to appear).

    « less
  4. Abstract

    We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble$$\hbox {CLE}_{\kappa '}$$CLEκfor$$\kappa '$$κin (4, 8) that is drawn on an independent$$\gamma $$γ-LQG surface for$$\gamma ^2=16/\kappa '$$γ2=16/κ. The results are similar in flavor to the ones from our companion paper dealing with$$\hbox {CLE}_{\kappa }$$CLEκfor$$\kappa $$κin (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\hbox {CLE}_{\kappa '}$$CLEκin terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a$$\hbox {CLE}_{\kappa '}$$CLEκindependently into two colors with respective probabilitiespand$$1-p$$1-p. This description was complete up to one missing parameter$$\rho $$ρ. The results of the present paper about CLE on LQG allow us to determine its value in terms ofpand$$\kappa '$$κ. It shows in particular that$$\hbox {CLE}_{\kappa '}$$CLEκand$$\hbox {CLE}_{16/\kappa '}$$CLE16/κare related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {FK}_q$$FKqpercolation and theq-state Potts model (which makes sense evenmore »for non-integerqbetween 1 and 4) if and only if$$q=4\cos ^2(4\pi / \kappa ')$$q=4cos2(4π/κ). This provides further evidence for the long-standing belief that$$\hbox {CLE}_{\kappa '}$$CLEκand$$\hbox {CLE}_{16/\kappa '}$$CLE16/κrepresent the scaling limits of$$\hbox {FK}_q$$FKqpercolation and theq-Potts model whenqand$$\kappa '$$κare related in this way. Another consequence of the formula for$$\rho (p,\kappa ')$$ρ(p,κ)is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.

    « less
  5. Abstract

    We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$2O and D$$_2$$2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$ρ(T), isothermal compressibility$$\kappa _T(T)$$κT(T), and self-diffusion coefficientsD(T) of H$$_2$$2O and D$$_2$$2O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$CP(T)obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$2O and D$$_2$$2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$2O and D$$_2$$2O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$2O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$Pc=167±9 MPa,$$T_c = 159 \pm 6$$Tc=159±6 K, and$$\rho _c = 1.02 \pm 0.01$$ρc=1.02±0.01 g/cm$$^3$$3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$2O is estimated to be$$P_c = 176 \pm 4$$Pc=176±4 MPa,$$T_c = 177 \pm 2$$Tc=177±2 K, and$$\rho _c = 1.13 \pm 0.01$$ρc=1.13±0.01 g/cm$$^3$$3. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effectsmore »(i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water,$$P_c = 203 \pm 4$$Pc=203±4 MPa,$$T_c = 175 \pm 2$$Tc=175±2 K, and$$\rho _c = 1.03 \pm 0.01$$ρc=1.03±0.01 g/cm$$^3$$3). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$T_c$$Tcfor D$$_2$$2O and, particularly, H$$_2$$2O suggest that improved water models are needed for the study of supercooled water.

    « less