In a recent Letter (Phys. Rev. Lett. vol 96, 066001 (2006), ref [1]), Choi
and Kim reported slip lengths of a few tens of microns for water on
nanoengineered superhydrophobic surfaces, on the basis of rheometry
(cone-and-plate) measurements. We show that the experimental uncertainty in the
experiment of Ref. [1], expressed in term of slip lengths, lies in the range 20
- 100 micrometers, which is precisely the order of magnitude of the reported
slip lengths. Moreover we point out a systematic bias expected on the
superhydrophobic surfaces. We thus infer that it is not possible to draw out
any conclusion concerning the existence of huge slip lengths in the system
studied by Choi and Kim.Comment: to appear in Physical Review Letter

K. Walters

Lydéric Bocquet

Patrick Tabeling

Sébastien Manneville

English

arXiv

A Comment on the Letter by Chang-Hwan Choi and Chang-Jin Kim, Phys. Rev. Lett. 96, 066001 (2006). The authors of the Letter offer a Reply

BOCQUET, Lyderic

TABELING, Patrick

MANNEVILLE, Sébastien

Oskar Bordeaux

Physical Review Letters

Comment on "Large Slip of Aqueous Liquid Flow over a Nanoengineered Superhydrophobic Surface"

International audienceA Comment on the Letter by Chang-Hwan Choi and Chang-Jin Kim, Phys. Rev. Lett. 96, 066001 (2006). The authors of the Letter offer a Reply

Bocquet, Lyderic

Tabeling, Patrick

Manneville, Sébastien

HAL-ENS-LYON

Comment on ”Large Slip of Aqueous Liquid Flow over aNanoengineered Superhydrophobic Surface”Lyderic Bocquet, Patrick Tabeling, Se´bastien MannevilleTo cite this version:Lyderic Bocquet, Patrick Tabeling, Se´bastien Manneville. Comment on ”Large Slip of Aque-ous Liquid Flow over a Nanoengineered Superhydrophobic Surface”. Physical Review Let-ters, American Physical Society, 2006, 97 (10), pp.109601. <10.1103/PhysRevLett.97.109601>.<ensl-00527167>HAL Id: ensl-00527167https://hal-ens-lyon.archives-ouvertes.fr/ensl-00527167Submitted on 18 Oct 2010HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Comment on “Large Slip of Aqueous Liquid Flow over a NanoengineeredSuperhydrophobic Surface”Lyde´ric Bocquet1, Patrick Tabeling2, Se´bastien Manneville3(1) LPMCN, Universite´ Lyon I,UMR CNRS 5586, Lyon, France(2) PCT, ESPCI, UMR CNRS 7083, Paris, France(3) CRPP, UPR CNRS 8641, Pessac, FranceIn a recent Letter [1], Choi and Kim reported sliplengths of a few tens of microns for water on nanoengi-neered superhydrophobic surfaces, on the basis of rheom-etry (cone-and-plate) measurements. We show that theexperimental uncertainty in the experiment of Ref. [1],expressed in term of slip lengths, lies in the range 20 - 100micrometers, which is precisely the order of magnitude ofthe reported slip lengths. Moreover we point out a sys-tematic bias expected on the superhydrophobic surfaces.We thus infer that it is not possible to draw out any con-clusion concerning the existence of huge slip lengths inthe system studied by Choi and Kim.Choi and Kim performed torque measurements usinga commercial rheometer (AR2000, TA Instruments) witha cone-and-plate geometry. The slip length δ is deducedfrom the correction of the torqueM w.r.t. a reference no-slip value M0 : δ =23θ0R(1−M/M0). M0 =2pi3µΩR3/θ0is the prediction in the absence of slippage; R is thecone radius (≃ 3 cm) and θ0 its opening angle (2◦); µis the viscosity of the liquid; Ω is the rotational veloc-ity. Putting numbers in this expression shows that thereported 20µm slip length for water corresponds to a 3%correction to the (small) reference torque M0 ∼ 5µNm.The authors however claim a 3µm uncertainty on the sliplength, which corresponds to an overall 0.5% errorbar onthe relative deviation of the torque (M0 −M)/M0. Sucha precision is not attainable in the present experiment.To illustrate this uncertainty issue, we have performedbenchmark experiments using an AR2000 rheometer witha smooth, stainless steel cone-and-plate geometry (withthe same radius and cone angle), very close to that ofRef. [1]. This rheometer was calibrated using a referenceNewtonian silicon oil (BR0050CPS, µ = 48.4 mPa s at25◦C), which yielded the expected value to within 0.5%.Then, turning to distilled deionized water at 25◦C, weperformed torque measurements similar to [1] and mea-sured the torque standard deviation ∆M/M with thisliquid, yielding ∆M/M ≃ 1.4% at γ˙ = 150 s−1, up to3.5% at γ˙ = 50 s−1. This is far above the claimed 0.5%uncertainty. If the uncertainties on the filling volumeand on the gap size are included, the global uncertaintyon the measured torque is at least ∆M/M ≃ 3%. Fi-nally, using the expression δ(M) and adding a similaruncertainty on the reference viscosity µ in M0, leads to∆δ/δ ≃ 100-200%, so that ∆δ ∼ 20−40µm for water and∆δ ∼ 50 − 100µm for glycerin. The reported effect aretherefore within uncertainty and the experiment of Ref.[1] should be considered as inconclusive.Another source of difficulties in the interpretation ofthe experiment in Ref [1] is the role of secondary flows.The relevant reynolds number is Re = ρΩR2θ20/µ & 2,and inertial effects should lead to an increase in thetorque up to two percent (M −M0 = 6.10−4Re2 [2]). Inview of the claimed resolution, this correction should bemeasurable in the experiment of Ref. [1] and interpretedas an apparent negative slip length up to ∼ −15µm forthe smooth hydrophilic surfaces. This effect is not de-tected in [1], which furthermore confirms the weaknessin the interpretation of the measurements. At this stage,it is worth pointing out a systematic bias on the super-hydrophobic surfaces. Indeed, for the same liquid vol-ume filling the gap in the cone-and-plate, the meniscusat the edges makes the radius R slightly smaller on thesuper-hydrophobic surface (with very large contact an-gle), w.r.t. the other surfaces with smaller contact angles.The variation inR is predicted to be of the order of a frac-tion of the gap at the border ∆R ∼ −αθ0R (with α . 1).Assuming no-slip at the surfaces, the resulting decreaseof the solid-liquid area leads to a reduction of torque onthe superhydrophobic surfaces, ∆Mcap/M0 ∼ −3αθ0, ofthe order of a few percents. The misinterpretation of thiseffect using Eq. (1) thus erroneously predicts a slippageeffect with a slip length δeff ∼ αθ20R, of the order of afew tens of micrometers.In summary, the experimental uncertainty that we es-timate is comparable to the amplitude of the effect theauthors have observed. Moreover a systematic bias couldbe wrongly interpreted in terms of very large slippage onsuperhydrophobic surfaces. The experiments of Ref. [1]are therefore inconclusive.[1] C.-H. Choi and C Kim, Phys. Rev. Lett. 96 066001 (2006).[2] K. Walters, Rheometry (Chapman Hall, London, 1975).

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Comment on ``Large Slip of Aqueous Liquid Flow over a Nanoengineered
  Superhydrophobic Surface'' by C-H Choi and C Kim

Comment on ``Large Slip of Aqueous Liquid Flow over a Nanoengineered Superhydrophobic Surface'' by C-H Choi and C Kim

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