The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Intermolecular And Surface Forces

流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Journal of Fluid Mechanics创刊50周年

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Philosophical Transactions of the Royal Society of London. for the Year Mdcccxxvii. Part I. Volume Cxvii:355–388, 1827

From a physical perspective, nanofluidics represents an extremely rich domain. It hosts many mechanisms acting on the nanoscale, which combine together or interact with the confinement to generate new phenomena. Superfast flows in carbon nanotubes, nonlinear electrokinetic transport, slippage over smooth surfaces, nanobubble stability, etc. are the most striking phenomena that have been unveiled over the past few years, and some of them are still awaiting an explanation. One may anticipate that new nanofluidic effects will be discovered in the future, but at the moment, the technological barrier is high. Fabrication of nanochannels is most often a tour de force, slow and costly. However, with the accumulation of technological skills along with the use of new nanofluidic materials (like nanotubes), nanofluidics is becoming increasingly accessible to experimentalists. Among the technological challenges faced by the field, fabricating devices mimicking natural nanometric systems, such as aquaporins, ionic pumps or kidney osmotic filtering, seems the most demanding in terms of groundbreaking ideas. Nanoflow characterization remains delicate, although considerable progress has been achieved over the past years. The targeted application of nanofluidics is not only in the field of genomics and membrane science – with disruptive developments to be expected for water purification, desalination, and energy harvesting – but also for oil and gas production from unconventional reservoirs. Today, in view of the markets that are targeted, nanofluidics may well impact the industry more than microfluidics; this would represent an unexpected paradox. These successes rely on using a variety of materials and technologies, using state-of-the-art nanofabrication, or low-tech inexpensive approaches. As a whole, nanofluidics is a fascinating field that is facing considerable challenges today. It possesses a formidable potential and offers much space for creative groundbreaking ideas.

Physics and technological aspects of nanofluidics

We present global heat-transfer and local temperature measurements, in an asymmetric parallelepiped Rayleigh-Benard cell, in which controlled square-studs roughnesses have been added. A global heat transfer enhancement arises when the thickness of the boundary layer matches the height of the roughnesses. The enhanced regime exhibits an increase of the heat transfer scaling. Local temperature measurements have been carried out in the range of parameters where the enhancement of the global heat transfer is observed. They show that the boundary layer at the top of the square-stub roughness is thinner than the boundary layer of a smooth plate, which accounts for most of the heat-transfer enhancement. We also report multistability at long time scales between two enhanced heat-transfer regimes. The flow structure of both regimes is imaged with background-oriented synthetic Schlieren and reveals intermittent bursts of coherent plumes.

https://hal.archives-ouvertes.fr/hal-00920342/document

Thermal boundary layer near roughnesses in turbulent Rayleigh-Bénard convection: Flow structure and multistability

We investigate experimentally the electrokinetic properties of soft nanofluidic channels that consist in soap films with nanometric thickness, covered with charged surfactants. Both the electric and fluidic responses of the system are measured under an applied voltage drop along the film. The electric field is shown to induce an electro-osmotic hydrodynamic flow in the film. However, in contrast to systems confined between solid surfaces, the soft nature of the nanochannel results furthermore in a thickening of the film. This effect accordingly increases the total electro-osmotic flow rate, which behaves nonlinearly with the applied electric field. This behavior is rationalized in terms of an analogy with a Landau-Levich film withdrawn from a reservoir, with the driving velocity identified here with the electro-osmotic one.

/pdf/soft-nanofluidic-transport-in-a-soap-film-37k21qejrg.pdf

Soft nanofluidic transport in a soap film.

Several Rayleigh–Benard experiments in water are performed with smooth or rough boundaries. We present new thermal transfer measurements obtained with large roughness elements arranged in a square lattice. The data are compared to previous data obtained with smaller elements in the same cell (Tisserand et al., Phys. Fluids, vol. 23, 2011). Experiments in the same apparatus without roughness are presented, as reference results, to allow for comparison. In the rough case, several regimes of heat transfer are identified: one similar to the smooth case, an enhanced heat transfer regime characterized by a modification of the Nusselt versus Rayleigh number relation and a third part where the relation can be similar to a smooth one with a corrected prefactor.

/pdf/thermal-transfer-in-rayleigh-benard-cell-with-smooth-or-1delagnkub.pdf

Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and temperature frequency spectra is shown and discussed. In particular, we observe that temperature spectra exhibit an anomalous f^2.5 frequency scaling, likely representing the ubiquitous passive and active scalar behavior of temperature

Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection

In this experimental work, the aim is to understand how turbulent thermal flows are enhanced by the destabilization of the boundary layers. Square-stud roughness elements have been added on the bottom plate of a rectangular Rayleigh–Benard cell in air, to trigger instabilities in the boundary layers. The top plate is kept smooth. The cell proportions are identical to those of the water cell previously operated and described by Salort et al. (Phys. Fluids, vol. 26, 2014, 015112), but six times larger. The very large size of the Barrel of Ilmenau allows detailed velocity fields to be obtained using particle image velocimetry very close to the roughness elements. We found that the flow is quite different at low Rayleigh numbers, where there is no heat-transfer enhancement, and at high Rayleigh numbers where there is a heat-transfer enhancement due to the roughness. Below the transition, the fluid inside the notch, i.e. between the studs, is essentially at rest, though it is slowly recirculating. The velocity profiles on the top of obstacles and in grooves are fairly compatible with those obtained in the smooth case. Above the transition, on the other hand, we observe large incursions of the bulk inside the notch, and the velocity profiles on the top of obstacles are closer to the logarithmic profiles expected in the case of turbulent boundary layers.

/pdf/boundary-layer-structure-in-a-rough-rayleigh-benard-cell-22ckshi2b1.pdf

Olivier Liot

Papers

Thermal boundary layer near roughnesses in turbulent Rayleigh-Bénard convection: Flow structure and multistability

Soft nanofluidic transport in a soap film.

Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection

Boundary layer structure in a rough Rayleigh-Bénard cell filled with air