A review on slip boundary conditions at the nanoscale: recent development and applications

• Ruifei Wang,
• Jin Chai,
• Bobo Luo,
• Xiong Liu,
• Jianting Zhang,
• Min Wu,
• Mingdan Wei and
• Zhuanyue Ma

Beilstein J. Nanotechnol. 2021, 12, 1237–1251, doi:10.3762/bjnano.12.91

• slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists

• and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the

• effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed. Keywords: boundary condition; interfacial properties; nanofluidics; slip length; unconventional

Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet

• Santoshi Misra and
• Govardhan Kamatam

Beilstein J. Nanotechnol. 2020, 11, 976–990, doi:10.3762/bjnano.11.82

• proportional to the local sheet stress, and l is the slip length constant. The similarity transformations The similarity transformations to solve the governing equations are as follows: By substituting the similarity transformations in Equation 9 into the governing boundary layer Equations 1–4 they reduce to

Effects of surface charge and boundary slip on time-periodic pressure-driven flow and electrokinetic energy conversion in a nanotube

• Mandula Buren,
• Yongjun Jian,
• Yingchun Zhao,
• Long Chang and
• Quansheng Liu

Beilstein J. Nanotechnol. 2019, 10, 1628–1635, doi:10.3762/bjnano.10.158

• Economics, Hohhot, China 10.3762/bjnano.10.158 Abstract Time-periodic pressure-driven slip flow and electrokinetic energy conversion efficiency in a nanotube are studied analytically. The slip length depends on the surface charge density. Electric potential, velocity and streaming electric field are

• significant because the ratio between slip length and channel height becomes considerable large. For example, the velocity distribution for Stokes slip flow through a circular tube [11][12] is where a is the radius of the circular tube and b0 is the Navier slip length. The last term 2b0/a becomes considerable

• electrokinetic effect and boundary slip condition. Goswami and Chakraborty [17] investigated electrokinetic energy conversion through streaming effects in time-periodic pressure-driven nanochannel flows with boundary slip. In the above mentioned references [11][12][13][14][15][16][17], the slip length is

Friction force microscopy of tribochemistry and interfacial ageing for the SiO_x/Si/Au system

• Christiane Petzold,
• Marcus Koch and
• Roland Bennewitz

Beilstein J. Nanotechnol. 2018, 9, 1647–1658, doi:10.3762/bjnano.9.157

• irregularities were likely caused by the nanoscale topography of the oxide surface. Patterns with larger characteristic slip length and signs of stronger tip–surface interactions were recently reported for similar tip–surface pairings at low pressure [22]. The difference between the observations could be caused

Optimal fractal tree-like microchannel networks with slip for laminar-flow-modified Murray’s law

• Dalei Jing,
• Shiyu Song,
• Yunlu Pan and
• Xiaoming Wang

Beilstein J. Nanotechnol. 2018, 9, 482–489, doi:10.3762/bjnano.9.46

• the fractal tree-like microchannel network to achieve the minimum hydraulic resistance. The optimal diameter ratio to achieve minimum hydraulic resistance is not only dependent on the branching number, as stated by Murray’s law, but also dependent on the slip length, the level number, the length ratio

• between the daughter channel and the parent channel, and the diameter of the channel. The optimal diameter ratio decreases with the increasing slip length, the increasing level number and the increasing length ratio between the daughter channel and the parent channel, and decreases with decreasing channel

• diameter. These complicated relations were found to become relaxed and simplified to Murray’s law when the ratio between the slip length and the diameter of the channel is small enough. Keywords: fractal tree-like microchannel networks; hydraulic resistance; Murray’s law; slip; Introduction For the

Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol

• Yifan Li,
• Yunlu Pan and
• Xuezeng Zhao

Beilstein J. Nanotechnol. 2017, 8, 2504–2514, doi:10.3762/bjnano.8.250

• affect the effective value of slip length in measurements. Moreover, there are no studies on the effect of roughness on slip at interfaces between oil and superoleophilic/superoleophobic surfaces. A theoretical description of the real surface roughness is yet to be found. Results show that the effective

• slip length is negative and decreases with an increasing root mean squared (RMS) roughness of surfaces, as the increasing roughness enhances the area with discontinuous slip at the solid–liquid interface. The underlying mechanisms are analyzed. The amplitude parameters of surface roughness could

• is not zero. There is a relative motion that can be expressed by the so-called slip length [2]. Previous studies have shown that the presence of boundary slip leads to lower drag for the fluid flow in micro/nanochannels [3][4][5]. Boundary slip has been studied experimentally and theoretically on

Electroviscous effect on fluid drag in a microchannel with large zeta potential

• Dalei Jing and
• Bharat Bhushan

Beilstein J. Nanotechnol. 2015, 6, 2207–2216, doi:10.3762/bjnano.6.226

• EDL is first analytically solved. Then, the modified Navier–Stokes equation for the flow considering the effect of surface charge on the electrical conductivity of the electrolyte and slip length is analytically solved. This analysis is used to study the effect of non-overlapping EDL with large zeta

• the channel wall and the fast decay of electrical potential in the EDL when the zeta potential is large enough. Keywords: electroviscous effect; microchannels; pressure-driven flow; slip length; zeta potential; Introduction With the development of advanced fabrication techniques, micro/nano electro

• deionized water and saline solutions using the colloidal probe atomic force microscopy technique. They also found that an increasing surface charge density results in a decreasing slip length. Thus, the coupling between the surface charge and slip should be considered when study the combined effect of EDL

Stick–slip behaviour on Au(111) with adsorption of copper and sulfate

• Nikolay Podgaynyy,
• Sabine Wezisla,
• Christoph Molls,
• Shahid Iqbal and
• Helmut Baltruschat

Beilstein J. Nanotechnol. 2015, 6, 820–830, doi:10.3762/bjnano.6.85

• monolayer is given in Figure 9. The friction coefficient changes from 0.12 to 0.5 at a normal load of approximately 70 nN. This change corresponds to change in friction coefficient presented on Figure 3a. This transition in friction coefficient goes along with a change in slip length, as indicated by the

The study of surface wetting, nanobubbles and boundary slip with an applied voltage: A review

• Yunlu Pan,
• Bharat Bhushan and
• Xuezeng Zhao

Beilstein J. Nanotechnol. 2014, 5, 1042–1065, doi:10.3762/bjnano.5.117

• this review, the influence of an applied voltage on the surface wettability, nanobubbles, surface charge density and slip length are discussed. The contact angle (CA) and contact angle hysteresis (CAH) of a droplet of deionized (DI) water on a hydrophobic polystyrene (PS) surface were measured with

• applied direct current (DC) and alternating current (AC) voltages. The nanobubbles in DI water and three kinds of saline solution on a PS surface were imaged when a voltage was applied. The influence of the surface charge density on the nanobubbles was analyzed. Then the slip length and the electrostatic

• , boundary slip and the drag of liquid flow are summarized. With a smaller surface charge density which could be achieved by applying a voltage on the surface, larger and fewer nanobubbles, a larger slip length and a smaller drag of liquid flow could be found. Keywords: atomic force microscopy; boundary

Biomimetics inspired surfaces for drag reduction and oleophobicity/philicity

• Bharat Bhushan

Beilstein J. Nanotechnol. 2011, 2, 66–84, doi:10.3762/bjnano.2.9

• degree of boundary slip at the solid–liquid interface is characterized by a slip length. The slip length b is defined as the length of the vertical intercept along the axis orthogonal to the interface when a tangent line is drawn along the velocity profile at the interface (Figure 2, right). Recent

• and turbulent flows [21]. Model for calculation of pressure drop and slip length The pressure drop Δp of an incompressible fluid flow between two points along the channel of thickness H, width W, and length L for a hydrophilic flat surface can be calculated by [55] where ρ is the fluid density, V is

• of the friction factor for turbulent flow in a rectangular channel, Jones [56] developed an improved equivalent diameter, De = 64DH/k, thus the friction factor for turbulent flow can be modified as Next, we present an analysis to calculate slip length in laminar flow. Using the Navier slip boundary