Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary

Wu, Yonghong; Wiwatanapataphee, Benchawan; Hu, Mao-Bin

doi:10.1016/j.physa.2008.06.043

Cited by 26 publications

(16 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This study provides pressure drop data for pulsatile flow of water in rectangular microchannel. This is among the first such experimental study at the microscales, although some theoretical results with gas flow in microchannel (involving slip at the wall) are available (Chakraborty and Bhalla 2007;Wu et al 2008). Some very recent theoretical studies (Brereton 2009;Haddad et al 2010) have revisited the problem.…”

Section: Introductionmentioning

confidence: 99%

Measurement and modeling of pulsatile flow in microchannel

Tikekar

Singh

Agrawal

2010

Microfluid Nanofluid

View full text Add to dashboard Cite

An experimental study of pulsatile flow in microchannel is reported in this paper. Such a study is important because time-varying flows are frequently encountered in microdevices. The hydraulic diameter of the microchannel is 144 lm and deionized water is the working fluid. The pressure drop across the microchannel as a function of time is recorded, from which the average and r.m.s. pressure drops are obtained. The experiments have been performed in the quasi-steady flow regime for a wide range of flow rate, frequency of pulsations, and duty cycle. The results suggest that the pressure with pulsations lies between the minimum and maximum steady state pressure values. The average pressure drop with pulsation is approximately linear with respect to the flow rate. The theoretical expression for pressure has also been derived wherever possible and the experimental data is found to lie below the corresponding theoretical values. The difference with respect to the theoretical value increases with an increase in frequency and a decrease in flow rate, with a maximum difference of 32.7%. This is attributed to the small size of the microchannel. An increase in frequency of square waveform leads to a larger reduction in pressure drop as compared to rectangular waveform, irrespective of the duty cycle. The results can be interpreted with the help of a firstorder model proposed here; the model results are found to compare well against the experimental results. A correlation for friction factor in terms of the other non-dimensional governing parameters is also proposed. Experimental study of mass-driven pulsatile flow in microchannel is being conducted for the first time at these scales and the results are of both fundamental and practical importance. Keywords Microchannel Á Pulsatile flow Á Microfluidics Á Flow modeling Á Microscale flow Á Pressure drop List of symbols A Area of cross-section of channel (m 2 ) C Capacitance (F) D h Hydraulic diameter of the channel (=4A/perimeter) (m) f Average friction factor pD h 1 2 qv 2 L À Á f rms Friction factor r.m.s p rms D h 1 2 qv 2 L À Á F Dimensionless form of frequency ¼ D h ðt N þt F Þa i Current (A) L Length of the microchannel (m) m F Minimum flow rate (kg/s) m N Maximum flow rate (kg/s) p Pressure (Pa) p Time-averaged pressure drop (Pa) p rms Root mean square value of the pressure drop (Pa) Q Volumetric flow rate (m 3 /s) R Resistance (ohm) Re Reynolds number ¼ vD h a À Á Re N On-time Reynolds number ¼ v N D h a À Á t Time (s) t F Off-time. Time for which minimum flow (m F ) occurs (s) t N On time. Time for which maximum flow (m N ) occurs (s) T Duty cycle or ratio of on-time to off-time (t N /t F ) u Streamwise velocity (m/s) v Time-averaged velocity of the flow over the crosssection (m/s), normalized voltage V Voltage (V) v F Average velocity over the cross-section, during the state of minimum flow (m/s) v N Average velocity over the cross-section, during the state of maximum flow (m/s) x Streamwise coordinate (m) a Kinematic viscosity of the fluid (m 2 /s) b Womersley para...

show abstract

Section: Introductionmentioning

confidence: 99%

Measurement and modeling of pulsatile flow in microchannel

Tikekar

Singh

Agrawal

2010

Microfluid Nanofluid

View full text Add to dashboard Cite

show abstract

“…For finite s , as the radius of tube decreases the importance of this term increases. Consequently, as discussed by Wu et al [2008], the implementation of slip boundary conditions adds a rigid body translation term to the axial velocity. The slip solution becomes a superposition of the no-slip solution and rigid body translation.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…Fluid flows through rigid microtubes have been studied in the slip flow regime [Sbragaglia and Prosperetti, 2007], and this study determined that an effective Navier slip boundary condition is valid. Other studies have investigated steady-state [Matthews and Hill, 2007] and transient [Wu et al, 2008] flows through rigid microtubes with slip boundary conditions. Wu et al [2008] showed that the influence of boundaryslip on the flow behavior is different for different types of pressure gradients driving the flow.…”

Section: Introductionmentioning

confidence: 99%

“…Other studies have investigated steady-state [Matthews and Hill, 2007] and transient [Wu et al, 2008] flows through rigid microtubes with slip boundary conditions. Wu et al [2008] showed that the influence of boundaryslip on the flow behavior is different for different types of pressure gradients driving the flow. Since there is no wave motion in the rigid tubes, the fluids oscillate in the bulk, and hence the effect of wave propagation was not modeled in those studies.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of Pulsatile Flows Through Elastic Microtubes

San

Staples

2012

Int. J. Appl. Mechanics

View full text Add to dashboard Cite

We investigate the dynamics of pressure driven transient flows of incompressible Newtonian fluids through circular microtubes having thin elastic walls under the longwavelength and small deformation assumptions, which are valid for many industrial and biological processes. An analytical solution of the coupled fluid and solid equations is found using Navier slip boundary conditions and is shown to include some existing Womersley solutions as limiting cases. The effect of the slip length at the fluid-solid interface is analyzed for oscillatory pressure gradients using a range of slip ratio and frequency parameters. The solutions for elastic and rigid walls are compared for the cases with and without slip boundary conditions for a broad range of the relevant parameters. It is shown that the elastic behavior of the microtube couples nonlinearly with the slip velocity, which greatly enhances the achievable flow rate and pumping efficacy compared to the inelastic case. In addition, it is observed that increasing the slip length produces less shear stress, which is consistent with the nearly frictionless interfaces observed in many microscale experiments.

show abstract

“…Bao et al investigated the flow and heat transfer in micro Couette and Poiseuille flow using the Burnett simulation method [12][13][14]. Wu et al studied the pressure driven transient flow of an incompressible Newtonian fluid in micro tubes with a Navier slip boundary condition [15]. Furthermore, the velocity slip of the lubrication film was experimentally investigated by Yuan et al [16], Miao et al [17], Zhou et al [18] and Wu et al [19], including its existence in sliding bearings.…”

mentioning

confidence: 99%

Boundary velocity slip of pressure driven liquid flow in a micron pipe

2011

View full text Add to dashboard Cite

The velocity slip of gas flow in a micron channel has been widely recognized. For pressure driven liquid flow in a macro pipe, the minute velocity slip at the wall boundary is usually neglected. With a decreasing scale in the cross section of the flow passage, the effect of velocity slip on flow and heat transfer behaviors becomes progressively more noticeable. Based on the three Hamaker homogeneous material hypotheses, the method for calculating the acting force between the solid and liquid molecular groups is established. By analyzing the forces exerted on the liquid group near the pipe wall, it is found that the active force arising from the rough solid wall can provide the component force to resist the shearing force and keep the liquid group immobile. Based on this a velocity slip criterion is proposed. Considering the force balance of a slipping liquid group, the frictional force caused by the solid wall can be obtained and then the velocity of the liquid group can be calculated using the derived coefficient of friction. The investigation reveals that, in a micron pipe, a small velocity slip may occur when the flow pressure gradient is relatively large, and will cause errors in the pipe flow estimates. velocity slip, pressure driven, liquid molecular group, coefficient of friction Citation:Zhou J F, Gu B Q, Shao C L. Boundary velocity slip of pressure driven liquid flow in a micron pipe.

show abstract

Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary

Cited by 26 publications

References 38 publications

Measurement and modeling of pulsatile flow in microchannel

Measurement and modeling of pulsatile flow in microchannel

Dynamics of Pulsatile Flows Through Elastic Microtubes

Boundary velocity slip of pressure driven liquid flow in a micron pipe

Contact Info

Product

Resources

About