Electroviscous effect and convective heat transfer of pressure-driven flow through microtubes with surface charge-dependent slip
Introduction
Micro/nanofluidic systems have been widely used in various fields including lab-on-a-chip for bio-/medical analysis [1], [2], [3], cooling of micro/nanoelectronic devices[1], [2], delivery of drug in micro/nano scale [2], and micro/nano heat exchangers [1], [2], [4] in recent decades. Nevertheless, the complete understanding of the fundamental physical mechanisms, which can effectively promote the design and application of these micro/nanofluidic systems, is still a huge challenge. Among these physical mechanisms, the fluidic transportation and heat transfer in micro/nanofluidic systems have inspired wide scientific attentions. It is experimentally and theoretically found that the fluidic transportation and heat transfer in the micro/nanoscale deviate significantly from those in macroscale. The interfacial properties, such as surface charge [5], [6], [7], [8], nanobubbles [9], [10], boundary slip [11], [12] and surface texture and roughness [13], have been widely studied to explain the derivation of fluidic transportation and heat transfer in the micro/nanoscale and in the macroscale. The present work focuses on the effect of surface charge and boundary slip on the fluid flow and convective heat transfer in the micro/nanoscale.
In many cases of a solid contacting with an electrolyte, the solid–liquid interface develops surface charge and becomes charged spontaneously [7], [14], [15], [16]. The charged interface then changes the distribution of charged ions in the electrolyte by electrostatic interaction and produces a so-called electrical double layers (EDL) with net local electrical charge near the interface [7], [14], [15], [16]. Taking the simplest fluid transportation in a micro/nanofluidic device under an external pressure (pressure-driven flow) as an example, the EDL obviously affects the transportation of fluid flow, decreasing the velocity of the fluid flow by applying an electrical field force in the opposite direction of driven pressure on the fluid flow. This phenomenon is known as the electroviscous effect and has been widely studied [7]. In addition, when studying the fluid flow in a fluidic system, the boundary slip condition at the solid–liquid interface is a prerequisite needed to be determined. Usually, no-slip boundary condition at the solid–liquid interface, that is, there is no relative motion between the solid and liquid at the interface is valid in macroscale. However, in the micro/nanoscale, the boundary slip, indicating a status of relative motion between the solid and liquid, at some solid–liquid interfaces cannot been neglected when analyzing the fluidic behavior [12], [17], [18], [19]. Considering the convective heat transfer of the fluid flow is related to the fluidic behavior, thus, the existence of surface charge and boundary slip inevitably affect the convective heat transfer of fluid flow in a micro/nanofluidic system by affecting the fluidic behavior. Both the separate effects and the combined effect of EDL and boundary slip on the fluid flow and convective heat transfer in the micro/nanoscale have been widely studied [5], [6], [7], [8], [11], [13], [20], [21], [22].
Nevertheless, the surface charge and the boundary slip at the solid–liquid interface are not independent. Although wide studies have been carried out to investigate their combined effect on the fluidic behavior and convective heat transfer in the micro/nanoscale, the effect of surface charge on the slip is missed in most previous studies. As mentioned above, the existence of surface charge at a solid–liquid interface will produce an EDL near the interface, which has net local charge with the opposite sign with the charged interface. Then, this status of charge distribution near the interface produces an attracting electrostatic force between the charged solid surface and the liquid near the interface, and this strengths the interaction between the solid and liquid and affects the boundary slip condition. This phenomenon has been theoretically and experimentally validated. Joly et al. [23] theoretically studied this phenomenon based on molecular dynamics simulation and found the negative dependence of slip on surface charge. Furthermore, they established a mathematic model to describe this negative dependence. In addition, Jing and Bhushan [12] and Pan et al. [19] experimentally studied the surface charge-dependent slip based on the atomic force microscope technique and found similar relationship between surface charge and slip as the work of Joly et al. [23].
Although the dependence of slip on surface charge has been found, and wide studies have been carried out to analyze the effect of surface charge and slip on the electroviscous effect and convective heat transfer in the micro/nanoscale, a few studies has considered the dependence of slip on surface charge. For the studies of the electroviscous effect, Jing and Bhushan [12], [24] considered the dependence of slip on surface charge and studied their combined effect on the electroviscous effect in a microchannel formed by two infinite parallel plates. However, there is no reported study on the effect of surface charge and slip on the convective heat transfer when considering the surface charge-dependent slip.
In this paper, theoretical models considering the dependence of slip on surface charge are established by introducing the combined effect of EDL and slip into the Navier–Stokes equation and energy equation. The analytical solutions of velocity distribution and temperature distribution of the pressure-driven flow in a microtube are solved based on the simplification of Debye–Hückel linearization. Based on these, the effect of surface charge and slip on flow rate and Nusselt number are studied to analyze the electroviscous effect and the convective heat transfer of pressure-driven flow in a microtube with surface charge-dependent slip. The underlying mechanisms of the present work are analyzed.
Section snippets
Modeling
Pressure-driven flow in a microtube with a radius of R is considered and the schematic and geometry of the present physical problem is shown in Fig. 1. To perform the analysis, the following assumptions are used:
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The pressure-driven flow is in steady and laminar state, and is both hydrodynamically and thermally fully developed.
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The liquid in the microtube is a symmetric electrolyte.
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The radius of the microtube is assumed to be much larger than the Debye length.
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Zeta potential at the microtube wall
Results and discussion
After establishing the models regarding the electroviscous effect and convective heat transfer of pressure-driven flow in a microtube with surface charge-dependent slip, parameters and properties of the electrolyte are chosen to carry out the analysis of electroviscous effect and convective heat transfer in the microtube. A group of 1:1 symmetrical electrolyte of saline (NaCl) solution with different ionic concentrations is used. A finite slip length and a zeta potential in the range of −50 mV
Conclusions
In this paper, the combined effect of surface charge and boundary slip is introduced into the Navier–Stokes equation and energy equation to study the electroviscous effect and the convective heat transfer of pressure-driven flow in a microtube. The dependence of slip length on the surface charge are considered. Closed form expressions of velocity distribution, temperature distribution and Nusselt number for hydrodynamically and thermally fully developed pressure-driven flow in a microtube are
Acknowledgement
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (No. 51505292).
References (26)
- et al.
Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions
J. Colloid Interface Sci.
(2003) Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients
Int. J. Heat Mass Transfer
(2006)- et al.
Combined effects of streaming potential and wall slip on flow and heat transfer in microchannels
Int. Commun. Heat Mass Transfer
(2014) - et al.
The coupling of surface charge and boundary slip at the solid–liquid interface and their combined effect on fluid drag: a review
J. Colloid Interface Sci.
(2015) - et al.
Analytical solutions for thermo-fluidic transport in electroosmotic flow through rough microtubes
Int. J. Heat Mass Transfer
(2016) - et al.
Heat flux and slip effects on liquid flow in a microchannel
Int. J. Therm. Sci.
(2007) - et al.
Analytical solutions of fluid flow and heat transfer in parallel-plate micro-channels at high zeta-potentials
Int. J. Heat Mass Transfer
(2009) - et al.
Combined influences of viscous dissipation, non-uniform Joule heating and variable thermophysical properties on convective heat transfer in microtubes
Int. J. Heat Mass Transfer
(2012) - et al.
Heat Transfer and Fluid flow in Minichannel and Microchannels
(2006) Encyclopedia of Microfluidics and Nanofluidics
(2008)
Springer Handbook of Nanotechnology
Microfluidics: Technologies and Applications
Heat transfer and fluid flow in microchannels
Int. J. Heat Mass Transfer
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