Electroviscous effect and convective heat transfer of pressure-driven flow through microtubes with surface charge-dependent slip

Highlights

• Electroviscous effect and convective heat transfer of pressure-driven flow in a microtube are studied.

• Dependence of slip on surface charge is considered.

• The effect of surface charge-dependent slip on the electroviscous effect and convective heat transfer is studied.

• The underlying mechanisms are analyzed.

Abstract

Although electroviscous effect and convective heat transfer of pressure-driven flow in a microtube have been widely studied, the effect of surface charge on the boundary slip is less considered in previous studies in these fields. This present work develops closed form expressions of velocity distribution, temperature distribution and Nusselt number for hydrodynamically and thermally fully developed pressure-driven flow in a microtube considering the dependence of slip on the surface charge. On basis of these, the combined effect of surface charge and surface charge-dependent slip on the electroviscous effect and convective heat transfer of the pressure-driven flow are studied. The results show that slip length decreases with increasing magnitude of zeta potential of the solid–liquid interface, and this dependence of slip on surface charge inevitably affect the fluidic behavior and convective heat transfer. The slip can increase the Nusselt number by increasing the velocity of the pressure-driven flow, however, the zeta potential leads to a decrease in the Nusselt number by decreasing the velocity. When considering the dependence of slip on surface charge, there is a further reduction on the Nusselt number due to a further decreasing velocity induced by the decreasing slip length. Both a larger magnitude of zeta potential and a larger slip length lead to a larger misestimate of the flow rate and Nusselt number without considering the surface charge-dependent slip. The underlying mechanisms of these phenomena are analyzed.

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.