Rate of capillary rise in quartz nanochannels considering the dynamic contact angle by using molecular dynamics

doi:10.1016/j.powtec.2020.06.018

Powder Technology

Volume 372, 15 July 2020, Pages 477-485

https://doi.org/10.1016/j.powtec.2020.06.018 Get rights and content

Highlights

•
Molecular dynamic is used to study the capillary rise behavior of water in quartz nanochannels.
•
The Washburn capillary rise technique may obtain an overvalued equilibrium contact angle.
•
A modified L-W equation is proposed showing a good agreement with the penetration rate.
•
The upper bound of adsorptive water density and thickness of water film is 1.14 g/cm³and 0.3 nm.

Abstract

As a universal phenomenon in nature, capillary rise not only strongly influences the physical properties and industrial processes of powder materials but can also be applied as an important technique to measure their wettability. In this paper, molecular dynamics (MD) was implemented to investigate the capillary transport behavior of water flow through α-quartz nanochannels considering the channel height. The results showed that the Capillary rise method (CRM) with the classical Lucas-Washburn (L-W) equation may obtain an overestimated equilibrium contact angle, and the value decreases with increasing channel height. Through the introduction of the concepts of effective viscosity, slip length and dynamic contact angle, a modified L-W equation was proposed. The equilibrium contact angle calculated by the equation was more accurate and independent of channel size. Additionally, the pore-water can be divided into absorption water and capillary water. The upper bound of the absorption water density was determined to be 1.14 g/cm³.

Graphical abstract

Introduction

Capillary rise phenomena are ubiquitous in nature and play roles in important applications in the fields of powder engineering, geotechnical engineering, irrigation engineering and barrier engineering [[1], [2], [3], [4]]. Particularly in powder systems, capillary rise phenomena are of great importance in wetting processes and agglomeration processes for all types of powders, as well as in many physical behaviors involving the interaction between powders and water. For instance, the capillary rise effect can induce a dissolving liquid into agglomerate pores to improve the instant properties of food aggregations, which is widely applied in the food industry [5]. Another significant application for capillary rise is as a measurement technique to investigate the wettability [[6], [7], [8]] and surface free energy [9,10] of powders. The corresponding techniques indirectly calculate the above parameters by monitoring the rate of capillary rise. Therefore, insightful research on the capillary rise phenomenon and accurate calculation on the rising rate is essential for relevant industrial processes and measurement techniques of powder materials.

The wettability of powdered and granular solids as the description of particle-water interfacial interactions plays an important role within several operations such as granulation, rehydration, flotation and dissolution [4,11]. According to Young's .[12], the contact angle is a crucial indicator of the wetting properties of powders, as shown in Fig. 1(a), that can be measured in experiments. Several approaches, such as the sessile drop method, can be implemented to measure the contact angle. However, due to the particle size and surface roughness of powders, the measurement accuracy of these techniques is unsatisfactory [7]. Another measurement technique called the Capillary rise method (CRM) [13,14] is commonly used to assess the contact angle of powders or granular materials, in which CRM utilizes the capillary rise phenomenon along with Lucas-Washburn (L-W) equation [15,16]. A typical experimental setup for CRM is illustrated in Fig. 1(b). Although CRM has several advantages such as broad applicability and convenience, the measured contact angle measured during the wetting process is actually a non-equilibrium advancing contact angle, also called dynamic contact angle, and this parameter is dependent on the equilibrium value as well as the rate of capillary rise [17,18]. CRM neglects the dynamics process of contact angle, leading to an overestimated value of the equilibrium contact angle.

Molecular dynamics(MD) simulation is a valuable computational approach for elucidating the dynamic and thermodynamic properties of materials [19]. This method can calculate interparticle forces well, including van der Waals attractive, double-layer repulsive and capillary forces, which are the dominant forces between powder particles. Several MD simulations have been conducted on different capillary flows in nanometer pores made of different solid materials [[20], [21], [22], [23]]. However, these reports mainly focus on the transport behavior of capillary flow in nanochannels without considering the dynamic variation in the contact angle during the capillary rise. Moreover, to the best of our knowledge, few studies have involved the capillary rise phenomenon in powder materials even though it has a great impact on the physical and chemical behavior and processing technology of powder materials as mentioned above.

In this paper, the experimental process of CRM in the nanometer channels of α-quartz was simulated by using molecular dynamics. Three quartz models with different channel height were established to study the impact of the geometric restriction on the capillary rise phenomenon of water. The penetration rate and dynamic contact angle of water were measured during the capillary rise process. A modified L-W equation taking into account the concept of the effective viscosity, dynamic contact angle and slip length was proposed. The accuracy of the equilibrium contact angle obtained by the classical and modified L-W equation was discussed. Finally, the interface structure of water in the slits was further analyzed.

Section snippets

Theoretical analysis

Lucas and Washburn discovered that the capillary filling process is proportional to the square root of time, through a large number of capillary rise tests. On macroscopic scales, the $H (t) \propto \sqrt{t}$ law has been verified in various capillary imbibition systems, which are often used to characterize porous media [24]. The classic L-W equation demonstrates that capillary rise in the nanochannel is controlled by the balance force of capillary and viscosity forces [25], which can be expressed by: $\frac{σ cos θ}{H} = \frac{3}{H^{2}} μL dL$

Simulation method

To investigate the capillary interaction of α-quartz (the most common type of quartz) channels with water in the imbibition process, we established three models with different channel height of 1.5 and 2.5, 3.5 nm. Each model consisted of two parts of the α-quartz nanochannel and water reservoir. As an illustration, Fig. 2 shows the initial configuration of the water imbibition model with a 3.5 nm height. The nanochannel was built by two parallel α-quartz sheets with 9.8 nm depth, 2.2 nm

Results and discussion

In the capillary simulations, water in the reservoir can spontaneously flow into the quartz channels. Fig. 3 displays the meniscus displacement of water fluid in the 3.5 nm channel during the capillary rise process. The snapshots of the meniscus at 50, 200 and 700 ps in Fig. 3 show that the wetting frontier maintains the shape of a concave interface, and the angle of the meniscus and the capillary wall drops gradually as the height of the water column increases. The water penetration depth with

Conclusions

In this paper, molecular dynamics were used to investigate the capillary rise process of water in quartz with channels of different sizes. The change in the dynamic contact angle, the rate of penetration and the interface structure of pore water were studied by using MD method. A modified L-W method has been developed by introducing the effective viscosity, slip length and dynamic contact angle. The differences in equilibrium contact angles calculated by the classical and modified L-W equations

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research has been supported by the China National Key R&D Program during the 13th Five-year Plan Period (Grant No. 2018YFC1505104 and 2017YFC1503103) and National Natural Science Foundation of China (Grants No. 51778107). The work was carried LvLiang Cloud Computing Center of China, and the calculations were performed on TianHe-2.

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Rate of capillary rise in quartz nanochannels considering the dynamic contact angle by using molecular dynamics

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Theoretical analysis

Simulation method

Results and discussion

Conclusions

Declaration of Competing Interest

Acknowledgements

Powder Technol.

Powder Technol.

Powder Technol.

Powder Technol.

Colloids Surfaces A Physicochem. Eng. Asp.

Powder Technol.

Powder Technol.

Powder Technol.

Geoderma.

Colloid Surf A Physicochem Eng Asp.

Powder Technol.

Constr. Build. Mater.

Int. J. Heat. Mass Tran.

Chem. Eng. Sci.

Adv. Colloid Interf. Sci.

J Colloid Interf. Sci.

Adv. Colloid Interf. Sci.

J. Colloid Interface Sci.

J. Comput. Phys.

J. Colloid Interface Sci.

Int. J Multiphas Flow.

J. Colloid Interface Sci.

Int. J. Heat. Mass Tran.

Powder Technol.

Powder Technol.

Powder Technol.

Appl. Clay Sci.

Colloids Surfaces A Physicochem. Eng. Asp.

Rate of capillary rise in soil

J. Geotech. Geoenvironmental Eng.

Water movement in glass bead porous media 3. Theoretical analyses of capillary rise into initially dry media

Water Resour. Res.

A study of the applicability of the capillary rise of aqueous solutions in the measurement of contact angles in powder systems

Powder Technol.