The temperature distribution in a nanofluidic channel with the presence of wall-fluid interaction energy strength (ε )was studied [116]. Their result is similar to this study. They also reported
a Fourier like behaviour of the temperature profile in the nanochannel. They further observed a temperature jump at the fluid-wall interface which they reported was due to molecules of the fluid close to the wall boundary having different thermal velocity from the wall. The local temperature is mostly defined by the thermal velocities of particles that also cause momentum transfer between the fluid and the wall. If the wall-fluid interaction is weak the momentum transfer will be small, However, if the fluid-fluid interaction is stronger and dominantly affects closer molecules, more thermal motion is produced, hence an increase in temperature. The situation of these scenario brings about quick changes in the distribution of local kinetic energy, which is responsible for the jump in temperature at the interface. This jump is also due to the scattering of phonons due to different phonon frequencies of the two media. Fig.4.21-4.23 shows a linear temperature jump at the walls of the nanofluidic channel, which is similar to previous study [116]. The temperature jump increases with an increase in stiffness in the lower wall and decreases with an increase in stiffness at the upper wall. The temperature profiles cross each other almost at the same point, due to the difference in lower and upper wall temperature.
4.1.3
Chapter Summary
An investigation into the effect of the atomic mass on the Kapitza resistance has been carried out. The temperature jump have indicated that for higher values of the atomic mass, the frequency of oscillation must decrease in order to satisfy constant average kinetic energy constraints dictated by the fixed temperature of the wall. The lower frequency translated into a smaller number of collisions between the wall and liquid particles, which inevitably led to a less efficient transfer of energy and temperature jump at the solid-liquid interface. As a result, for low values of κ, the Kapitza resistance was dominated by the mass of the wall particles, while as κ increases, the mass effect faded and the bonding stiffness dictated the temperature jump. The density profiles of the walls have indicated that for lower values of the wall bonding stiffness, the amplitude of oscillation of its atoms is unaffected by a change in mass. Finally, the temperature jump correlated with the product of the bonding stiffness and wall mass log(mwk), rather than the frequency of harmonic
Effect of Wall Interaction on the Kapitza resistance
5.1
Introduction
Previous MD studies focused on the energy interaction strength of fluid-solid interaction in in- terfaces and fluid confined in nanochannels or nanopore [107-116], with none of these studies investigating how the vibrating wall interaction intermolecular energy strength affects the Kapitza resistance, temperature and density distribution across interfaces and nanofluidic channels. Studies of the effect of the energy interaction strength between particles in the solid wall, on the Kapitza resistance at the solid-liquid interfaces, and nanofluidic channels are very scarce if not non-existent. Therefore, the purpose of this chapter is to implement MD wall-wall thermal model in investigating the effect of the energy interaction strength (εww)of a vibrating solid wall on the Kapitza resistance,
temperature and density distribution across solid-liquid interfaces and nanofluidic channels. The objectives of this chapter are to develop a 3D molecular dynamics algorithms and codes of the simulation domain and thermal wall model with wall-wall intermolecular interaction energy (εww). To determine the frequency of the vibrating wall atoms using molecular dynamics sim-
ulation. To investigate the effect of wall-wall lattice intermolecular interaction energy strength (εww)for pore size of 20.5σ at various vibrating frequencies and stiffness constant, ranging from
κ = 100εσ−2− 1600εσ−2 on the Kapitza resistance, temperature profiles and density distribution
across solid-liquid interfaces and nanofluidic channels. Finally, to compare the effect of the high- est and lowest εww on the Kapitza resistance, temperature, and density distribution across the
interfaces and nanofluidic channels.
The investigation shows the effect of the presence of wall particle energy intermolecular in- teraction strength (εww)on the temperature jump, Kapitza resistance, temperature profiles and
κ(εσ2) εww εwf 4T Mass(m) Time step (τ) Simulation run time Case 1 100-1600 0.2 0.4 0.1 mw= 2mf 0.001 4 × 107 Case 2 100-1600 0.2 0.6 0.1 mw= 2mf 0.001 4 × 107 Case 3 100-1600 0.2 0.8 0.1 mw= 2mf 0.001 4 × 107 Case 4 100-1600 0.4 0.4 0.1 mw= 2mf 0.001 4 × 107 Case 5 100-1600 0.4 0.6 0.1 mw= 2mf 0.001 4 × 107 Case 6 100-1600 0.4 0.8 0.1 mw= 2mf 0.001 4 × 107 Case 7 100-1600 0.6 0.4 0.1 mw= 2mf 0.001 4 × 107 Case 8 100-1600 0.6 0.6 0.1 mw= 2mf 0.001 4 × 107 Case 9 100-1600 0.6 0.8 0.1 mw= 2mf 0.001 4 × 107
Table 5.1.1: Simulation Matrix for Wall-Wall intermolecular interaction energy strength effect on Kapitza resistance with 10 High Powered Computing Nodes used and 2800 simulation runs. wall in the nanoscale was implemented using simple harmonic formulations. The mass of the wall is mw = 2mf with different values of eww and ewf and bonding stiffness κ. The results show
different density profiles in two lattice sites in the solid, and density profiles in the liquid near the wall. Higher values of spring constant κ, and wall-wall with wall-fluid intermolecular interaction energy strength ( ewwand ewf) gave maximum density peaks in the solid and fluid, developing a
temperature jump at the solid-liquid interface. Lower values of ewwproduce a higher temperature
jump and Kapitza resistance. This study provides an insight into the relationship between the temperature jump, mass ratio of the solid and liquid, the bonding stiffness κ, the wall-wall and wall-fluid intermolecular interaction energy strengths eww and ewf at the solid-liquid interface of
nanofluidic channels.