Moreover, most studies available in the literature considered the two-dimensional domain for the analysis. LIST OF FIGURES xxi 5.15 The shape of the droplet iny−z plane in double grooves at x = 40.
Lattice Boltzmann method
In this field, the understanding of the fluid transport inside the reservoir is thus fundamental to find out the amount of unrecovered oil and the technical parameters to be used in the design of the extraction system. In this case, an important effect is given by the wetting conditions of the porous medium and also by other dimensionless parameters.
Comparison of LBM with N-S equations solver
Literature review
- Review on lattice Boltzmann method
- Review on droplet displacement
- Review on droplet moving past a solid cylinder
- Review on flow through porous media
It was also observed that the effect of viscosity ratio on the displacement of the drop also depends on capillary number. The surface features play a major role in the displacement or spread of the droplet on the channel wall.
Motivations and research objectives
The researchers have tried in the past to replicate this irregularity in terms of small grooves on the surface of the canal wall. A critical review of the literature on multiphase and multicomponent flows shows that the multiphase and multicomponent flow can be found extensively in porous media flows or through pores in a channel.
Thesis outline
The effect of low viscosity ratio on the dynamic behavior of the drop displacement on a wet wall of the three-dimensional channel is presented in Chapter 4. In Chapter 6, an attempt is made to remove the fluid that is trapped inside the. groove of the three-dimensional channel wall.
Introduction
Lattice structure
If the length of the domain is L and there are N lattice units along its entire length, the unit space is defined as δx=L/N. Therefore, the discrete time unit can be given as δt= δcx, where the denominator cis is the mesh speed.
Boltzmann transport equation
- Background of LBM
- Boltzmann transport equation
- BGK model equation
- Streaming and collision steps
- Equilibrium distribution function
The collision operator (Ω) gives the rate of change between the final and initial states of the distribution function. The above equation gives that the total rate of change of the distribution function is equal to the collision velocity.
Boundary conditions in LBM
- Periodic boundary condition
- Bounce back boundary condition
- Mirror/symmetry boundary condition
- Free-slip boundary condition
The periodic boundary condition is the simplest condition in LBM used to isolate repetitive flow conditions. For this situation, the periodic boundary condition in terms of distribution functions are as follows.
LB models for multiphase flow
Shan and Chen model
In the interaction force, these aspects are modeled using the Green function. The molecules of the same substance interact with each other, then gkk 6= 0, and also with those of other substances gkk′ 6= 0.
Wettability on solid surfaces
Validation of LBM code
When a static droplet is formed, the contact angle is evaluated from the final steady-state values of the droplet radius R, the droplet height a0, and the wetted droplet length b0, as shown in the figure. A contact angle greater than 90° is formed. when g2w is positive; indicating that phase 2 is non-wettable and the wettability state is characterized as hydrophobic.
Summary
Most researchers analyzed the coalescence of droplets without considering the wetting effect of the channel walls. The main objective of the present study is to investigate the dynamic behavior and initiation time of the coalescence of two droplets on the wettable channel wall.
Problem specification
The time taken by the two droplets for different parameters to merge is also investigated.
Results and discussion
Effect of centre distance on the coalescence
Looking at the wetted area and the wetted length, we see that both the wetted area and the wetted length initially increase up to the point where two droplets merge and after this point starts to decrease in the case of the hydrophilic surface. It is observed that the coalescence time of two drops is shorter in the mixed wettable surface compared to the uniform hydrophilic surface.
Effect of the capillary number on coalescence
The wetted area and wetted length increase gradually as the capillary number increases in the case of a hydrophilic surface, as shown in Fig. It is also observed that the increase in wetted area is less than the increase in wetted length.
Summary
Figures 3.6(a)-(b) show the wetted area and wetted length on the mixed wettable surface for three capillary numbers. It is also observed that the extent of the wetted region is larger in the uniform hydrophilic case compared to the mixed wettability case.
Introduction
Dynamic drop behavior on wetted flat and grooved surface of channel for low viscosity ratio.
Problem specification
Results and discussion
Effect of viscosity ratio on droplet displacement behaviour
It is found that the viscosity ratio initially does not greatly affect the displacement and deformation of the droplet. A clear picture related to the contact surface of the drop on the wall is in Fig.
Effect of the capillary number on droplet displacement behaviour 66
The height of the groove is a parameter that plays a key role in the movement of the droplet on the channel wall. The results are presented at the second time when the drop passes through the groove on the wall.
Summary
The large fraction of the drop liquid that adhered to the upper surface of the groove and remaining liquid moves down the lower surface of the channel wall. It is also found that after the break-up, a small amount of drop liquid in the form of drop sits on the bottom surface of the groove.
Results and discussion
A very small portion of the droplet liquid remains attached to the upper surface of the groove and spreads completely over the surface. When the droplet reaches the groove opening, in the case of the hydrophobic wetted groove as shown in Fig.
Summary
When the groove is located in the bottom of the channel, i.e. at 40-60 lu in z-direction as shown in Fig. In the case of two grooves on the wall, the trapped liquid is almost double that of the single groove case.
Problem specification
Results and discussion
Droplet dynamics on a grooved wall
The effect of this gravitational force can be seen in the change of shape of the droplet as well as the liquid trapped within the groove (Fig. At the same instant a weak velocity vortex is also generated within the previously trapped liquid on the lower surface of the groove.
Effect of wettability on the sweep out behaviour
It is important to mention here that both the quantities, i.e. wet area and wetting length, are calculated on the surface of the channel wall on which the groove is created. However, in the case of hydrophobic groove, as the droplet reaches the groove and passes through the groove surface, the wetted area and the wetted length of the channel wall decrease.
Effect of the capillary number and groove height
At later stages, when the coalesced droplet is translated to the channel wall below the groove, the droplet itself breaks into two parts and hence the wetted area and wetted length are found to decrease as shown in Fig.
Summary
On the other hand, the study of the point passing a solid target has recently been an active field of research for its great importance in many fields. The main objective of this study is to investigate numerically the dynamic behavior of the point moving under gravity in a three-dimensional channel.
Problem specification
But the study is lacking in the more detailed study in three-dimension; the study was only focused on the two-dimensional assumption. Therefore, the study also considers the direct impact of droplet and obstruction, as well as the distribution of droplet liquid over the solid obstruction.
Results and discussion
Effect of capillary number
The drop liquid film breaks at the upper surface of the obstruction due to the curvature of the obstruction as shown in Fig. However, a small portion of droplet fluid remains attached to the upper surface of the obstruction.
Effect of surface wettability on droplet dynamics
The investigation also shows that droplet liquid deposition occurs in the case of a hydrophobic wetting surface on the upper surface. It is interesting to see that the droplet liquid deposition on the top surface of the barrier is zero in the case of neutral wetting (θ = 0◦).
Effect of the size of the obstruction
As a result, the dissolution of the liquid film on the upper surface of the barrier occurs rapidly. Because of this, the large surface area allows the drop liquid to deposit more liquid on the top surface of the barrier in the case of r=60 lu (compared to tor=30 lu).
Effect of obstruction structure
In the case of hydrophobic wettability, θ = 120◦, the deposition of the droplet liquid is significantly increased for r=50 lu andr=60 lu, as shown in figure. However, it is observed that upon obstruction of the SC structure, the droplet fluid becomes trapped at the upper center of the obstruction due to the presence of a throat region, as shown in Fig.
Summary
For a better understanding of droplet liquid deposition on the barrier surface, the deposited volume fraction was measured and found to be equal to 15.50% for SC, BCC, and FCC structures, respectively. The porosity of a porous medium is defined as the fraction of the total volume of the medium that is occupied by void space.
Problem specification
It should be noted that all the solid walls are considered wetted and three different wetting conditions are taken for the study. The relaxation parameters for fluid 1 (WP) and fluid 2 (NWP) are considered equal to 1 and 1.42 giving a dynamic viscosity ratio approximately equal to 2.
Results and discussion
Effect of wettability on liquid transport
150 Mesoscopic pore-scale study of fluid flow through porous medium particles can be seen in Fig. Since the pore surface is non-wet, it does not allow the liquid to spread over it and block the path of further penetrating liquid.
Effect of porosity on liquid transport
Effect of pressure gradient on liquid transport
Summary
The validation of this code was found to be in good agreement with the available literature. The present thesis presents a particularly detailed insight into the interactions of capillarity and wettability on the movement and spreading of droplets on channel walls and the flow of an immiscible liquid through porous media with a ball pack.
Scope of future work
D3Q19 lattice structure
Position and velocity vector before and after applying force
Pre-streaming and post-streaming conditions in LBM
Pre-collision and post-collision conditions in LBM
Periodic boundary condition in LBM
Bounce back boundary condition in LBM
Mirror boundary condition in LBM
Free-slip boundary condition in LBM schematic
Contact angle of a liquid droplet wetted to a solid surface
Static droplet after steady state
Variation of contact angle with g 2w
