Can homogeneous slip boundary condition affect effective dispersion in single fractures with Poiseuille flow?

Slip Backflow of Polymers in Elastic Fractures for Subsurface Heat Recovery

“…The efficiency of employing this numerical technique for solving nonlinear ODEs has been previously validated in our earlier research, particularly in the context of studying the one-dimensional drainage of power-law fluids from a finite-length fracture edge [31]. In our numerical studies, we adopt a dimensionless slip number of N s = k/h 0 ≈ 0.01 which has been derived from experimental findings by Zheng et al [32]. Their research reports h 0 = 500 µm as the value of the initial fracture aperture and k = 8.84 µm as the slip length.…”

“…To achieve this, we conduct a parametric analysis, specifically investigating the impact of slip length across three scenarios: N s = [0, 0.01, 0.1]. These values span two orders of magnitude, aligning with experimental data from Zheng et al [32], broadening the previous analysis conducted for a single N s value.…”

Backflow Dynamics of Newtonian Fluids in an Elastic Fracture with Slip Walls

“…We seek the numerical solution of Equation ( 25) by exploiting MATLAB subroutine 'ODE45' to solve the nonlinear first-order ODE, subjected to the initial condition of Equation (20). Figure 3 shows the numerical solutions obtained for five values of dimensionless pressure P e = {0.0, 0.1, 0.5, 0.9, 1.0}, and a slip number of N s = 0.017 obtained from the data included in the experimental study of Zheng et al [15]. While the numerical result of the singular limit scenario P e = 0 tends to zero with a slope of m = −1/2.53 in log-log scale, the late-time solutions (T 1) of P e = 0 asymptotically approach a constant value H(T 1) ≈ P e .…”

“…For example, for a fracture surface wetted with creosote in a fracture half a millimeter wide, the increase in the flow rate was 10.0% compared to a surface wetted with water [14]. The change in the flow rate, however, seems to insignificantly influence the longitudinal dispersion rate [15].…”

Effects of Slip Length and Inertia on the Permeability of Fracture with Slippery Boundary Condition

“…The slippery BC, in fact, has been tested to enhance fracture flow (i.e., permeability) via both laboratory and numerical experiments [20,21]. Note that the enhanced fracture flow might not increase the longitudinal dispersion coefficient within the simplified parallel plate model [21,22] for the first time investigated the competition between the inertial force and slippery BC effects in changing fracture permeability, where inertial force on the one hand reduces permeability, while slippery BC, on the other hand, enhances permeability. By employing a homogeneous slip length along fracture boundary, they found out that slippery effects dominated over inertial effects when the pressure gradient was small, and the inertial effects gradually caught up with that caused by the slippery BC with a further increase in pressure gradient [21].…”