There has been a recent interest in integrating external fields with inertial microfluidic devices to tune particle focusing. In this work, we analyze the inertial migration of an electrophoretic particle in a 2-D Poiseuille flow with an electric field applied parallel to the walls. For a thin electrical double layer, the particle exhibits a slip-driven electrokinetic motion along the direction of the applied electric field, which causes the particle to lead or lag the flow (depending on its surface charge). The fluid disturbance caused by this slipdriven motion is characterized by a rapidly decaying source-dipole field which alters the inertial lift on the particle. We determine this inertial lift using the reciprocal theorem.Assuming no wall effects, we derive an analytical expression for a phoretic-lift which captures the modification to the inertial lift due to electrophoresis. We also take wall effects into account at the leading order, using the method of reflections. We find that for a leading particle, the phoretic-lift acts towards the regions of high shear (i.e. walls), while the reverse is true for a lagging particle. Using an order-of-magnitude analysis, we obtain different components of the inertial force and classify them on the basis of the interactions from which they emerge. We show that the dominant contribution to the phoretic-lift originates from the interaction of source-dipole field (generated by the electrokinetic slip at the particle surface) with the stresslet field (generated due to particle's resistance to strain in the background flow). Furthermore, to contrast the slip-driven phenomenon (electrophoresis) from a force-driven phenomenon (buoyancy) in terms of their influence on the inertial migration, we also study a non-neutrally buoyant particle. We show that the gravitational effects alter the inertial lift primarily through the interaction of the background shear with the buoyancy induced stokeslet field.

Code verification is the process of ensuring, to the extent possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is a rigorous technique that is employed here for code verification of the main components of an open-source, multiphase flow code-MFIX. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. Currently, the algebraic gas-solid exchange terms are neglected as these can be verified via techniques such as unit-testing. The no-slip wall, free-slip wall, and pressure outflow boundary conditions are verified. Temporal orders of accuracy for first-order and secondorder time-marching schemes during unsteady simulations are also assessed. The presence of a modified SIMPLE-based algorithm in the code requires the velocity field to be divergence free in case of the singlephase incompressible model. Similarly, the volume fraction weighted velocity field must be divergence-free for the two-phase incompressible model. A newly-developed curl-based manufactured solution is used to generate manufactured solutions that satisfy the divergence-free constraint during the verification of the single-phase and two-phase incompressible governing equations. Manufactured solutions with constraints due to boundary conditions as well as due to divergence-free flow are derived in order to verify the boundary conditions.

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An error equidistribution-based r-refinement method for structured mesh adaption is implemented for 1D and 2D Euler equations. A subsonic diffuser case and a subsonic converging-diverging nozzle case are analyzed for 1D Euler equations while a 2D expansion fan case is analyzed for 2D Euler equations. Truncation error is used as the criterion for performing mesh refinement. As the exact solutions are known for these problems, truncation error can be evaluated exactly and does not need to be estimated. Details and some nuances of the equidistribution process are provided for SAM (a newly developed structured adaption module). It is found that with a simple equidistribution approach it is possible to obtain about an order of magnitude reduction in discretization error for these problems as compared to unadapted meshes.

Our approach to the Sandia Verification and Validation Challenge Problem is to use probability bounds analysis (PBA) based on probabilistic representation for aleatory uncertainties and interval representation for (most) epistemic uncertainties. The nondeterministic model predictions thus take the form of p-boxes, or bounding cumulative distribution functions (CDFs) that contain all possible families of CDFs that could exist within the uncertainty bounds. The scarcity of experimental data provides little support for treatment of all uncertain inputs as purely aleatory uncertainties and also precludes significant calibration of the models. We instead seek to estimate the model form uncertainty at conditions where the experimental data are available, then extrapolate this uncertainty to conditions where no data exist. The modified area validation metric (MAVM) is employed to estimate the model form uncertainty which is important because the model involves significant simplifications (both geometric and physical nature) of the true system. The results of verification and validation processes are treated as additional interval-based uncertainties applied to the nondeterministic model predictions based on which the failure prediction is made. Based on the method employed, we estimate the probability of failure to be as large as 0.0034, concluding that the tanks are unsafe.

Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a computational fluid dynamics (CFD) code. In order to perform code verification, the Method of Manufactured Solutions (MMS) is a rigorous technique that can be used in the absence of exact solution to the problem. This work addresses major aspects of performing code verification for multiphase flow codes using the open-source, multiphase flow code MFIX which employs a staggered-grid and a modified SIMPLE-based algorithm. Code verification is performed on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. Currently, the algebraic gas-solid exchange terms are neglected as these can be tested via unit-testing. The no-slip wall, free-slip wall, and pressure outflow boundary conditions are verified for 2D and 3D flows. A newly-developed curl-based manufactured solution for 3D divergence free flows is introduced. Temporal order of accuracy during unsteady calculations is also assessed. Techniques are introduced to generate manufactured solutions that satisfy the divergence-free constraint during the verification of the incompressible governing equations. Manufactured solutions with constraints due to boundary conditions as well as due to divergence-free flow are derived in order to verify the boundary conditions. Use of staggered grid and SIMPLE-based algorithm for numerical computations in MFIX requires specific issues to be addressed while performing MMS-based code verification. Lessons learned during this code verification exercise are discussed.