Research projects

Buoyant Flow during alloy Solidification

This research topic considers linear and nonlinear convective flow in horizontal mushy layers which can be present during alloy solidification.During alloy solidification, such as mushy layers, which are composed of solid dendrites and liquid, can produce chimneys that contain convective flow under some conditions. It is known that the convective flow within the chimneys can produce freckles in the final form of the produced solidified alloy. Freckles are imperfections that reduce the quality of the solidified materials. Higher quality alloy crystal can, thus, be produced if the undesirable effect of the convective flow within the mushylayer is reduced as much as possible. We already have done a number of investigations in the subject area (Riahi, 2003JFM, 2006JFM; Okhuysen and Riahi, 2008JFM; Riahi, 2016PRSA, 2017TIPM) based on analytical and computational modeling for binary and ternary alloy cases, which provided good agreement with the available experimental results. Presently, We are working on extension of such modeling to other problems  for the alloy and non-alloy cases. 

Electrically Driven Jet and Electrospinning

Electrospinning is process that can produce nano-scale fibers continuously under the action of an externally imposed electric field from a polymeric solution or melt. In the electrospinning process, a meso-scale fluid jet is forced through a nozzle under the influence of high electric field. Even though this process is known for many years, the vivid understanding of the process, the instabilities involved and the parameters affecting the properties of the fibers are not known to a large degree. Understanding the complex electro-hydrodynamic instabilities that are involved, is the key to successful applications of these nano-fibers in many areas in applications such as in aerospace, biotechnology, health care and defence. We investigated several problems involving spatial and temporal instabilities as linear and nonlinear stages for electrically forced jets under a uniform or variable applied electric field (Riahi, 2009, 2011AMM; Orizaga and Riahi, 2011NA-RWA, 2014, 2015IJNLM) and detected new instabilities and new mechanisms under which the jet’s radius becomes as small as possible. Presently, we investigate further extension of our modeling efforts to non-linear domains under which optimal conditions for production of nano-fibers can be possible.

Two-Phase Flow in Catheterized Elastic Artery with Atherosclerosis

Diseases in the blood vessels and in the heart are the major causes of mortality worldwide. The use of catheter is very important and has become a rather standard tool for diagnosis and treatment in modern medicine.In this project we investigated unsteady blood flow through a narrow catheterized elastic artery and in the presence of atherosclerosis, whose generated experimental data provide us a more accurate assessment of our results as compared to those medically tested ones. We represented blood flow by a two-phase model composing of a suspension of erythrocytes (red cells) in plasma. We solved the coupled partial differential equations for the elastic wall displacements and two-phase flow using a combination of theoretical, modeling and computational approaches. We determined results for various quantities such as the radial and axial displacements of the elastic artey’s wall, plasma and red cell speeds, blood pressure driven force, impedance (flow resistance), stress excerted by the blood flow on the elastic artery or vice versa, etc. (Riahi, 2016EST, 2017IJACM). Our present research work is on what human operating conditions are best as it relates to the flow in the present artery system and under what operating conditions presence of atherosclerosis can pose clear danger to the life of the patience. 

 Air Flow over Structured Surfaces

 The subject of air flow and understanding its effects on structured surfaces like aircraft’s wing, vehicle, building, etc, is of great interest and importance in aerodynamics and technological applications as well as for our daily living on Earth. Understanding the effects of air flow and especially those of more violent nature such as severe storm on the structured surfaces and the roles played by such surfaces on the evolving air flow is important, in particular, for the technological advancement and for the well being of the human and other living species and, in addition, it can provide useful information to minimize the negative effects of the air flow forces on the structured surfaces. In this project we develop mathematical modeling and use computational and theoretical methods to determine the roles played by such surfaces in terms of the amplitudes, scales and modal decomposition on the air flow and how to construct such structured surfaces that can minimize the air flow effects. 

Modeling and Computation of Drug Delivery to Solid Tumors

It is known that the most effective way to cure cancer due to a malignant tumor is a successful removal of the tumor by surgery and then delivering in an efficient way certain anticancer drugs. However, presence of drugs in  the patient can lead to side effects and interactions of drugs may negatively affect the efficiency of the drug delivery and its usefulness. In this project we already developed a simple model for a brain tumor (Gracia etal. 2016IJFMR; Roy et al., 2017IJACM), and we developed for the first time more realistic and new theoretical models for solid tumors to understand the effects of drug concentrations in the tumor in the presence of other anticancer drugs and how interactions of drugs can affect the overall usefulness of such drugs. We presently plan to investigate the effects that the rate of drug delivery to the tumor site can have on the tumor growth for the actual operating conditions for the corresponding patients. We look for ways that our models can predict tumor growth control in an optimizing manner for given constraints due to the drug delivery systems.

Modeling Fiber Jets during Forcespinning Process

Forcespinning (FS) is a new experimental process which produce nano scale fibers under the action of rotating forces from a polymeric fluid. In this project we do theoretical and computational modeling of rotating fiber jets with curved centerlines during FS process. We are interested to understand such process, jet evolution in time and space, roles of possible instabilities involved and to detect optimizing jet flow modes with no breakup or beading that could produce high quality and stable nanofibers with very high yield, very small nanofiber diameters and desired properties. We compare our results with the available experimental results. Achieving such optimizing scheme for the FS can be the key to successful applications of nanofibers in many important application areas such as in aerospace, energy, biotechnology and health care.  Our already completed research work (Riahi, 2017IJNLM, 2018ASCE-JEM, 2020ASME-JFE, 2021JNNFM) already provide new theories for both polymeric fiber jets and the inclusion of aerodynamic effects on the fiber jets, that aris due to the ambient flow. We are now extending our modeling to new viscoelastic fiber jets and beneficial effects for nano-fiber production due to FS process.

Flow in an Aquifer Layer with Environmental Application 

In this recently developed research project we studied flow in an aquifer layer as in the case underground water layer and its transport process subjected to variable hydraulic resistivity and diffusivity. We are presently extend such flow process to cases with more environmental implications such as inclusion of the chemical and/or pollusion concentrations within the liquid flow zone. We are interested to determine results under which such concentrations can affect the transport processes to the top upper (ground) level and the subsequent environmental impacts.

Modeling Nonlinear Dynamics of Blood Glucose Regulatory System

Many millions of people have diabetes worldwide and the severity of this disease has been rising in recent years. Clinical effects of diabetes often is not readily observable, and, thus, it is necessary to develop more improved diagnostic methods that can result in more accurate clinical outcome. In particular, proper mathematical modeling can help in such aspects. Very recently, we have developed such research project to investigate dynamics of glucose, insulin and other hormones within the blood glucose regulatory system and to be able to diagnose diabetes with more accurate results, which can hopefully help public health aspects of our community.