Fluid Mechanics colloquium

The presentation will be divided into two parts which are connected by the observation that evaporation from micro-drops and the resulting phenomena can provide insights into diverse processes wherein the surface and intermolecular forces play pivotal roles leading to potential applications. In the first part, we will examine the theoretical and experimental investigation of an evaporating aqueous droplet, over a viscoelastic liquid substrate. In the second part, the role of the differences in the overall interaction energy during droplet drying, leading to the development a definitive bio-marker will be presented.

Viscoelastic liquids can be used as potential substrates in microfluidics paradigm. The theoretical and experimental investigations of an evaporating aqueous droplet, over a viscoelastic liquid substrate, provide a glimpse of the complex interplay amongst capillarity, viscosity, and elasticity, and intriguing dynamics. The evaporation dynamics of a water droplet atop an un-crosslinked polydimethylsiloxane film (polymeric liquid substrate) are examined and the resulting data are used to estimate the contact angles, velocities, and other parameters of relevance. The viscoelasticity of the film, in conjunction with evaporation, triggered a self-propulsion in the droplet, leading to crumpling of the polymeric film, and finally culminating in the encapsulation of the water drop by the polymer. A semi-analytical model is used to explain the role of the relevant forces.

Dried blood droplet morphology may potentially serve as an alternative biomarker for several

patho-physiological conditions. The second part of the presentation will discuss a dried blood droplet morphology-based detection of a specific haematological disorder “Thalassaemia”. Identifying distinctive morphological traits from a large sample size and proposing confirmatory explanations based on the differences in the overall interaction energies of the system are necessary to establish the signatory pattern to be used as a potential biomarker to differentiate between healthy and diseased samples. A first-generation theoretical analysis, with mean field approximation, explored the role of cell-surface and cell-cell interactions pertinent to the formation of the distinct dried patterns.

Fluid mechanics has a rich history, as of course does mechanics more generally. Modern research themes introduce new questions, some of which can be understood using fundamental concepts. Just as significantly, the ideas bridge science and engineering disciplines, even as they generate new fundamental research questions in fluid mechanics. In this talk I sketch some recent themes from my research group, which bridge a wide range of length scales, including (i) problems of fluid-structure interactions at low Reynolds numbers, where the flow of a liquid and the deformation of a solid are coupled, (ii) ways in which gradients of chemical concentrations can drive the motion of small particles, highlighting the role of the difference of ion valences and background electrolyte, and, if there is time, (iii) I illustrate an experimentally motivated similarity solution involving three independent variables. The research described was performed by many people in my research group, as well as some external collaborations.

Leonardo da Vinci (1452 – 1519) was a genius of the High Renaissance and was recognized as one among the greatest painters in the history of art, having apparently no great influence as recognized by modern fluid dynamists. However, with numerous lost, unpublished and unfinished works that were premised to disrupt human knowledge—he created some of the most influential paintings that reflected supreme technological ingenuity, including understanding the functionalities of individual parts of the body, delving into the internal organs that were interpreted by him to act as the motors orchestrating human life. William Harvey (1578-1657), by training a medical doctor, focused much of his work on the mechanics of blood flow in the human body. He first showed that valves in the veins, discovered by his teacher Fabricius, permit the blood to flow only in the direction of the heart and act as lifelines of the circulatory system. He also postulated the existence of tiny capillaries between arteries and veins, that were later discovered in 1661 by Marcello Malpighi. Jean Léonard Marie Poiseuille (1797 –1869) was a French physicist who delved deeply into the understanding of the flow of human blood in narrow tubes, and in 1840’s, disseminated the celebrated Poiseuille's law. All these developments took place in an era when fluid dynamics research was not colonised by the present-day snobbery of distinguishing great mastery in solving complex partial differential equations relating idealized problems that may not otherwise address mundane quests of understanding realities of life and nature. Despite the subject being taken over by illustrious mathematicians and physicists who have revolutionized the subsequent understanding of fluid dynamics, an apparently simple proposition of understanding the mechanics of blood flow in physiological pathways in human bodies remained to be an unsolved proposition.

Over the past century, advancements in fluid dynamics hallmarked deeper studies on complex fluids, though. Fluid dynamics of blood, possibly the most critical complex fluid impacting human lives, is primarily dictated by red blood cells (RBCs) that are flexible biconcave discs spending their lives suspended in blood plasma that is elusively more complex than simple water. Commonly, RBCs stack together to form structures called rouleaux like cylindrical packs of coins that reform continuously. Contrary to intuition, instead of clogging, such reforms result in easier flow of blood as it passes through extremely narrow channels. An influential theoretical premise of blood flow has been rationalizing this by drawing analogies of RBCs with compound liquid droplets in which the cytoplasm is more viscous than the outer fluid that triggers a series of complex shape transitions. However, a stiffening of RBC membranes under certain conditions contradicts this analogy and may alter ATP release that happens due to shape deformation. This may signify specific diseased conditions and influence a plethora of ailments ranging from cardiovascular irregularities to cancer metastasis. The role of unique flexibility of microvasculature and morphology of the microenvironment, dynamical signals of pressure pulsation and disease-specific blood rheology make it extremely deceptive and patient-specific and difficult to model within the known territories of expertise of fluid dynamics. I discuss here various computational, in-vitro and in-vivo studies conducted in my group that have attempted to address some of the pertinent outstanding questions, unresolved paradoxes, and present a deeper challenge that makes even a ‘simple’ blood flow strikingly more complicated than its intuitive analogy of pipe flow in engineering fluid mechanics. I also suggest a way forward with a convergence of physics-based modelling and data science, where blood flow is not merely perceived as an ‘inert’ physical phenomenon but recognized as an exclusive hallmark of ‘life’ with all individualism intrinsic to humans.