«Droplet impact and spreading of viscous dispersions and volatile solutions Daniel A. Bolleddula A dissertation submitted in partial fulﬁllment of ...»
Droplet impact and spreading of viscous dispersions and
Daniel A. Bolleddula
A dissertation submitted in partial fulﬁllment of
the requirements for the degree of
Doctor of Philosophy
University of Washington
Program Authorized to Oﬀer Degree: Mechanical Engineering
University of Washington
This is to certify that I have examined this copy of a doctoral dissertation by
Daniel A. Bolleddula
and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the ﬁnal examining committee have been made.
Chair of the Supervisory Committee:
Alberto Aliseda James J. Riley Lucien N. Brush
In presenting this dissertation in partial fulﬁllment of the requirements for the doctoral degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this dissertation is allowable only for scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright Law. Requests for copying or reproduction of this dissertation may be referred to Proquest Information and Learning, 300 North Zeeb Road, Ann Arbor, MI 48106-1346, 1-800-521-0600, to whom the author has granted “the right to reproduce and sell (a) copies of the manuscript in microform and/or (b) printed copies of the manuscript made from microform.” Signature Date University of Washington Abstract Droplet impact and spreading of viscous dispersions and volatile solutions Daniel A. Bolleddula
Chair of the Supervisory Committee:
Professor Alberto Aliseda Department of Mechanical Engineering Spray coating processes require accurate control over the impact of highly complex and viscous liquid droplets on solid surfaces. Here we use theory and experiments to investigate aqueous colloidal dispersions and acetone-based solution droplets impacting solid surfaces of varying wettability. Over a range of impact speeds and eﬀective viscosities, W e ∼ O(1 − 300) and Oh ∼ O(0.01 − 1), we observe that the spreading dynamics follows a decaying function in characteristic times, D/U, where D and U are the initial drop diameter and impact speed, respectively. The spreading diameter decays to an asymptotic value referred to as the maximum spreading diameter.
The maximum spreading diameter βmax during inertial times O(D/U ) is shown to be in good agreement with three models available in the literature. The centerline height dynamics reveal an unstudied resonant regime for W e ∼ 30. In this regime, the centerline height sinks below the formation of a thick rim. As the centerline height recovers, the rim height hr is shown to increase linearly with time for our complex liquids and equivalently viscous Newtonian solutions. Immediately following this inertial driven regime, the drop continues to spread by capillarity until equilibrium. The transient spreading dynamics of an aqueous colloidal dispersion on nearly fully wettable substrates reveals that Tanner’s law, d(t) ∼ t1/10, is approached but not in a consistent manner. The eﬀects of residual inertia inﬂuence these short term spreading dynamics of both colloidal dispersions focused on herein and glycerol/water solutions. In particular, the spreading dynamics is found to obey a robust power law d(t) ∼ C(t/µD/σ)n, where C is found to be an O(1) constant and 1/9 n 1/5.
ACKNOWLEDGMENTSThis work would not have been possible without the generous support of Pﬁzer, Inc. and a quarter of funding from the Washington NASA Space Grant Consortium.
I’m grateful for the guidance of my committee which has been priceless throughout my time here at the University of Washington. I thank Prof. Riley for his attention to detail and developing my mathematical interests. I am also indebted by the generosity of Prof. Berg and Prof. Pozzo for use of their experimental facilities. I have developed a deeper appreciation for education in research and teaching from experiencing Prof.
Berg’s passion for science in and out of the classroom.
I have also beneﬁtted by working closely with Prof. Brush on theoretical modeling.
His insight and interest in science has been a constant source of inspiration. Finally, I am grateful to my advisor Prof. Aliseda for giving me the opportunity to learn, teach, and conduct research at the highest level. His patience, insight, and work ethic has been a constant source of inspiration and has served me well during my time at the UW. I hope to be a credit to him in the future.
The staﬀ in the Department of Mechanical Engineering have been a friendly distraction during the work day. I’m grateful to each one of them for their kind assistance along the years.
I’m particularly thankful for the support of my friends here in Washington, Oregon, and Colorado. My life has been rich because of the great friends I have made and sustained during my time in graduate school and I count each one a blessing.
They have motivated me to work hard and stay focused on the big picture.
I thank my family for their support and encouragement throughout my studies v here at the University of Washington. My mother continues to be a constant source of inspiration both professionally and personally. I would not be where I am without her unconditional love.
Finally I want to thank my wife for her love, support, and most importantly, friendship. I dedicate this work to her.
DEDICATION To Shanna
INTRODUCTION: SPRAY COATING AT A GLANCE
1.1 Overview The impact of a liquid droplet on a solid surface is a problem ubiquitous in nature and industry. Despite the considerable amount of eﬀort devoted to droplet impact over the past century, there has been little attention directed towards complex rheology liquids used in various industrial applications, such as spray coating. In these settings, a liquid stream is broken into small droplets (typically ranging from a few microns to a few millimeters in diameter) and those droplets impact a solid surface, applying a thin coating on the surface. An analog to spray coating is the process of spray painting where a distribution of droplets exits the nozzle oriﬁce, impact a surface, and subsequently cure through evaporation of the solvent resulting in a thin dry ﬁlm.
These processes serve varying purposes such as preventing rust formation, providing water resistance, or simply for aesthetic qualities. Fundamentally, the process of a spray making contact with a solid surface can be broken down into individual droplets impacting, spreading, coalescing, and drying on a solid surface. All these processes are critical to providing a uniform and thin coat on a surface, however, the initial impact and spreading forms the foundation of a coat. Some of the liquids of interest in those processes are broadly classiﬁed as colloidal dispersions and high volatility solvents, and most of them have high viscosities with slightly non-Newtonian characteristics. When these liquid drops impact and spread on a solid surface many seemingly naive questions come to mind. How do suspension droplets diﬀer from pure liquids? What mechanisms drive spreading? What conditions (impact velocity, drop size, etc.) enhance spreading?
These questions will be addressed under the driving motivation of spray coating processes and yet I will simultaneously explore a class of ﬂuids with complex rheology that have received little attention in droplet impact and spreading processes. The focus of my eﬀort will explore these questions under the context of a viscous complex rheology liquid droplet impacting perpendicular to a solid substrate. These results will provide a data set particularly relevant for spray coating operations and viscous colloidal dispersions and volatile solutions at large. A brief background on the driving motion of this study and the collaborative eﬀorts of this initiative are described in the following section.
In the pharmaceutical industry, tablets are coated for various purposes including masking unpleasant taste, delivering a time released active agent, or brand recognition, Aliseda et al. . A simpliﬁed schematic of the cross section of a coating apparatus is seen in Figure 1.1. An atomizer placed in the center of a rotating drum sprays droplets in the size range of O(10 − 100µm) at speeds of U ∼ 1-10 m/s. The tablets tumble and are dried by a secondary ﬂow of air. The coating process is a complex thermodynamic process, yet at the tablet interface, it becomes a classic mechanics problem: droplets are impacted and may rebound, splash, or deposit cleanly as is desirable.
The present research is building oﬀ a collaborative eﬀort between Pﬁzer Inc., UCSD, and UW exploring three fundamental problems. The initial phase of this work consisted of characterizing the atomization of these coating liquids using a high speed coaxial gas jet to promote break up of the liquid jet into droplets. The experiments conducted produced size and velocity measurements with a Phase Doppler Particle Analyzer (PDPA). The results were compared to a model and resulted in good agreement. In fact, the model is used currently by Pﬁzer, Inc. in predicting droplet size distributions for scale-up processes.
Figure 1.1: Simple schematic of spray coating operation.
Atomizer at the center sprays tablets as they are turned. Drying air (not shown) subsequently cures coating.
Following complete atomization of the coating solutions, a collection of droplets downstream of the atomizer are transported to the tablet bed. The droplets undergo evaporation, shrinkage, and in some cases precipitous ﬁlm formation on the periphery of the drop. The dynamics of these droplets between the initial plane and the tablet bed is another problem of importance. Currently, there is an ongoing eﬀort to model the droplets using computational ﬂuid dynamics with a Lagrangian approach.
The goal is to predict the rheological changes occurring within the droplet as it travels toward the surface of the tablet bed. We have assisted Pﬁzer in this eﬀort by providing some benchmark numerical solutions using realistic sizes and velocities of droplets from atomization experiments. Preliminary results revealed the spray angle and distribution of droplets approaching the tablet bed which is not highlighted in this document. Furthermore, our collaborators at UCSD have provided a model to measure the decrease in drop size as function of time, Sartori . Finally, once droplets reach the tablet bed, they impact the tablet surfaces at various angles, velocities, and sizes. The summation of all these events sets the ﬁlm thickness and uniformity of the ﬁnal coat.
These coatings formed by liquids are classiﬁed broadly as aqueous colloidal dispersions and acetone-based solutions. The latter are particularly useful in creating controlled-released functionality. Before one of these coatings is applied, the tablets, referred to as tablet cores, are in some cases loaded with a hydrophobic lubricant in powder form which is added with the drug in powder form before being compressed into a tablet. This sets the rate of dissolution of the coat but may also inhibit clean deposition of droplets on the surface. The parameter space for these operations is quite large as we set out to study 13 diﬀerent liquid formulations varying in solid content and solvent and 12 tablet cores with varying surfaces properties quantiﬁed by tablet breaking force, percent of hydrophobic lubricant, and precoated tablets.
Our study implements realistic droplet size and velocity data from prior atomization experiments to set the parameter space indicative of spray coating processes.
From the scientiﬁc perspective, this study investigates highly viscous liquids, with values of the Ohnesorge number ∼ 1 which are higher than previously studied before.
The Oh = µ/(ρσD)1/2 where ρ, µ, and σ denote the liquid density, viscosity, surface tension, respectively, and D the diameter of the drop, is strictly a function of geometry (D) and liquid properties and deﬁnes a balance between the shear resistance of the liquid and the restoring forces of surface tension. The ability of the droplets to impact, spread, coalesce, and dry are all critical to producing an eﬀective tablet coat. If the scaling parameters in any of these processes, atomization, transport, and impact are not properly understood, the inevitable failure of the coat will result in wasted resources.
This dissertation consists of three distinct studies investigating the eﬀects of particles and eﬀective viscosities in the spreading of colloidal dispersions and acetone-based solutions on surfaces of varying wettability. Each chapter is meant to be read individually as they are self contained bodies of work. Chapter 2 begins with a detailed description of the materials and methods and post processing of the data. Chapter 3 begins with a review of topics relevant to drop impact studies. Furthermore it investigates the eﬀects of spreading of colloidal dispersions over a range of Weber and Ohnesorge numbers. We ﬁnd that the colloidal dispersions resist spreading only slightly and the spreading dynamics agrees well with three diﬀerent models. Chapter 4 explores the capillary spreading dynamics of colloidal dispersions on hydrophilic surfaces. In this transient regime, spreading follows a robust power law, but the exponents measured deviate from Tanner’s law due to the inﬂuence of residual inertia and non-Newtonian rheology. The impact and spreading dynamics of acetone-based solutions particularly important for time released functionality is investigated in Chapter
5. Here we highlight a previously unreported regime in which the rim height is found to increase linearly as the centerline height oscillates to equilibrium. This regime is also present in the case of colloidal dispersions and viscous Newtonian solutions in a narrow range of parameters. Chapter 6 contains a summary of the key results from this study and a few potential next steps in this research initiative.