The first page of Chapter 2 about surface tension in the sixth edition of Intermediate Physics for Medicine and Biology.
For those interested in a preview of the 6th edition of Intermediate Physics for Medicine and Biology, I want to tell you about a new chapter on surface tension. This is the new Chapter 2, following immediately after the chapter about mechanics. It is the shortest chapter in the book. Below is the first paragraph.
Many biological processes occur at the interface between
air and water where surface tension is important.
Section 2.1 introduces the concept of surface energy, and
then Sect. 2.2 relates surface energy to surface tension.
Section 2.3 reviews adhesion and cohesion, which indicate
if water molecules are more attracted to each other
or to an adjacent surface. Section 2.4 describes how surface
tension can make water climb up a hollow tube, a
process called capillary action. The Bond number is introduced
in Sect. 2.5, a dimensionless number that characterizes
the relative importance of gravity and surface
tension. The ability of an animal to live on the water surface
depends on the Bond number. Section 2.6 reviews
microfluidics, a modern experimental technique in which fluids flow in tiny chambers where surface tension plays
a central role.
I was particularly anxious to include microfluidics in IPMB. We did, although we don't go into much detail. Here is the final section of the chapter.
Scientists have begun performing experiments and analyses
using microfluidics: small volumes of fluid (nanoliters)
passing through tubes tens of microns wide. In
microfluidics, the Reynolds number is small, so flow is
laminar, which implies that mixing of different fluids is
difficult and must occur by diffusion rather than convection
(See Chap. 5). Microfluidic systems often rely on
capillary action to pump fluid. When mixing immiscible
liquids, surface tension causes droplets to form and the
droplet radius is determined by the tube size and the capillary number, a dimensionless number that highlights
the competition of viscosity and surface tension
(see Problem 18 or Squires and Quake, 2005).
Microfluidics is used for microanalysis of biomarkers,
for cell biology where the tubes have a size similar to the
size of single cells, and for drug development. It offers
the possibility of analyzing samples rapidly and in parallel,
using minute amounts of reagent. Whitesides (2006)
discusses many of these applications in detail.
Viruses are rarely mentioned in Intermediate Physics for Medicine and Biology. We do discuss them in the very first section of the book, when we talk about distances and scales. Perhaps we should say more, because viruses and their vaccines are such a hot topic today. Unfortunately, vaccines have become politically controversial. The science often seems to play a secondary role to politics.
This was a huge clinical trial, involving over a million children in 44 states. There were essentially two parts, or arms, in the trial. In one arm about 400,000 children in second grade were injected with either the vaccine or a placebo. This part was randomized and double-blind (neither the children, their parents, nor their doctors knew if they received the vaccine or a placebo). In the other arm, about a quarter million second graders received the vaccine, and their results were compared to about three quarters of a million “observed controls” in first and third grades who did not receive an injection.
The trial design had many controversies. First, Salk’s vaccine was based on a virus killed using chemicals. A competing virologist, Albert Sabin, created a vaccine based on an attenuated but live virus. Many medical doctors had concerns about safety, especially with a live virus. Although the implications of contracting polio were terrible, often leading to paralysis or life spent breathing in an iron lung, the incidence of polio in the general population was low. In that case, the safety of the vaccine must be extraordinarily high in order to justify its use. Moreover, the trial needed to be huge in order to have enough statistical power to provide reliable results. Salk had enough confidence in his initial results that he wondered if the use of a placebo was even ethical (an issue often raised today among vaccine advocates and opponents). However, most virologists (including Thomas Francis of the University of Michigan, who was recruited to oversee the study) insisted that at least part of the study include a placebo injection. There were three different strains of polio virus, and the vaccine had to protect against all three. Many epidemiologists worried about bias influencing the “controlled observation” arm of the study. This part was not randomized, and parents consenting to have the vaccine may have represented a subset of families with a different economic or educational background compared to the controls, which could be a confounding factor influencing the results. Above all, the trial would be conducted on children, heightening any ethical concerns.
Given the distrust of scientists and doctors that many have today, I was impressed by the public support for this trial. The number of polio cases was at its peak in the early 1950s,
and parents were terrified of the disease and desperate to
slow its spread. The trial was conducted with funding from the National Foundation for Infantile Paralysis (commonly known as the “March of Dimes”). Thousands of volunteers went door to door to raise over $40 million dollars, with the average donation being 27 cents. More than 200,000 lay volunteers helped with the trial, along with 60,000 doctors and nurses and 64,000 teachers and school principals. The study had no difficulty finding parents willing to sign up their children; about two thirds of the parents chose to have their kids participate. There was truly a national ownership of the trial. It was a time, unlike our own, when scientists and medical doctors were held in high regard.
Children received their vaccines between April 26 and June 15, 1954. Blood samples were taken from 40,000 children after inoculation to check for the production of antibodies. On April 12, 1955 the results were announced at the University of Michigan. The overall trial results were clearly positive for all three strains of polio. In the placebo part of the trial, about 200,000 children received the vaccine and another 200,000 the placebo, and roughly twice as many unvaccinated children contracted polio compared to vaccinated children (80 versus 160). A nationwide vaccination program began two weeks later. Within a decade, the number of deaths per year in the United States from polio dropped from about 1000 per year to about 10 per year. Now polio is nearly eradicated from the USA. Let’s do our best to keep it that way.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
