A nifty little Matlab code to show why we need to wet the backsides of the membranes

I couldn’t really make sense of what was happening in this post, and in particular this figure threw me for a loop:

 

So to help myself understand the relationship I whipped up a little matlab app to show the relationship a little clearer:

 

Moving the sliding bar on the bottom changes the y-position of the center of the ‘droplet’. Note that there is a very apparent maximum at 184ATM, when the drop’s radius is the same as the capillary’s radius.

 

I apologize for the messiness of the code – I’m very out of practice.

function laplaceslider

foo = 0;

bar = 0;

hplot = plot(foo,bar);

h = uicontrol(‘style’,’slider’,’units’,’pixel’,’position’,[0 0 300 20],…

‘min’,-100E-9,’max’,10E-9);

addlistener(h,’ActionEvent’,@(hObject, event) laplace(hObject, event, hplot));

 

function laplace(hObject,event,hplot)

poreRadius = 7.5E-9;

airWaterTension = 0.07; %in N/m

centerpointY = get(hObject,’Value’);

bubbleRadius = sqrt(centerpointY.^2 + poreRadius.^2);

pasPressure = 2*airWaterTension/bubbleRadius; %bubble radius by LaPlace’s Law

 

PSIpressure = pasPressure/6894;

if(centerpointY <= 0)

theta = asin(poreRadius/((2*airWaterTension)/pasPressure));

distBubtoLip = sqrt((bubbleRadius).^2 – (poreRadius).^2); %distance from the bubble center to the lip of the capillary

else

theta = (pi) – asin(poreRadius/((2*airWaterTension)/pasPressure));

distBubtoLip = -sqrt((bubbleRadius).^2 – (poreRadius).^2);

end

k=0;

t = pi/2 – theta;

step = (pi/1000);

x = 0;

y = 0;

while t < pi/2 + theta

k = k+1;

x(k) = bubbleRadius*cos(t);

y(k) = bubbleRadius*sin(t) – distBubtoLip;

t = t+step;

end

 

set(hplot,’xdata’,x,’ydata’,y);

xlim([poreRadius*-2 poreRadius*2])

ylim([poreRadius*-1, poreRadius*3])

axis equal;

pressureText(1) = {‘Pressure in ATM:’;};

pressureText(2) = {num2str(pasPressure*9.87E-6);};

rectangle(‘Position’,[poreRadius*(-1),poreRadius*-1,poreRadius*2,poreRadius],’FaceColor’,’White’);

text(-poreRadius*2/3,-poreRadius*.5, pressureText);

drawnow;