% [H,gE]=CalcMagField(d) % % Calculates the magnetic field strength H and normal force (actually % acceleration due to gravity and magnetic field) gE acting on droplet at % given distance from magnet surface. % % d = distance between the magnet surface and the bottom of 10 mul droplet. % (mm) % % H = Magnetic field (Oe) % gE = Acceleration due to gravity and magnetic field (g) % % H is given in Oersteds, a unit used in CGS (centimetre–gram–second) % system of units. Oersted is often more convenient to use than ampere per % meter used in the SI system. gE is given relative to the gravitational % acceleration (thus the unit is g). function [H,gE]=CalcMagField(d) % d is the distance between magnet surface and the bottom of the droplet. % We are interested in the mean field droplet experiences. Thus we need to % take into account the size of the droplet and calculate the field % strength in the middle of the droplet. For 10 mul droplet the center is % approximately 1 mm from the bottom of the droplet. z = d + 1; % The field strength along the axis of the main magnet was measured with % gaussmeter. Data was fitted with theoretical model with 3 coefficients, % R, L, M. These coefficients and the model can be used to calculate field % strength H and field gradient dH (in vertical direction, i.e. dH/dz.) R=10.168458546157993; L=43; M=1.301974338420206e+04; H=M./2.*((L+z)./sqrt(R.^2+(L+z).^2)-z./sqrt(R.^2+z.^2)); dH=-M./2.*R.^2.*((R.^2+(L+z).^2).^(-3/2)-(R.^2+z.^2).^(-3/2)); % Next we need to calculate the effective magnetization ME of the fluid at % this field. It is used in calculation of the magnetic forces. The fluid % magnetization M was measured with SQUID magnetometer and the data was % fitted with a smoothing spline. % ME = M + H (dM/dH) magfit=importdata('Ferrofluid magnetization fit.mat'); ME=feval(magfit,H)+(feval(magfit,H*1.001)-feval(magfit,H*0.999))./(1.001-0.999); % Normal force is the sum of gravitational and magnetic forces. The sum of % these forces is here examined relative to gravitational force. Actually % we are working with effective gravitational acceleration gE, unit of % which is g (the gravitational acceleration of Earth, 9.82 m/s^2). If % there is no magnetic forces, gE = 1 g. If the magnetic force is as large % as gravitational force, gE = 2 g and so on. This makes it easy to % understand the magnitude of the forces. % F = m*gE = m*g + V*ME*dH/dz % gE = g + V/m*ME*dH/dz = g + 1/rho*ME*dH/dz % Here we are still using CGS units: g = 982 cm/s^2. rho is the fluid % density, 1.0069 g/cm^3. dH was calculated earlier, its unit is Oe/mm. % Thus we need to multiply it by 10 to get to Oe/cm. gE=(982+ME./1.0069.*dH*10); %in CGS units gE=gE/982; %the unit is now g.