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\author{deemaalhajri}
\pdfinfo{
  /Title (surface-and-interfacial-tension.pdf)
  /Creator (Cheatography)
  /Author (deemaalhajri)
  /Subject (surface and interfacial tension Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{surface and interfacial tension Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{deemaalhajri} via \textcolor{DarkBackground}{\uline{cheatography.com/195734/cs/41058/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}deemaalhajri \\
  \uline{cheatography.com/deemaalhajri} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 26th October, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{0.89586 cm} x{4.08114 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Surface and Interface}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{surface} & boundary between 2 phases, one of them is in the gaseous state \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{interface} & boundary between 2 immiscible phases has context menu \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.04425 cm} x{1.54549 cm} x{1.16956 cm} p{0.4177 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Types}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{gas-liquid} & surface tension &  &  \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
gas-solid & adsorption & e.g., \seqsplit{antiflatulents} &  \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\seqsplit{liquid-liquid} & interfacial tension & e.g., emulsions &  \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\seqsplit{solid-liquid} & wetting & e.g., tablets &  \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}----}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{0.9954 cm} x{3.9816 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Surface tension definition and units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Definition} & Force per unit length that must be applied to counterbalance the net inward pull. \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
 & the work done to increase the surface area of a mass of liquid by 1 cm2. (Units: erg/cm2) \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Units & dyne/cm \tn 
% Row Count 7 (+ 1)
% Row 3
\SetRowColor{white}
 & Nm-1 \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
 & mNm-1 \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
 & erg/cm2 \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.14471 cm} x{3.83229 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{surface tension (γ)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Cohesive & intermolecular forces between like molecules \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Adhesive & intermolecular forces between unlike molecules \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
inward force & Molecules of the liquid at the surface exhibit an inward force toward the bulk, therefore contract the surface \& pull it towards the inside. \tn 
% Row Count 9 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.44333 cm} x{3.53367 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Net force}}  \tn
% Row 0
\SetRowColor{LightBackground}
Surface molecule & somewhat down because of the inward force \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Bulk molecule & zero (cancel each others) \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Examples on ST}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{1. Water film on hand Water} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{2. Water dipping from a tap} \tn 
% Row Count 2 (+ 1)
% Row 2
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% Row Count 3 (+ 1)
% Row 3
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% Row Count 4 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{5. Paper clip on water surface} \tn 
% Row Count 5 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{6. Coin on water surface} \tn 
% Row Count 6 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{ST of water}}  \tn
% Row 0
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Unit & 73 dyne/cm at 25C \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Why are water droplets spherical? & High stability, low energy, low SA \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & A sphere has the smallest possible surface area to volume ratio \tn 
% Row Count 6 (+ 3)
% Row 3
\SetRowColor{white}
Surface free energy & Surface \textgreater{}  Bulk \tn 
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% Row 4
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 & The surface layer of a liquid possesses additional energy as compared to the bulk liquid. This energy increases when the surface of the same mass of liquid increases. \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Cleansing effect between hot and cold water}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{There is an inverse relation between surface tension \& temperature} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{1. high temp.} \tn 
% Row Count 3 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{2. more kinetic energy} \tn 
% Row Count 4 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{3. weakens cohesion} \tn 
% Row Count 5 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{4. lower ST, which is defined as specific temp.} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Hot water is better cleaning agent than cold water, because it has lower ST, so can get better into pores and fissures, while cold wate can form only bridges between them} \tn 
% Row Count 10 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{IT (Interfacial Tension)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Definition & the force per unit length existing at the interface between two immiscible liquid phases \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
 & the work required to separate the 2 sections of liquids. \tn 
% Row Count 8 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Unit & dyne/cm \tn 
% Row Count 9 (+ 1)
% Row 3
\SetRowColor{white}
 & erg/cm2 \tn 
% Row Count 10 (+ 1)
% Row 4
\SetRowColor{LightBackground}
The interfacial tension reflects the interaction between the 2 phases: & 1. high IT \tn 
% Row Count 14 (+ 4)
% Row 5
\SetRowColor{white}
 & 2. low molecular interactions \tn 
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% Row 6
\SetRowColor{LightBackground}
 & 3. low adhesive \tn 
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% Row 7
\SetRowColor{white}
 & 4. high cohesive \tn 
% Row Count 18 (+ 1)
% Row 8
\SetRowColor{LightBackground}
 & 5. immiscible liquids \tn 
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% Row 9
\SetRowColor{white}
completely miscible & high interactuins \tn 
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% Row 10
\SetRowColor{LightBackground}
immiscible & low interactions \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Measurements of ST and IT}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{1. Capillary rise method} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{2. Du Nouy ring method} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{3. Wilhelmy plate method} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{4. Pendent drop method} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{5. Spinning drop method} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{6. Bubble pressure method} \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{1. Capillary rise method}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Capillary placed in a liquid contained in a beaker, the liquid generally rises up the tube a certain distance} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{liquid rises due to the ST, at some point it will stop due to its weght. so the upwaed movement will be balanced by the downward force of gravity} \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{ST determined by measuring the rise in the capillary} \tn 
% Row Count 8 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{ST= 0.5 rhpg} \tn 
% Row Count 9 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{r = radius, h = hight, p = density, g = gravity} \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{2. DuNouy ring method}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{slowly lifting a platinum-irridium ring from the surface of a liquid.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The force required to detach the ring from the liquid surface is recorded in dynes on a calibrated dial.} \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{This force is equivalent to the maximum pull exerted on the ring by the surface)} \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{3. Wilhelmy plate method}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{a thin plate usually made from glass or platinum-oriented perpendicular to the interface and attached to a  scale or balance via a thin  metal wire} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The force on the plate due to wetting is measured and used to calculate the surface tension.} \tn 
% Row Count 5 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{4. Pendant drop method (Drop weight)}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{A liquid drop hanging on the bottom of a capillary tube starts to fall when the weight of the drop is in an equilibrium state with the surface tension.} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The drop is falling when the weight (mg) is equal to the circumference (2πr) multiplied by the surface tension (σ).} \tn 
% Row Count 7 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{mg = 2 π r σ} \tn 
% Row Count 8 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{we can use a reference liquid of known surface tension (mostly using water as a reference) to compare with the liquid which we are interested in} \tn 
% Row Count 11 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Methods used to measure IT between 2 liquids}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Solid-liquid interface (Contact angle θ)}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{If a drop of liquid is placed on a flat, smooth, horizontal solid surface, it forms a drop.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{contact angle (θ): drop will exhibit a definite angle against the solid. It's contact angle (θ): the angle the tangent to the liquid surface makes with the solid surface over which it spreads.} \tn 
% Row Count 6 (+ 4)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{θ is determined by the interactions across the three interfaces; solid/liquid/gas.} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{θ depends on the nature of both the solid surface and the liquid drop.} \tn 
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% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{θ (range of 0 = 180)} \tn 
% Row Count 11 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{θ for pure water-pure silver is 90°} \tn 
% Row Count 12 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Contact angle differs depending on surface type "even same types of drops"} \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{θ reflects wetting of the surface} \tn 
% Row Count 15 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{On contact of a liquid droplet with a surface, the behavior of the liquid drop will depend on the balance between the cohesive forces of the liquid and the adhesive forces with the solid surface.} \tn 
% Row Count 19 (+ 4)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{If the attractive forces between the liquid \& solid exceed the cohesive forces in the liquid drop \textgreater{} low contact angle (α \textless{} 90°) \textgreater{} good wetting} \tn 
% Row Count 22 (+ 3)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{e.g., water drop on glass surface} \tn 
% Row Count 23 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{High θ = bad wetting} \tn 
% Row Count 24 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}