Admittedly, I haven't really been in any situations as a freelancer that required me to be on call 24 hours a day.  But one thing that may help you communicate with international clients is **working a split shift**, if possible.  This is an idea I got from my college days, working in retail.  While our store was doing inventory, they would have me work the morning to set the sales floor and then come back in the evening to do inventory.

In my previous corporate job, I was officially supposed to work 40 hours per week, roughly 9am - 5:30pm (I wasn't paid for lunch breaks).  However, I would usually get tired  around 2-3pm and accomplish very little in that period - even after I started taking short exercise breaks in the afternoon.  I ended up frequently working late because of this.  At this workplace, we also had an offshore contractor who had almost a 12-hour time difference from us.  One or two days a week, their team would stay late and we would come in early to do a phone call with them.

So since I've been freelancing, I've rarely worked an entire afternoon.  Instead, *I take about 3 hours off every afternoon* to exercise. Then, I work well into the evening when I don't have to go somewhere else.  I'll usually work a schedule like this: 8 - 8:30 am, 9:30am - ~2:30pm, 5:30pm - 7pm, 7:45pm - (anywhere between 9pm and midnight).

How a split shift schedule would impact interfacing with clients:

 - Since I have an "about 10 hours out of about 14" workday, I'm more available to clients without working a great deal of hours myself.  And I tend to get more done because I'm working at my peak times.
 - In proposals, I list my core hours as 10am-2pm.  I say that communication from me can generally be expected between 8am and 10pm.
 - I try to respond to emails within 24 hours (aside from weekends).  For improved productivity, I only open my email client about 3 times a day most days.
 - I send status emails at least once a week. Frequency varies based on project needs and the stage of the project.
 - Although I haven't had to do this as a freelancer yet, I would recommend scheduling status meetings at a mutually agreeable time at least once a week. (Edit: One of my current clients and I mutually agree on times for status meetings.  These generally take place during my core hours.) 
 - I'm more responsive on the phone or if somebody tags me in a Facebook
   work group post.
 - Some freelancers, such as the 1WD.tv founders, recommend charging a higher hourly rate for a certain number of support hours per month.  I am considering implementing this sort of policy.